MSCI+Math+Specialist+Capstone

= =  ** Black Hills State University ** = =  ** June 2013 **
 * A Portfolio of Professional Growth **  ** By: Tammy Jo Schlechter **   ** Master of Science in Curriculum and Instruction **


 * Portfolio Vitae**
 * I. General Information**


 * 1) **Tammy Jo Schlechter**
 * 2) **Hermosa School, P.O. Box 27, Hermosa, SD 57744**
 * 3) **Teach mathematics to grades 6-8**
 * 4) **Total years of teaching experience: eighteen**
 * 5) **Years in present position: three**


 * II. Educational History and Professional Development**

Black Hills State University (BHSU) – Spearfish, SD (2012-present)
 * 1) **Universities**
 * Master of Science in Curriculum and Instruction to be completed by summer 2013

Black Hills State University (BHSU) – Spearfish, SD (1992-1994)
 * Elementary/Middle School/K-12 German Certification

South Dakota State University (SDSU) – Brookings, SD (1989-1992)
 * Graduated with high honor with a Bachelor of Arts in Arts and Sciences – Major: English; Minor: German

Hermosa School – Hermosa, SD (2009 – present)
 * 1) **Teaching Employment History**
 * 6th - 8th mathematics, 8th grade reading and American History, 5th grade, Standards of Mathematical Practice module facilitator (2012), Curation for myOER.org facilitator (2012), Math Counts Teacher Leader (2009 – present), Science on the Move Teacher Leader (2009-2010), assistant grade school basketball coach, PTA teacher liaison (2009 – present)

Fairburn School – Fairburn, SD (2007 – 2009)
 * 3rd – 8th grade classroom teacher, Science on the Move Teacher Leader (2007-2009), PTO teacher liaison (2007-2009)

Witten School – Witten, SD (2003-2007)
 * 4th – 8th grade classroom teacher, Infinite Campus Teacher Trainer (2003-2007), DACS Assessment Teacher Leader (2003-2007), Teacher as Assessor Teacher Leader (2006), Science on the Move Teacher Leader (2004-2007)

Todd County Middle School – Mission, SD (2002-2003)
 * 6th-8th science, 6th-8th social studies, Harry Wong’s classroom management course participant

Springfield Middle School – Springfield, SD (2001-2002)
 * 6th – 8th science, 6th language arts

Tammy Jo’s Preschool – Scotland, SD (1999-2001)
 * Preschool ages 3-5

Bairoil School – Bairoil, WY (1997-1999)
 * K-8th communication arts; Instructional Steering Committee, Communication Arts Committee Chair

Star Prairie School- Clearfield, SD (1996-1997)
 * 3rd – 8th grades, coordinator for South Dakota Public Television site for mock election

Burton School – Burton, NE (1994-1995)
 * 4th – 8th grades


 * 1) **Professional Associations**
 * South Dakota Council of Teachers of Mathematics (2002-present)


 * South Dakota Council of Teachers of Science (2002 – present)


 * International English and German Honor Societies - Sigma Tau Delta and Delta Phi Alpha (lifetime member since 1991)


 * Member of SDEA/NEA


 * 1) **Leadership Activity**
 * District facilitator for Common Core (present)


 * Higher Order Thinking Skills and Assessment (Modules 5 and 6) facilitator (present)


 * Hermosa PTA Member (2009-Present)


 * Curation for myOER facilitator (2012-2013)


 * Standards of Mathematical Practice facilitator (2012)


 * Custer Co. 4-H Leaders Association Treasurer (2010-present)


 * Math Counts Teacher Leader (2009 – present)


 * Science on the Move Teacher Leader (2004-2010)


 * DACS Assessment Teacher Leader (2003-2007)


 * Teacher as Assessor Teacher Leader (2006)


 * Scotland-Lesterville PTO Member (1999-2002), Vice President (1999-2000), President (2000-2001)


 * Communication Arts Curriculum Committee Chair, Carbon County District #1 (1997-1999)


 * Instructional Steering Committee, Carbon County District #1 (1997-1999)


 * Bairoil PTA Member (1997-1999), Vice President/Historian (1998-1999)


 * 1) **Teaching Awards and Recognition**
 * ESA 7 Regional Teacher of the Year 2013


 * Custer School District Teacher of the Year 2013


 * Black Hills Recovery Network Grant Recipient 2013


 * TEACH grant 2012-2013


 * Custer Area Arts Council Grant Recipient 2011


 * Wood School District Teacher of the Year 2006


 * TEACH grant 1992-1994

Building my own conceptual understanding of math, adopting strategies that engage kids, and adhering to the philosophy outlined in “I’m a Life Toucher” by Bill Sanders, my pedagogy reflects my perpetual ambition to positively impact the lives of those around me. To truly meet the needs of my students, the learning environment that I create has to transcend our classroom’s four walls and envelope my students and their families. My community is involved. I collaborate with my colleagues from within my school to those across the state. My quest for best practices stems from my own needs as a student. My humble beginnings in a little two room country schoolhouse in rural South Dakota still impact how I teach today. I wanted to be that teacher who memorably positively influenced lives of students. **Reflection of My Graduate Experience** An exercise for math journaling can be summing up what we learned after a particular math lesson using six words or less. If I had to sum up what my graduate adventure for my Master of Science in Curriculum and Instruction, I would say: __Beginning with the end in mind__. Why did I choose these six words? I would like to elaborate to take a look back at my graduate experience. Ironically, to begin my story, I did not begin my master’s program with the end in mind. I can remember clearly how this adventure started, but it was not necessarily to earn a master’s degree. At the time, I just wanted to learn how to teach math in such a way that all my students would walk away with the math tools they needed. Not only the math tools they need but also a positive attitude about math…period! I knew this combination would create an intrinsic motivation to persist and tackle even the toughest of math problems along their path in life. Mr. Chip Franke, my principal, in 2008 recognized my desire to further my training on how to teach math well. He saw that I was attempting cognitively guided instruction and recommended me for the SD Math Counts training offered through TIE. As a result, I became a member of the second round of teachers for Math Counts. Little did I know how much this training would impact my instructional strategies or how much it would increase my joy in teaching in the math classroom. I am very thankful to Mr. Franke for giving me the opportunity to pursue learning more about cognitively guided instruction (CGI), because it has definitely made a difference in how I meet the various needs of students in my classroom. So my saga began in a two room country schoolhouse in 2010 where I taught all the subjects to grades three through seven, and my emphasis was teaching all subjects well, including math and science. I loved my setting there, but my journey would not keep me in my comfortable little country school. The following school year (2010-2011) found me in Hermosa School teaching 5th grade with two dozen students. I had to adjust to one grade level with two dozen students as opposed to multiple grade levels and ten students. I also began my Math Counts training that year. I remember setting goals about improving my questioning of students and working on my wait time when my students needed time to answer my questions. Now, I had not decided to earn my master’s this first year in Math Counts, because that is not why I was training. I felt that I wanted to learn the best practices for teaching math, but I did not feel I needed to have a graduate degree at this point in my teaching career. I had looked at the cost of getting my master’s when they offered this option as part of our Math Counts training. It just did not look like something I could afford to invest in. Getting my master’s was not going to happen. It was not in my plans. Well, someone once told me, “Tell God your plan and then He will show you His.” That is exactly what happened to me! As I continued my Math Counts training over the next three years by attending week long math camps whose topics I reveled in: the strands of mathematical proficiency, geometry and algebra, I heard the teachers in my cohort discuss their graduate courses they were taking as they completed their master’s programs. Admittedly, I wished I was earning my graduate degree too, but again, wanting to spend time with my family more in the summer and the great expense kept me from pursuing that dream. I happily continued learning more about how students learn the math and trying to apply it in my classroom. Then, unexpectedly I realized that indeed my master’s was calling. In February of 2012, I was sitting in a Module Two training that the South Dakota Department of Education was conducting at the Ramkota in Rapid City. At my table, a young lady and I were visiting about our teaching experiences. Somehow, our conversation led to where I was in my Math Counts training. She suggested that I look into the TEACH grants available to teachers. I took her advice and because of her suggestion, I am here today writing about my graduate experience. Little does she know how she impacted my life. I should just email her and tell her. She is in my ED 790 Seminar course! In the end, what I learned the most throughout my experience is to plan my assessments first then plan my instructional strategies and questioning moments, know when and how to use assessment to help my students succeed, use research and my own action research as a basis for my instructional decisions, and really examine my methods as a guide on the side in my classroom. My graduate experience positively continues to mold and shape me into the lifetoucher I am destined to be. And even though, my master’s degree was not in my initial plan, it just reminds of those moments in the classroom where the best teachable moments were the ones you never planned at all. **Proposition One: Teachers that are committed to their students and their learning.** **Artifact One: Research Action Proposal** Does guided play time increase student achievement and productive disposition in the math classroom? I explored this idea as part of my action research project, which began last fall with Dr. Fuller and culminated into a final summation with Dr. Linn for ED 750 Action Research in Education. My pedagogy was influenced by two factors during the creation and implementation of my action research. The requirement of writing an action research proposal forced me to find actual research conducted in my field that was related to the questions I had in regards to how I instruct in my math classroom. In the past, I had read articles in my scholarly journals and publications about topics such as cognitively guided instruction and brain-based learning. However, I did not consider that I was getting my information second hand. I have learned that I need to search for primary sources i.e. research that has been conducted in the field to study myself. I also learned that I need to conduct my own action research and have a methodical way of recording the results and begin with a sound design based on the research I have uncovered. These two big discoveries have impacted my professional practice and have altered how I plan lessons and assessments for my best students in the whole world. By choosing my action research proposal as the artifact to support that I am not only proficient as a teacher committed to students and their learning, but I may even dabble in the distinguished category as I reference Charlotte Danielson’s domains within her very in depth framework for teaching. As I reflect on my proposal, one side of the instructional design portion of this plan lends itself well to the distinguished category in Domain One. To share some distinct characteristics of the assessments I designed for my proposal, if one assesses the component examining designing student assessments, the assessment portion of my proposal can be described within the distinguished categories: “[p]roposed approach to assessment is fully aligned with the instructional outcomes in both content and process…” and “[t]eacher plans to use assessment results to plan future instruction for individual students” (Danielson, 2007, p.63). In another component referencing the design of coherent instruction, the distinguished category shares, “The lesson’s or unit’s structure is clear and allows for different pathways according to diverse student needs. The progression of activities is highly coherent” (Danielson, 2007, p. 61). I believe the guided play time aspect of my proposed action research falls into this realm of distinction. However, the traditional classroom simulation aspect of my action research proposal not only would be considered unsatisfactory or basic according to the rubric on page 60, where Danielson wrote for the unsatisfactory category, “Learning activities are not suitable to students or to instructional outcomes and are not designed to engage students in active intellectual activity,” but the results that my action research unveiled also supports the unsatisfactory conditions that my traditional classroom setting produced. To elaborate on the stark contrast between the two types of instruction I modeled in my action research, I would like to flashback to how guided play time became my focal point based on the educational theories that I have studied. As a teacher committed to my students and their learning, the idea of actually doing a formal action research project in my classroom energized me last fall. As I read empirical research and formed my ideas about the questions I had in regards to my instruction in my classroom, I found myself really enjoying the thought of doing research too. Training in Math Counts had already given me a purpose for exploring cognitively guided instruction and zone of proximal development (Vygotsky, 2011), which is making more and more sense. Having students think about their thinking and determining what they cannot do yet, what they can do with assistance, and what they can do independently gives way to gradual release of responsibility model that I facilitate in Modules 5 and 6, currently for the South Dakota Department of Education. Could I implement what I found in research and also in my modules training in my classroom to improve the productive dispositions (Kilpatrick, 2001) and math achievement of my students? Based on my own observations of providing inquiry-based lessons and the recent research I had studied, I pondered the idea about allowing my students to have play time, guided and structured of course, to learn the math concepts as required by Common Core State Standards (National Governor’s Association, 2010). My interest really piqued when I discovered a blog by Anne Marie Thomas. Her quote would later become the crux of my action research design. Ms. Thomas (January, 2010), as a university faculty member, wrote, “So my goal these days is to figure out how to make the basic math and science that lie beneath the surface as exciting as playing with the cool toys the math and science produced.” Eventually, trash cans turned upside down would find their way to my classroom. This inspiration explicitly related to the cool toys in Ms. Thomas’s blog. Trash cans may or may not be considered something like a toy, but the novelty of using a trash can to study surface area of cylinders hooked my students and became a terrific motivational mindset. Before continuing on with how my action research proposal proceeded, I would further elaborate that my own instructional strategies are evolving based on the gradual release of responsibility model (Fisher & Frey, 2008). I have discovered, through my training with the South Dakota State Department of Education, that there is an important addition needed to make the gradual release model a best practice. This instructional model does not explicitly include a motivational mindset. A blend of ideas and practice are coming to play as I continue on my journey as a lifetoucher in the math classroom! The South Dakota Department of Education (SDDOE) emphasizes questioning, higher order thinking skills, assessment, and best practices that engage students for Modules 5 and 6 for that “active intellectual activity” (Danielson, p. 60). The SDDOE and TIE (Technology and Innovation in Education) built Modules 5 and 6 with the emphasis on how to incorporate higher order thinking in Common Core instruction in addition to how to assess the higher order thinking as part of our Common Core instruction. As part of my role as facilitator for these modules, I had to attend training various times as we built our conceptual knowledge for higher order thinking instructional strategies and assessment. During the several Module 5 and 6 meetings I attended this past school year, I was exposed to the book entitled //How to Teach Thinking Skills Within the Common Core// by Bellance & et al. (2012). This book incorporates the gradual release of responsibility within an instructional model where the authors added the motivational mindset to not only engage students but also help incorporate specific higher order thinking skills. Within the gradual release model shared during this module training, motivational mindset sets the stage and tone for the upcoming lesson. So, the hook I usually use to interest my students just has a new name (motivational mindset) and the jazzed up capability of using higher order thinking skills, as I enhance my own instruction with the practices suggested by Fisher & Frey (2008), which includes the “I do it, We do it, You do it collaboratively, You do it independently.” Now, back to the evolution of my research proposal! The spring 2013 semester found me in ED 750 with Dr. Linn, who graciously guided me along as I fine tuned my action research proposal. She encouraged me to complete my proposal and implement it in an abridged format, so that I would have something to share as part of my capstone. As a result, my action research proposal did not reach its most formal level, as it still has revisions that could be made and has major areas that need improvement. For instance, my students and I discussed the format and length of my pre/post assessment tool and agreed that I can improve upon it to make it more student friendly. Another aspect I would like to develop includes how to possibly modify this lesson to honor the generalization-concept-topic-fact sequencing in my planning, after studying the conceptual lens model that I recently read about in //Concept-Based Curriculum and Instruction for the Thinking Classroom// (Erickson, 2007). Perhaps, I have already followed this model too in some aspects of my instructional strategies just as I found I had been doing after being introduced to the formal term of gradual release of responsibility (Fisher & Frey, 2008). Before the end of the 2012-2013 school year, my action research proposal informally took place. Using a pretest and posttest assessment tool, numerous noteworthy patterns were viewed on how students performed prior to instruction and after the teacher’s instruction as part of my action research. The number one take away I had from my observations included the idea of just comparing the pretest to the posttest to see how much students grew (or the lack of in some cases). This may seem simple enough. But, in the past, I have always tried to attach a grade and from that grade determine if students had grown in their studies. By looking at the pre- and posttest items and without assigning points, I could really tell if a student had advanced in their learning. Looking back, I feel I should have Webb Leveled the questions I created for this assessment. Ironically, the comparing and contrasting of these assessment tools models the very same strategy students use in my classroom during their best math investigations, which remind me of Marzano’s research on instructional strategies that impact student achievement. I have found too that determining similarities and differences (Marzano, p. 7) promotes deeper levels of thinking and use of higher order thinking skills. Evidence or mathematical proof and writing on these assessments also signified if they were really engaged in the math lesson. All the students that were included in the scored assessments for the guided play time group shared indications that they were engaged in the math by how they described how they would transfer their learning to real world examples. The traditional classroom group did not share similar details. On the contrary, students in the traditional classroom group were observed to rather move away from the math to real life connection in their writing. For instance, one question on the assessment involved filling in the symbolic and picture forms of the words shared. The words shared represented in essence the formula for finding the surface area of a cylinder. The students in the guided play time group seemed more adaptive in their reasoning as they attempted to fill out this table. On the other hand, the traditional classroom students exhibited limited ideas for this same test item. This just reinforced my original conjecture or generalization of what is happening in our classrooms. The instructional model, where the teacher lectures and acts as the giver of knowledge, does not lend itself to the gradual release of responsibility. The instructional strategy of completely lecturing to students actually strips away the natural problem solving ability and curiosity that students have. It takes away their innate problem solving approaches that help them make sense of the math. So, the observations in my action research corroborated with the empirical research in the literature review segment of my action research proposal. Another observation that could be debated finds the guided play time group edging out the traditional classroom group in their overall math achievement. However, one cannot really attest which group had the greater productive dispositions, because all the students seemed tickled to be part of the research project. I do feel, although I cannot quantify this suggestion, that the guided play time group participants appeared to persevere longer with the math problems at hand and could contextualize/decontextualize problems more adeptly. The standards of mathematical practice have an important place in the math classroom, and the guided play time group modeled practice standard one and two (Common Core, 2010). Another interesting observation included the fact that some students really do like to do worksheets, because they are straight forward and can be quickly done. I would note, however, that these same students did not illustrate the depth of knowledge for surface area as did the students who were involved in the hands-on investigation in the guided playtime group. The desire for worksheets just reminded me that some students do prefer this type of learning activity and I can provide that variety within my instruction as long as they can prove they have conceptual understanding of the math involved in the task. The last observation to share requires an even harder look at how I am providing interventions for the students who do not understand the math lesson. In both groups, it was evident that my struggling students still require much needed interventions. Some of my at-risk students did show growth. However, two students in both groups showed little growth. To the observer, this means there is still work to do. Something is not quite right when it comes to the questioning procedures or possibly the planning procedure for my lesson plan design. I did not use my Webb Leveling document enough while designing my assessment, so that will be something that I will take a harder look at in the future. I truly believe that the students who did not show growth needed me to scaffold the lesson back with questioning to possibly Webb Level one and take them up from there. That did not happen. However, this reflective point will not be viewed as a negative. Areas of improvement in instruction and assessment have been identified along with all the other wonderful patterns involving guided play time that can make a difference for students in their overall math achievement and productive disposition. The insight gained from my action research project as I plan for my upcoming moments in math support the proposition that evidence has been shown about how instructional practice is modified according to the needs of my students. By continuing to thread the elements of the instructional strategies found in the empirical research and the books I read, I grow in my understanding of how my students process their ideas and learn. I maintain that students experience equitable moments in my math classroom. I am on a mission to be a lifetoucher that models learning for life for her students. I have demonstrated with my action research proposal artifact my commitment to my students and their learning. **References** Bellanca, J., Fogarty, R., & Pete, B. (2012) //How to teach thinking skills within the common core.// Bloomington, IN: Solution Tree Press. Danielson, C. (2007). //Enhancing professional practice: A framework for teaching.// Alexandria, VA: Association for Supervision and Curriculum Development. Fisher, D. & Frey, N. (2008) //Better learning through structured teaching: A framework for the gradual release of responsibility//. Alexandria, VA: Association for Supervision and Curriculum Development. Kilpatrick, J., Swafford, J. & Findell, B. (Eds.). (2001). //Adding it up//. Washington, D.C.: National Academy Press. Marzano, R., Pickering, D. & Pollock, J. (2001). //Classroom instruction that works.// Alexandria, VA: Association for Supervision and Curriculum Development. Module 5 and 6: Higher Order Instruction and Assessment. B. Nelson, Chairperson. Meetings conducted by South Dakota Department of Education and T.I.E. in December 2012, February 2013, March 2013, and May 2013. National Governors Association Center for Best Practices and Council of Chief State School Officers. (2010). //Common core state standards.// Washington, D.C.: National Governors Association for Best Practices and Council of Chief State School Officers. Thomas, A. (2011, January 25). Why are we afraid of math? Retrieved from [] Vygotsky, L. (2011). The dynamics of the school child's mental development in relation to teaching and learning. //Journal of Cognitive Education and Psychology 10//(2), 198-211.
 * III. My Teaching Philosophy Abridged**

**Artifact: Action Research Proposal**

Guided Play Time, Student Achievement, and Productive Disposition in Math by   Tammy Jo Schlechter ED 750 Action Research in Schools Research Proposal Master of Science Curriculum & Instruction College of Education Black Hills State University Spearfish, South Dakota 2013

**Introduction** Finding ways to efficiently engage students in math so they can master our math goals motivates many teachers to ask the question, “How do I infuse my math instruction with the right stuff?” Too often, our students are anxious about math (Meece, Wigfield, & Eccles, 1990). Teachers see students who do not want to participate in class discussions about how to solve the math problems at hand. Students who do not complete math homework enter classrooms daily. These students often share that they do not even know how or where to begin, even when they have gone over problems in class. Educators see students not persevering during problem solving and wonder what //barriers// prevent students from engaging productively in math. Teachers see frustrated students and struggling students who are falling farther and farther behind in math. These students walk into school each day feeling horrible about math. Anxiety related to test scores is another issue**, **notonly for the students but for the staff who teaches them as well and has been probed by researchers for decades (Wigfield & Meece, 1988). On the world scene, an ongoing debate takes place about how math should be taught. The vast majority of educators would argue that instruction that promotes commitment to learning, a positive nature towards school, and increased //student achievement// leads to success in our educational centers (Abbott, O'Donnell, Hawkins, Hill, Kosterman, & Catalano, 1998). Literature suggests that experimentation or play time could be the teaching strategy that needs to exist in the math classroom. Jiang, White and Rossenwasser reported in 2011 that a traditional method of geometry instruction is based on the teacher’s own perspective regarding what needs to be covered. This is especially evident when it comes to defining vocabulary, theorems, and proofs. As a result, very little attention is spent on whether or not the learners discern the teacher’s lecture. However, Jiang and et al. (2011) shared results from their study that illustrated significant growth in student learning when students were allowed to play around or experiment with geometrical concepts while making their own observations, jotting down their own data, and forming their own conjectures and proofs. These results could indicate that interactive math labs or guided play time is a form of instruction that needs to be developed in our math classrooms. Instructional design that determines what the student needs to acquire or master at a particular point in their educational journey to become proficient or improve whether it’s a standardized test or 4-H project are also well-grounded in the context of research (Tennyson and Fisk, 2011). As educators seek clarification on best practices in the math classroom, they may ask, “Could playing with the math help students make gains in mastery, positive perceptions, and //productive dispositions//?” Perhaps, educators can think outside the box and change the overall paradigm of math instruction. Consider the words of AnnMarie Thomas (2011), a university faculty, “So my goal these days is to figure out how to make the basic math and science that lie beneath the surface as exciting as playing with the cool toys the math and science produced.” The purpose of this mixed methods study is to explore the effects of //facilitated or guided play time// during math instruction on students’ productive math dispositions and students’ math achievement. This study will focus on instruction and assessment of a critical area of math instruction, according to the //Common Core State Standards for Mathematics// (2010), involving the study of three-dimensional shapes that involve solving problems about surface area. It will also canvass students about their math perceptions. This action research will address this encompassing question: Does guided play time influence student achievement and productive disposition in the math classroom? This action research study will contribute to an increased understanding of teaching strategies that influence students’ productive dispositions in math and how integral productive dispositions are in student achievement in math. The strands of mathematical proficiency are intertwined with productive disposition being an important interdependent element that studies have shown increase student math achievement (Kilpatrick & et al., 2001). The sampling procedure for this study will involve only one sixth grade section of math students being divided into two groups in an attempt to evenly divide the students based on ability. Of the twenty-two students in this class, six students historically struggled with completing assigned tasks and their on-task physiognomy. One third of this small group is on IEP’s that include cognitive learning disability and behavioral issues. Limitations of this study include its small range of affected learners and time allotted for the research to be conducted. Also, productive disposition is so intertwined with the other mathematical proficiencies that can one truly tease it out from the other proficiencies without considering the other proficiencies during the research? Other variables that may influence the direction of this study could include the evolving teaching practices of the instructor directing the study and the increasing implementation of curriculum that incorporates activities that inherently facilitate play time or experimentation of math concepts to build and apply all of the mathematical proficiencies (Kilpatrick, Swafford, & Findell, 2001). My current timeline to conduct this research has been condensed, so time will be a factor before meeting my deadline, which is the end of the school year in two months. These factors will limit the generalizability of the findings to other student populations. **Review of Literature and Research** In America, many people may identify with the teacher in Charles Schultz’s cartoon comic strip “Peanuts” and the tell-tale dripping nervous sweaty look that Charlie Brown had as his teacher said, “"Wah wah woh wah wah” (Webley, 2011). Once upon a time, many teachers believed their role in the classroom was to dispense knowledge. Through their hands passed the page upon page of notes that their students copied to commit to memory the concepts for the day. These teachers had the choice of droning on like the teacher on Charlie Brown or adding a little zest to their discourse to aid their students in their memorization of all they needed to learn. Sometimes a very memorable teacher just made lessons come to life. As former students, we remember those teachers who “fulfill[ed] the didactical contract” with us and made decisions about “what and how to teach based on [his/her] sense of responsibility to the students” (Martin, Soucy, McCrone, Bower, and Dindyal, 2005, p. 99). In order to facilitate effectively in the classroom and uphold their part of the contract, today’s teachers need to be comfortable in their content area and seek strategies that engage students. Their lesson designs should create opportunities for students to overcome learning barriers and provide for ample cognitive conflicts (Patsiomitou & Emvalotis, 2010; Monaghan, 2000). Research is showing how effective (or ineffective) we are as teachers. “The preparation of U.S. preschool to middle school teachers often falls far short of equipping them with the knowledge they need for helping students develop mathematical proficiency” (Kilpatrick, Swafford, & Findell, 2001, p. 4). If we are going to make a difference for our students and help them close the gap, students cannot be spoon fed their education; they need to build their own ideas, memories, and connections through a seeking of knowledge (Patsiomitou & Emvalotis, 2010). Students need guidance through lessons that promote students thinking about their thinking and evaluating their perceptions about math, unlike the procedures where worked examples are solely used in direct instruction (Kirschner, Sweller, & Clark, 2006). How do educators become more effective? “When we remain open to embracing new ideas and new practices, particularly when those changes are supported by research, we are in the best possible position to improve our professional (and personal) effectiveness ” (Jones & Kottler, 2006, p. 145). To really teach well, educators must know their content, along with classroom management techniques that help students transition. The prevalent notion permeating literature is that the more a teacher knows about their content and the way their pupils learn, the more effective this teacher will be in “nurturing mathematical understanding” (Swafford, Jones, and Thornton, 1997, p. 467). Becoming more effective at cultivating mathematical understanding also includes seeking out predictors and/or assessments that shed light on where a student is on her/his math journey. Predictors, such as the van Hiele levels as studied by Zalman Usiskin in 1982, can aid a teacher in planning for instruction and use of curricula. Teachers play a significant role in translating the curriculum into activities experienced by their pupils (Patsiomitou & Emvalotis, 2010; Remillard, 1999, p. 318). Teachers must recognize “when materials and instruction are operating at a higher level than a student’s level of understanding” (Unal, Jakubowski, & Corey, 2009, p. 1008) and be prepared to make the changes needed. Students need teachers to facilitate and guide their students through lessons that best fit their zone of proximal development(Vygotsky, 2011). Students’ self-efficacy and students thinking about their thinking and evaluating their perceptions about math appeared as another pattern in the literature. Empirical research alludes to students being more positive about math after they had successful interactions in the math classroom. For instance, while reporting his research in 2012, Guven shared that dynamic geometry software positively impacted student achievement, because the students were in control of their own learning while they interacted with the computer software as they tested their ideas and reacted to the immediate feedback provided. Students creating and making the designs themselves led to a deeper understanding of the concepts, because the students were not predisposed to a worksheet or something the teacher had tried to tell them. In this study, the teacher was the guide, whose role was to question and encourage students as they worked through tasks. The students constructed their own meaning. As students become immersed in learning activities, their productive dispositions grow. According to Bergeson et al., (as cited by Duatepe-Paksu & Ubuza, 2009) “the development of positive attitudes toward mathematics [being linked] to the direct involvement of students in activities”(p. 283). In the many articles read in educational literature circles, students were required to either make constructions during the instruction and/or describe their thinking as they solved math problems. The teacher’s role again and again involved questioning and assisting students to scaffold learning. Thus, educators are directed back to those instructional decisions being made by highly effective teachers while they focus on students’ constructs of ideas and concepts. This in turn can lead to student satisfaction as they master math concepts. The implications are students needing more “construction” time in the classroom. Construction in this context means to have time to build upon the things we already know and time to think about new ideas. A student constructing his or her own meaning is a concept that has been previously referenced in this summary of literature. Construction of meaning includes students thinking about thinking, which pervades much of the research in this literature review. In order to present a balanced viewpoint for best strategies, research from various learning theories should be included in this literature review. However, the dominant theme of constructivism can be recognized. As a result, there could be more questions. Does the problem presented lend itself as finding a solution related to constructivism? Are there other learning theories being addressed in other studies that have not been read that would also address my questions? As the constructivist learning theory seemed to pervade the research found, what did the research have to tell us? A study conducted by Duatepe-Paksu and Ubuzashared data about middle school students building their own connections to make sense of the math. In their 2009 study, these authors shared that they could not find research done on drama-based lessons as the main approach to teaching and assimilating geometry. As a result, Duatepe-Paksu and Ubuza developed a mixed methods research that reported the following benefits from incorporating students in collaborative learning settings while using drama-based methods in the instruction of geometry: The implication of this study indicates that we should take a closer look at incorporating this strategy into the pedagogy of our core classrooms. Advocating for play time in the classroom, Duatepe-Paksu and Ubuza (2009)shared these thoughts: The most promising model [for enhancing student learning] is constructivism, whose fundamental premise is the idea that all knowledge is constructed by the learner using his or her past experiences and existing knowledge structures. The role of the teacher, from a constructivist point of view, is to create an environment in which learners can construct, develop, and extend students’ mathematical view of the world.… Play assimilates a new experience to cognitive structure, called schema. If the new information is completely new and there is no existing schema to incorporate it into, if it contradicts the existing schema, then this condition must be accommodated so that the new information may fit (p. 272). The preceding quote echoes the importance of creating cognitive conflict as presented in the relatively small research studies shared in this literature review, but these studies may hold a key to finding best practices for math instruction. Play time designed to meet the rigor of content and practice standards could make a difference in the math classroom, because students can craft their own conceptual understanding and relate their learning to real life. Play time facilitated in order for students to “self-instruct, self-question, and self-monitor” (Montague, 1992, p. 231). Ultimately, effective teachers armed with creative procedures and evolving perspectives create the most memorable moments of learning rich with cognitive conflict (Patsiomitou & Emvalotis, 2010; Monaghan, 2000). Antitheses of the Charlie Brown teacher, these facilitators guide their learners through their own construction zone of meaning and building conceptual understanding. These teachers are not afraid to employ a variety of methods as they actively involve students in the process of analyzing and solving problems, while promoting metacognition and the sheer joy of successfully doing mathematics. With so many of our students feeling anxiety about math, perhaps alternative instructional strategies need to be explored and researched further. Based on these observations, I suggest that play time should be developed for more than just the primary grades. How about we bring play time back into the math classroom for the upper grades? Does guided play time increase student achievement and productive dispositions in the math classroom? What could guided play time look like for middle school students? **Methods** The design of this study has been constructed to examine the influence of guided play time on student achievement and productive disposition. Specifically, this study will focus on the facilitation of a lesson about surface area. The purpose of this mixed methods study is to explore the effects of //facilitated or guided play time// during math instruction on students’ productive dispositions and students’ math achievement. This action research will encompass questions: This action research project will take place in a school where about 170 students attend in grades kindergarten through eighth grade. This school is located in a small town in rural South Dakota. Thirty students (twenty males and ten females) from sixth and seventh grade classes will be potential participants for this study. These students will be designated for this study, because both grades need to learn about total surface area of cylinders, as required by Common Core State Mathematical Standards (2010). Using systematic sampling, students will be assigned to groups by their student numbers. This sampling method was chosen, because these particular students know their student numbers and this will aid in the students grouping themselves prior to coming in for math class. Students with odd numbers will be assigned to a group; students with even numbers were assigned to another group. Then, the groups will be examined for number of students on an Individualized Education Plan (IEP). Each group will have one participant on an IEP. The next step includes appraising each group’s list for students who historically struggle to get their assignments done or appear apathetic towards math at times. The groups seem to be fairly evenly divided when considering these student characteristics. However, one group will have more males than females with a four to one ratio of male to female. The other group ended up eight males to seven females. Changing the sampling procedure was considered, but the need for ease in grouping students prior to movement to math class trumped over the imbalance of males and females in the one group. Students will be given a pretest (see Appendix B) the day before the facilitation begins for the lesson about surface area. A rubric for scoring the pre and post assessment will be used (see Appendix C). This rubric is similar to what has been used to evaluate tests and projects throughout the current school year in the math classrooms for these sixth and seventh graders. This rubric’s design incorporates the “Standards of Mathematical Practice,” which are central to the implementation of the CCSS in the math classroom (Common Core State Standards, pp. 6-8). A general math survey (n.d.) retrieved from the bc.edu website has been adapted for collecting data about students’ perceptions of math and their math classroom settings (see Appendix D ). Students’ responses will be coded according to a predetermined checklist for this survey. Students will fill out this general math survey once all students have taken the posttest. A final survey (see Appendix E) about the lesson has also been written to collect data in addition to the pre/post-test assessments. This survey about the surface area lesson will be given to students later after they have witnessed both lesson versions presented by the teacher. It will also be coded similarly to the general survey. The instruments being used to collect data for this study will yield a variety of results. The scores from the pre and posttests will yield quantitative data to study, while the student surveys will share information in a qualitative fashion. My role in the research will be as instructor and evaluator of the lesson and gatherer of surveys taken anonymously within the two groups. Objectivity will be difficult. I have been trained in cognitively guided instruction and have improved my ability to question and allow for student think time, which will pervade both settings for this study. I share this element of the study, because allowing students time to think and encouraging students to think about their thinking varies in math classrooms. The first day, students will be dispersed during period 2 and period 3 in their math groups for this study. They will all take the pretest for the lesson surface area of cylinders. Day two and subsequent days will be different for the two groups of students. On the second and third day, students in the traditional classroom setting group (also known as the TRC group) will have a lesson presented over a two day period using a traditional textbook lesson and worksheet with the teacher modeling problems and students solving similar problems independently. [An example of the worksheet and three story problems (McGraw-Hill Glencoe, 2006) used can be found in Appendix F and Appendix G.] Their post assessment (see Appendix H) will occur on the fourth consecutive day. This lesson will involve three normal 60 minute classes in three days. Students in the guided playtime group or GPT group will work on their lessons that will address the same concepts as in the other group. This group will experience seven normal 60 minute classes in seven school days. On day one, these students will experience an introduction stemming from what students bring in from their homework assignment (that was assigned after the pretest moments) about identifying cylinders out in their world. Students and the teacher should have assembled various objects to represent cylinders including but not limited to tires, cylinder-shaped trash cans, hollow pipes, oatmeal containers, etc. Students will see these bold-faced statements on display: “I can determine the surface area of a cylinder.” and “I can solve real-world problems involving area and surface area.” Students will record these “I can” sentences in their “Take Away Window” (Bellanca, 2012, p. 190) reflection tools each day until we are finished with this series of surface area lessons. (See an Appendix I for the example of “Take Away Window” reflection tool.) Students will view sites to read more about surface area for cylinders using the smart board. They will also answer guiding questions provided by the teacher and work through activities designed to help the student acquire the language and concepts that go along with surface area of cylinders. (Guiding questions and activities can be developed based on the student worksheet included in Appendix J.) The teacher will allow ten minutes at the end of the class period for students to reflect on the “I can” statements written at the beginning of class. The students hand in their “Take Away Windows” before leaving class for the day. Day two will continue with the discussion and observations made from the day before with the teacher encouraging the students in their small groups about surface area while using chosen cylinders to model their ideas. (Students should have received their “Take Away Window” as soon as they entered class and can use them again or add pages today as they will reflect about what they “can do” once again.) It is really important on this day for the teacher or facilitator to take a more backseat role and let students work through their investigation of determining the total surface area of any cylinder. Guiding questions are encouraged during this time of inquiry and are included in the Appendix K of this research plan. These questions should lead to the students creating a net of a cylinder (by cutting apart empty cardboard cylinders like those that house oatmeal cereal), naming the shapes in the net, and examining the relationship between the length of the rectangle and the circumference of the circular base of the cylinder. The facilitator will encourage students to review what they know about circumference and area of circles. If students are still working on developing the idea of finding area of a circle, the teacher should allow time to let them explore and model their ideas. The teacher will allow ten minutes at the end of the class period for students to reflect on the “I can” statements in their “Take Away Windows” and these reflection tools are collected before students leave class. Trash cans circular in shape will be upside down on student tables with cardboard cylinders cut apart under the trash cans as students walk in on the third day of instruction. This scene will launch guided play time on day three, which will include moments to explore how to find the area of the rectangle figure and the circular bases in the net of the cylinder created the day before in class. The trash cans will create a dramatic effect and are linked to the last question in the assessment used for this sequence of lessons. Students may be distracted by this scene, but they still need to construct their usual “Take Away Window” as the teacher hands back their reflections. (These are the “Take Away Windows” from the previous two days.) Each day, the teacher collects the “Take Away Windows” to assess where students are in their journey about surface area and provides feedback to each student. Grouping of students can be determined for each day of class by what the teacher observes in the “Take Away Windows.” Tear out groups (Bender, 2009) can be worked with as needed if the teacher feels there are students who need extra instruction in either homogenous or heterogeneous groups as they determine the skill level of their students. By day three of instruction, students in the GPT group should be moving towards forming an opinion or a conjecture about total surface area for a cylinder and be ready to apply it. Students’ conjectures or ideas will involve taking the area of the base(s) and adding the area of the base(s) to the area of the rectangle in the cylinder, if their inquiry moments went as planned. At this point, if some students are successfully developing their strategy for finding total surface area of their cylinder, encourage these students to use a compass as they design and create a model of a tire out of sturdy construction paper. These students will also need to determine the total surface area of the tire they are representing. (Remember, there should be tires on display in the classroom from the first day of these lessons.) This will allow for more time and modeling by those students who are still building their conceptual understanding of total surface area for the cylinders they see in their world. The teacher will allow ten minutes at the end of the class period for students to reflect on the “I can” statements and complete an assigned problem about finding total surface area independently; and students again hand in their reflections about surface area of cylinders and how they can apply what they know to real life problems. The fourth day of instruction is designed for students to apply the plan they have developed for determining total surface area for any cylinder and play around, so to speak, with the math ideas they have developed during the last few days. Students will be challenged to find the surface area of certain cylinders by working in small groups. The groups will then compare their strategies and solutions, looking for similarities and differences. Also, the groups will be challenged to represent their strategy for finding total surface area of any cylinder algebraically or with symbols. Students should continue to reflect in their “Take Away Window” tool at the end of the class period and turn in their thoughts to their teacher. A homework assignment involving the same three story problems given to the TRC group will be given to students at the end of class. Students will be encouraged to read through the stories and provide evidence on how to solve the problems by class the next day. They will also be aware that groups will role play the story problems in class as well. Fifth day of instruction or playing around will occur (the sixth day of this sequence) for the Guided Play Time Group. “Take Away Windows” complete with teacher’s feedback are returned from the previous math meeting. Students will role play the story problems from the previous night’s homework assignment. As the students role play their stories, strategies and solutions should evolve for class discussion. This activity will culminate into students being handed the naked number problems or the worksheet that the other group in this study also studied. Students will independently work on these problems not only to find the surface area of the cylinders, but they must also create a story for each cylinder and give these problems a context. This activity addresses standard of mathematical practice two and shows their ability to contextualize a problem. Students will be expected to continue their work with the naked number problems as homework with the intent of discussing the problems in small groups as their warm-up before the test the next day. “Take Away Window” reflection may be optional this day as students are working through problems independently to once assess their own conceptual understanding about cylinders. Assessment day for the GPT group will take place on day six after a warm-up session about the problems assigned the day before. The post assessment will be started day six and is expected to be completed by the end of the class period on day seven. After both groups have completed the post assessment, the general math survey will be administered. In the following two to three weeks after the research has been conducted, students will have follow-up class sessions where both lesson designs will be shared with both groups. After both sets of students have experienced both versions of the lesson and discussed their thoughts, a survey about the surface area lesson will be given to the students to canvass their opinions about the two types of instruction. Both math surveys will be coded and categorized to analyze the data provided by the students (See Appendices D and E). Results of the surveys will be organized in tables to illustrate any trends relating to positive and negative perceptions about math and the impact on math achievement. The pre and posttests will be compared to assess growth of students’ conceptual understanding of surface area from before instruction to post-instruction. As I analyze the pre and posttests, I will look for an increase in completion of problems correctly and the amount of evidence provided by the students. The post assessment will also be scored using a rubric similar in design to those rubrics used throughout the school year with these students. Based on the data shown by this rubric (See Appendix C), a graph illustrating growth between pre and post tests will be shared for each student. A box and whisker plot will display the rubric scores and illustrate the deviations for each group. Triangulation, or cross comparison, of the data will provide insight from multiple sources. These various analyses will lead to an increased understanding of teaching strategies that influence students’ productive dispositions in math and how integral productive dispositions are in student achievement in math. **Findings and Implications** Does guided play time influence student achievement and productive disposition in the math classroom? This question will not be totally answered after my action research because of the limited scope of this study. However, after this investigation into guided play time during math lessons, there will be some indication of what students need in place for learning math and developing their productive habits and perceptions of mathematics. I feel my students will have their voices heard about what types of lessons help them learn math best. Inspired by the text in chapter six of //Stringer’s Action Research in Education// (2008), the mode for sharing my action research will hopefully ignite a passion in families and the community to support best math practices that fit the students in their lives. Practices that will help their students prepare for career and college. After analyzing the post tests and surveys of my students, I will create graphs of my data analyses. This data collection will be ultimately shared with my students first. We will explore their reaction to what the data says. My students will share their ideas about my research and whether or not it has given valuable insight into how they think about math and how they learn the best in the math classroom. I will get their feedback on what was positive about this research event and what could have been done better. (This mirrors the type of discussions we have after we have studied math units.) Once I have discussed the findings of my research with my students, I will share what I learned with the families of my students and my principal. As I share the results of the study with my students, we will immediately begin looking at revising or enhancing the units of instruction that I am already planning for next school year. Students are actively involved in lesson design when possible. I often ask for student input at the end of a unit or the end of a school year about what procedures, activities, projects, and assessments worked well in my classroom. Next, the students will assist in developing a way to share the implications from our action research. The students will create some type of skit or role play situation that dramatizes the results of this study. They will help bring to life what our study unveiled and represent themselves, as they are “active agents in their own learning” (Springer, 2008, p. 163). The students will be encouraged to share their dramatization (complete with props) at a future math night at our school, a PTA meeting, our building’s staff development meeting, a school board meeting, and possibly a district-wide in-service setting. (Yes, students will need to be brave. If they are, that could be considered an attribute of a strong productive disposition about math.) Our school district is contemplating adopting a new math curriculum. The data I collect in my action research will help determine how our district decides to invest our precious school budget’s dollars. My students will help create an impact much greater than a written report and actually model what my action research was all about: the one talking and doing is the one doing the learning. J The results of my action research may involve what to do and perhaps what NOT to do when it comes to guided play time. However, the processes of analyzing how I instruct and how I conduct action research will send their own message to those around me. Hopefully, with this teacher leadership in action, my colleagues and administration will also be inspired to examine what they are doing in their niche of the world. In the end, this action research about guided play time will positively affect my students regardless of its outcome. After I have conducted a true action research study, I will do it again to more accurately assess the enterprises going on in my middle school math classroom! J
 * Statement of the Problem**
 * Significance of the Study**
 * Definition of Terms**
 * Productive disposition**, for the purpose of this study, has been taken from Center for Education’s //Adding It Up// (2001) that defines the strands of mathematical proficiencies as being conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. Productive disposition is defined as, “habitual inclination to see mathematics as sensible, useful, and worthwhile coupled with a belief in diligence and one’s own efficacy” (p. 5).
 * //Cognitive conflict//** as shared by Patsiomitou and Emvalotis and also Monaghan is described as a state of disequilibrium that leads students to build meaning and attach to what they already know. Cognitive conflict has much to do with the questioning and reflection process. In relation to this study, cognitive conflicts would take place as students experiment with or dramatize the math concepts they are studying.
 * Guided play time** is any activity or lesson that a teacher plans that involves the students doing most of the talking and experimenting, taking notes, predicting, testing ideas, forming conjectures, modeling, dramatizing, etc. as they learn more about math needed to solve the assigned scenarios or problems.
 * Math proficiency** will depend on the context in this study. In this action research, math proficiency could refer to one of the mathematical proficiencies as shared in //Adding It Up//, of which productive disposition is one strand. Or mathematical proficiency could mean when a student is proficient in math or has mastered what they need to learn at a particular level in math.
 * //Common Core State Standards (CCSS)//** is a current educational reform initiative in the United States endorsed by the National Governors Association, Council of Chief State School Officers, Achieve, Council of the Great City Schools, and National Association of State School Boards Association.
 * //Zone of proximal development (ZPD)//** for a child is defined by Vygotsky as the “distance between the level of his actual development, determined with the help of independently solved tasks, and the level of possible development, defined with the help of tasks solved by the child under the guidance of adults or in cooperation with more intelligent peers” (p. 204). ZPD has much to do with how comfortable a student performs math tasks and his/her productive disposition, which is a focus of this study.
 * //Self-efficacy//**, as it will be referenced in this study, involves how one perceives her/his own abilities and how well they can complete tasks (Bandura, 1993).
 * Barriers**, when referenced in this study, are any problem or situation that inhibits a learner from accessing curriculum, makes going to class formidable, or creates an arduous setting for a learner to concentrate and learn.
 * Limitations**
 * Teacher’s Role in Facilitating Effective Tasks for Student Learning**
 * Students Thinking about Their Thinking and Perceptions about Math**
 * Constructivism**
 * group work facilitated [students’] learning responsibility.
 * provided motivation to learn.
 * enabled [students] to acquire knowledge by seeing other’s behaviors, receiving different ideas, and understanding others’ points of view.
 * social interaction among the students assisted the construction of knowledge (Duatepe-Paksu and Ubuza).
 * Summary of Literature and Research Review**
 * 1) How does guide play time influence students’ productive dispositions in the math classroom?
 * 2) How does guided play time influence students’ achievement in 6th grade math?
 * Description of the Site and Candidates for the Study**
 * Procedures**
 * Instruments.** A cover letter (see Appendix A) explaining the purpose of this study and a permission slip will be sent home with the student candidates for research. In the letter, parents will be assured that their student’s identity will be protected and their information kept confidential. The letter will describe the purpose of this action research along with the minimal risks involved and the huge benefits that could result. Parents/guardians also learn through the consent form (see Attachment A) that this action research is under direct supervision of BHSU faculty.
 * Data Collection**
 * Data Analysis**

**References** Abbott, R., O'Donnell, J., Hawkins, J., Hill, K., Kosterman, R., & Catalano, R. (1998). Changing teaching practices to promote achievement and bonding to school. //American Journal of Orthopsychiatry, 68(4)//, 542-552. doi: [] Bandura, A. (1993). Perceived Self-Efficacy in Cognitive Development and Functioning. //Educational Psychologist, 28(2)//, 117-148. Bellanca, J., Fogarty, R., & Pete, B. (2012) //How to teach thinking skills within the common core.// Bloomington, IN: Solution Tree Press. Bender, W. (2009). //Differentiating math instruction.// Thousand Oaks, CA: Corwin Press. Duatepe-Paksu, A. & Ubuza, B. (2009, April/May). Effects of drama-based geometry instruction on student achievement, attitudes, and thinking levels. //The Journal of Educational Research, 102//(4), 272-286. Guven, B. (2012). Using dynamic geometry software to improve eight [sic] grade students' understanding of transformation geometry. //Australasian Journal of Educational Technology, 28//(2), 364-382. Jiang, Z., White, A., & Rosenwasser, A. (2011). Randomized control trials on the dynamic geometry approach. Journal of Mathematics Education at Teachers College Columbia University, 2 (Fall- Winter), 8-17. Jones, W. & Kottler, J. (2006). //Understanding research: Becoming a competent and critical// //consumer.// Saddle River, N J: Pearson Education, Inc. Kilpatrick, J., Swafford, J. & Findell, B. (Eds.). (2001). //Adding it up//. Washington, D.C.: National Academy Press. Kirschner, P., Sweller, J., & Clark, R. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, an inquiry-based teaching. //Educational Psychologist, 41//(2), 75-86. Retrieved from [] Martin, T., Soucy, S., McCrone, M., Bower, W. & Dindyal, J. (2005). The interplay of teacher and student actions in the teaching and learning of geometric proof. //Educational Studies in Mathematics,// //60,// 95–124. DOI: 10.1007/s10649-005-6698-0 McGraw Hill Eds. (2006). //Chapter 12 resource masters: geometry: measuring three-dimensional figures. mathematics applications and concepts: course 2//. New York, NY: Glencoe/McGraw Hill. Meece, J., Wigfield, A., & Eccles, J. (1990). Predictors of math anxiety and its influence on young adolescents’ course enrollment intentions and performance in mathematics. //Journal of Educational Psychology, 82//(1), 60-70. Monaghan, F. (2000). What difference does it make? Children's view of the differences between some quadrilaterals. //Educational Studies in Mathematics, 42//, 179-196. Netherlands: Kluwer Academic Publishing. Montague, M. (1992). The effects of cognitive and metacognitive strategy instruction on the mathematical problem solving of middle school students with learning disabilities. //Journal of Learning Disabilities, 25//(4), 230-248. National Governors Association Center for Best Practices and Council of Chief State School Officers. (2010). //Common core state standards.// Washington, D.C.: National Governors Association for Best Practices and Council of Chief State School Officers. Patsiomitou, S. & Emvalotis, A. (2010, February). Students movement through van Hiele levels in a dynamic geometry guided reinvention process. //Journal of Mathematics and Technology,// 18-48. ISSN: 2078-0257. Remillard, J. (1999). Curriculum materials in mathematics education reform: A framework for examining teacher’s curriculum development. //Curriculum Inquiry, 29//(3), 315-342. Stringer, E. (2008). //Action research in education//. Columbus, OH: Pearson Education, Inc. Swafford, J., Jones, G., & Thornton, C. (1997). Increased knowledge in geometry and instructional practice. //Journal for Research in Mathematics Education, 28//(4), 467-483. Retrieved from [] Student math survey. (n.d.) Retrieved from [] (n.d.) Tennyson, R. D., & Sisk, M. F. (2011). A problem-solving approach to management of instructional systems design. //Behaviour and Information Technology//, //30//(1), 3-12. doi:10.1080/0144929X.2010.490958 Thomas, A. (2011, January 25). Why are we afraid of math? Retrieved from [] Unal, H., Jakubowski, E. & Corey, D. (2009, December). Differences in learning geometry among high and low spatial ability pre-service mathematics teachers. //International Journal of// //Mathematical Education in Science and Technology, 40//(8), 997-1012. Usiskin, Z. (1982). Van Hiele levels of achievement in secondary school geometry. Chicago: University of Chicago. Vygotsky, L. (2011). The dynamics of the school child's mental development in relation to teaching and learning. //Journal of Cognitive Education and Psychology 10//(2), 198-211. Webley, K. (2011, June 11). Top 10 bad teachers: Charlie Brown’s teacher, //Peanuts.// Retrieved from [] Wigfield, A. & Meece, J. (1988). Math Anxiety in Elementary and Secondary School Students. //Journal of Educational Psychology, 82//(1), 210-216.

**Appendix A** Mrs. Schlechter at Hermosa School P.O Box 27--11 4th Street Hermosa, SD 57744 April ___, 2013__ REQUESTING PERMISSION TO ALLOW YOUR STUDENT TO PARTICIPATE IN AN ACTION RESEARCH PROJECT IN MRS. SCHLECHTER’S CLASSROOM Dear Very Important Families of Mrs. Schlechter’s students, Hello! You are receiving this letter, because with your permission, your student will be involved in an important project! J I have designed an action research study to examine the best practices in teaching math and promoting a student’s desire to be a life-long math learner. Yes, this is official research that could include your child. For your child to be included in this activity, I will need your permission to allow your child to be part of my action research project. Also and foremost, I am requesting that your child have a choice in the matter. If they choose to be a part of this very important task, I am going to encourage them to not visit about the math lesson we are investigating with students from the other group in this study until we are done with the research portion. In the end, all the students will experience both settings I am creating for the lesson I have chosen. If your student chooses not to participate or you do not want your child to participate, your child in no way will be penalized. They will just have the normal ongoing lessons I had previously planned to facilitate for this time of year. Some students may ask if they earn bonus for participating in this project. The answer is no. I am asking them to do it for the sake of teaching me about what works best in the classroom. If your child chooses to participate, their identity will be completely confidential. I promise to protect the identity of my students and there is minimal risk involved. Students will be exposed to different approaches for teaching the same lesson in math, which occurs already in a normal day to day setting in the classroom. For this particular lesson, I am going to collect data based on test scores and a math survey about this lesson, in addition to a general math survey. As I mentioned before, there is minimal risk. The benefits, however, include students helping me identify the best ways to teach math and help me examine how I teach in the classroom. Your student will not only benefit from our efforts with this research, but future students who grace my classroom will reap the rewards of this study. Your student will help me conduct research that will help make learning in my classroom more meaningful and aid me in my quest for improving my math instruction.  As your student can verify, I am both learner and teacher in the classroom just like your student. This research is part of my graduate work in the math specialist arena. This project will be conducted under the supervision of Dr. Vicki Linn of Black Hills State University. I plan to share my results about this study with my students, their families, my colleagues in our school district, my colleagues across the state, and with our school’s administration. I may even share details from my research with the community as they become more involved in our school. Please fill out the attached permission form. I look forward to hearing your response to my request! Thank you for all you do for your student and their education. Sparkling in education, Mrs. Tammy Jo Schlechter J Please have your student fill out the form below, share your signature and the date, detach this note from my letter and return to school.

__PERMISSION FORM:__ __(Students, please print your name in the blank.)__ __My name is__ ___, and I am a student at Hermosa Middle School in Hermosa, SD. I wish to be a part of Mrs. Tammy Jo Schlechter’s action research about the best practices in teaching math and promoting a student’s desire to be a life-long math learner. I understand that I will be working on a math lesson that Mrs. Schlechter has designed for me to study and learn about as part of her research project. This lesson will be about math concepts that are required to be learned and mastered at the middle school level by the Common Core State Math Standards. I will do my best to represent myself and what I learn for this lesson.__ __X___ date_ [student’s signature] As parent/guardian of this student, I grant permission to Mrs. Schlechter to include my child in her action research project. I have read her letter explaining the risks and benefits of this research. X___ date__ _ [parent/guardian’s signature]

[print your name, please, dear parent or guardian]

**Appendix B** MATH Pretest/Posttest: S_ A __of C__ __ N ___ __ D ___

Draw your favorite cylinder. Beneath your cylinder, draw the net of your cylinder.


 * ** What I’ve learned to do ** ||  ** What I’ve learned NOT to do **  ||  ** What I’ve seen others do—but this is why it doesn’t work! **  ||

Determine what shapes are used in the net you drew. List them here.

Generalize about the relationship between the two-dimensional shapes used to build a cylinder.

Describe and/or illustrate how to find the area of a rectangle.


 * ** What I’ve learned to do ** ||  ** What I’ve learned NOT to do **  ||  ** What I’ve seen others do—but this is why it doesn’t work! **  ||

Describe and/or illustrate how to find the area of a circle.


 * ** What I’ve learned to do ** ||  ** What I’ve learned NOT to do **  ||  ** What I’ve seen others do—but this is why it doesn’t work! **  ||

Describe and/or illustrate how to find the circumference of a circle.


 * ** What I’ve learned to do ** ||  ** What I’ve learned NOT to do **  ||  ** What I’ve seen others do—but this is why it doesn’t work! **  ||

Examine two rectangular prism examples. (The second example is on the next page.)


 * Figure **** 1 **** Find the total surface area for this box. **


 * Figure **** 2 **** Insert simple fractions that would make sense for the dimensions of this rectangular prism. Then find or determine the total surface area for this box. **

Determine the surface area of the rectangular prism of your choice from the two examples above.


 * ** What I’ve learned to do ** ||  ** What I’ve learned NOT to do **  ||  ** What I’ve seen others do—but this is why it doesn’t work! **  ||

The boxes or rectangular prisms you have seen during this activity, where in real life would you see this shape and what are they used for? Complete the table by filling in the blank cells and illustrate with your own drawing.


 * Words || The surface area of a cylinder || equals  || the area of two bases ||  Plus  || the area of the curved surface ||
 * Symbols ||  ||   ||   ||   ||   ||
 * Pictures ||  ||   ||   ||   ||   ||

How would you find the surface area of a cylinder with no top? Give your answer in words, pictures, and symbols.
 * ** What I’ve learned to do ** ||  ** What I’ve learned NOT to do **  ||  ** What I’ve seen others do—but this is why it doesn’t work! **  ||

PACKAGING What is the area of the label on a box of oatmeal with a radius of 9.3 centimeters and a height of 16.5 centimeters? Round to the nearest tenth.


 * ** What I’ve learned to do ** ||  ** What I’ve learned NOT to do **  ||  ** What I’ve seen others do—but this is why it doesn’t work! **  ||

CANS A cylindrical can has a diameter of 6 inches and a height of 7 3/10 inches. What is the surface area of the can? Round to the nearest tenth.


 * ** What I’ve learned to do ** ||  ** What I’ve learned NOT to do **  ||  ** What I’ve seen others do—but this is why it doesn’t work! **  ||

** OR **
 * Two options for the remainder of the test: **
 * 1) You may complete **two** of the problems from this page and the next page. If you choose to find the total surface area of the cylinders in the pictures, you must also include a story about the cylinder with your answer. The “manufacturing” problem needs to be solved AND illustrated if you choose to do this problem as one of your choices.
 * 1) You may measure the dimensions of two cylinders found in the classroom to the nearest 1/16 of an inch. Record your dimensions on the back of this test and determine the total surface area for the cylinders you chose. Create a story about the two cylinders you worked with. When would you need to know the surface area of these items?


 * MANUFACTURING How much sheet metal is required to make a cylindrical trash can with a diameter of 2 ½ feet and a height of 4 ¼ feet? (Remember, it is a trash can.) J ||


 * Figure **** 3 **** Find the total surface area for this cylinder. **


 * Figure **** 4 **** Find the total surface area for this cylinder. **

**Appendix C**
 * Rubric for Scoring Pre and Post Assessment**
 * CATEGORY || ** 4 ** || ** 3 ** || ** 2 ** || ** 1 ** ||
 * ** Mathematical Concepts ** || Explanation shows complete understanding of the mathematical concepts used to solve the problem(s). Extra details are used as evidence of this complete understanding. SMP 1 is highly evident. Correct solutions are shared.


 * 9 points ** || Explanation shows substantial understanding of the mathematical concepts used to solve the problem(s). SMP 1 is evident. If an incorrect solution is given, it is due to a calculation error, because evidence is shown for a correct procedure for solving the problem.
 * 7 points ** || Explanation shows some understanding of the mathematical concepts neded to solve the problems. SMP 1 is somewhat evident.


 * 5 points ** || Explanation shows very limited understanding of underlying concepts needed to solve the problem(s) OR is not written. SMP 1 needs work.


 * 3 points ** ||
 * ** Reasoning Quantatively and Abstractly ** || Can take numbers and put them into interesting real world context. Can take numbers out of context and work with them mathematically.
 * 9 points ** || Can take numbers and put them into real world context. Can take numbers out of context and work with them mathematically.
 * 7 points ** || Struggles to show problems in real world context. Struggles with taking numbers out of context to work with them mathematically.
 * 5 points ** || Little evidence of mathematical reasoning.


 * 3 points ** ||
 * ** Mathematical Errors ** || Identified errors or misconceptions that fellow students might make (in addition to their own possible errors) and shared strategies on what to do and NOT what to do.
 * 4 points ** || Used their own errors or misconceptions to teach what to do and NOT what to do.


 * 3 points ** || Realized their error(s), crossed out mistake(s), and reworked the problem.


 * 2 points ** || Erased or ignored errors.


 * 1 point ** ||
 * ** Diagrams and Sketches ** || Diagrams and/or sketches are clear and greatly add to the audience understanding of the procedure(s).
 * 3 points ** || Diagrams and/or sketches are clear and easy to understand.


 * 2 points ** || Diagrams and/or sketches are somewhat difficult to understand.


 * 1 point ** || Diagrams and/or sketches are difficult to understand or are not used.


 * 0 points ** ||
 * ** Mathematical Vocabulary and Notation ** || Correct vocabulary (terminology) and notation are always used, making it easy to understand what was done.
 * 8 points ** || Correct vocabulary (terminology) and notation are usually used, making it easy to understand what was done.
 * 6 points ** || Correct vocabulary (terminology) and notation are used, but it is not easy to understand what was done.
 * 4 points ** || There is little use or a lot of inappropriate use of vocabulary and notation.
 * 2 points ** ||
 * ** Neatness and Organization ** || The work is presented in a neat, clear, organized fashion that is easy to read.

“Investigation” here means project, activity, or test (assessment). || All sections of the investigation are completed. Optional Bonus Categories:
 * 9 points ** || The work is presented in a neat, clear, organized fashion that is usually easy to read.
 * 7 points ** || The work is presented in an organized fashion but may be hard to read at times.
 * 5 points ** || The work appears sloppy and unorganized. It is hard to know what information goes together.
 * 3 points ** ||
 * ** Completion **
 * 8 points ** || All but one section of the investigation are completed.
 * 6 points ** || All but two sections of the investigation are completed.
 * 4 points ** || An attempt was made to complete a section.
 * 2 points ** ||
 * ATTEMPT 1 2 3 4 5 for student # ___ date__ __** Optional bonus categories available.
 * ** Identifies a pattern(s) and/or shortcuts ** || Shares multiple patterns found in their math investigation. Created a conjecture about a shortcut as a result of their pattern observations.
 * 4 bonus points ** || Shares a couple patterns found in their math investigation.


 * 2 bonus points ** || Shares a pattern found in their math investigation.


 * 1 bonus point ** || Did not share a pattern.


 * 0 points ** ||
 * ** Working with Others ** || Student was an engaged partner, listening to suggestions of others and working cooperatively throughout the lesson.
 * 4 bonus points ** || Student was an engaged partner but had trouble listening to others and/or working cooperatively throughout the lesson.
 * 2 points ** || Student cooperated with others but needed prompting to stay on-task.


 * 1 point ** || Student did not effectively work with others.


 * 0 points ** ||

**Appendix D** **Student Math Survey** Write **your math teacher’s name** on the line below:
 * Your Math Teacher’s Name:**
 * _**
 * (Example: Mrs. J. Smith )**

For each question use a pen or pencil to “bubble in” the boxes. Please:

Bubble in **one box** if it is **not true** at all. Bubble in **two boxes** if it is **a little bit true**. Bubble in **all the boxes** if it is **very true**.

If you have any questions, please ask the person giving the survey for help. Thank you!


 * 1) I like learning math. o o o
 * 2) Math is boring. o o o
 * 3) I like to come up with new ways to solve math problems. o o o
 * 4) Learning new things in math is fun for me. o o o
 * 5) Math is important throughout life. o o o
 * 6) I believe that there is usually one right way to solve math problems. o o o


 * 1) I can explain how I get my answers to math problems. o o o
 * 2) In my math class, we practice things over and over until we get them right. o o o
 * 3) I work on math problems during class time with other students in my class. o o o
 * 4) My teacher tries to understand my way of doing math problems. o o o
 * 5) We copy notes from the board that the teacher creates. o o o


 * 1) We copy notes from the board that the students create. o o o
 * 2) My teacher asks me to show my work with pictures. o o o
 * 3) We have homework every, or almost every, night with fifteen or more problems to do. o o o
 * 4) We have quizzes or tests. o o o
 * 5) We do projects that are graded. o o o
 * 6) For class time, our teacher only gives us worksheets that have many short math problems. o o o
 * 7) In math class, we work on one big math problem for a long time. o o o
 * 8) We sometimes act out or dramatize math problems. o o o


 * 1) My teacher shows us how to solve math problems and then we practice similar problems. o o o
 * 2) My teacher introduces math problems to us and then lets us figure them out. o o o
 * 3) My teacher is interested in my work even if it is wrong. o o o
 * 4) When I don’t understand something, my teacher tries to help me by asking me questions about my thinking. o o o
 * 5) My teacher asks us to think about different ways to solve each math problem. o o o
 * 6) My teacher has us do math work on our computers during math class. o o o
 * 7) My teacher uses computers when s/he teaches the class. o o o


 * 1) The teacher does most of the talking in our math class. o o o
 * 2) Students are expected to work independently on their daily math assignments. o o o
 * 3) We use a lot of worksheets in our math class. o o o
 * 4) I use a math journal to record math vocabulary, strategies, and my ideas for math. o o o
 * 5) We usually work on lessons from out textbook. o o o
 * 6) The students do most of the talking about math in our math class. o o o
 * 7) I do a lot of talking about math in our math class. o o o


 * 1) I am encouraged to draw or build models of my math problems. o o o
 * 2) My teacher never uses anything but her/his voice or writing on the board to teach math. o o o
 * 3) I get one chance to take a quiz or a test. o o o
 * 4) Math class is just the teacher talking, students using pencil and paper to write down notes and solve problems. o o o
 * 5) Math class is one of my favorite classes. o o o
 * 6) When I think of math, I think of a textbook. o o o


 * 1) When I think of math, I think of the math projects I have done that helped me solve a problem. o o o
 * 2) We always sit in desks in straight rows in math class. o o o
 * 3) I may only use a pencil to do my math and must neatly erase all my mistakes. o o o

Coded for these reasons:
 * Student Number or Code: _**

Student productive disposition: 1, 2, 3, 4, 5, 6, 10, 33, 38

Classroom procedures for guided play time setting 7, 8, 9, 12, 13, 16, 18, 19, 21, 23, 24, 25, 32, 34

Classroom procedures for traditional classroom setting 11, 14, 17, 20, 27, 28, 29, 31, 35, 36, 37, 39, 41, 42

Could be in both settings 10, 15, 22, 26, 30, 33, 40


 * **Productive Disposition: Item Number** || Indicates a dislike for math or bored with math || In the middle || Likes math ||
 * 1 ||   ||   ||   ||
 * 2 ||   ||   ||   ||
 * 3 ||   ||   ||   ||
 * 4 ||   ||   ||   ||
 * 5 ||   ||   ||   ||
 * 6 ||   ||   ||   ||
 * 10 ||   ||   ||   ||
 * 38 ||   ||   ||   ||


 * **Setting: Item Number** || Indicates a more traditional type setting for learning || In the middle || Indicates a more guided play time setting where there is construction time for learning ||
 * 7 ||   ||   ||   ||
 * 8 ||   ||   ||   ||
 * 9 ||   ||   ||   ||
 * 11 ||   ||   ||   ||
 * 12 ||   ||   ||   ||
 * 13 ||   ||   ||   ||
 * 14 ||   ||   ||   ||
 * 16 ||   ||   ||   ||
 * 17 ||   ||   ||   ||
 * 18 ||   ||   ||   ||
 * 19 ||   ||   ||   ||
 * 20 ||   ||   ||   ||
 * 21 ||   ||   ||   ||
 * 23 ||   ||   ||   ||
 * 24 ||   ||   ||   ||
 * 25 ||   ||   ||   ||
 * 27 ||   ||   ||   ||
 * 28 ||   ||   ||   ||
 * 29 ||   ||   ||   ||
 * 31 ||   ||   ||   ||
 * 32 ||   ||   ||   ||
 * 34 ||   ||   ||   ||
 * 35 ||   ||   ||   ||
 * 36 ||   ||   ||   ||
 * 37 ||   ||   ||   ||
 * 39 ||   ||   ||   ||
 * 41 ||   ||   ||   ||
 * 42 ||   ||   ||   ||

**Appendix E**
 * Student Math Survey About The surface Area Lesson**

For each question use a pen or pencil to “bubble in” the boxes. Please: Circle the code for your group here: TRC GPT

Bubble in **one box** if it is **not true** at all. Bubble in **two boxes** if it is a **little bit true**. Bubble in **all the boxes** if it is **very true**.

If you have any questions, please ask the person giving the survey for help. Thank you!

1. I liked how the surface area math lesson was taught the first time around.    2. The surface area math lesson the first time around was boring.  3. I like to come up with new ways to solve math problems.  4. Learning new things with surface area was more fun the second time around.  5. Math is important throughout life.  6. I feel confident about the post assessment that I took after the first surface area lesson was presented.  7. I wished I could have taken the post assessment after the second surface area lesson was given.  8. I believe that there is usually one right way to solve math problems. 9. I really did not learn anything new and/or I did not enjoy the second math lesson about surface area. 

10. In your opinion, which version of the lesson about surface area would help kids learn about this math concept the best? Why?
 * Short answer response is requested.**

11. Which lesson would you most likely remember a year from now? Why? _


 * Student Math Survey About The surface Area Lesson**

This survey is designed to be given after students have been exposed to both versions of the surface area lesson. Note: they will have taken the post assessment BEFORE they are presented the second version of the lesson.

It is to be administered where students circle what group they are in as instructed by the facilitator giving the survey. Students take this survey anonymously after they have circled their group code.


 * Circle Group Code: TRC or GPT
 * **Lesson Indication: Item Number** || Indicates the traditional setting is more conducive to learning. || In the middle || Indicates the guided play time is more conducive to learning. ||
 * 1 ||   ||   ||   ||
 * 2 ||   ||   ||   ||
 * 3* ||  na  ||  na  ||  na  ||
 * 4 ||   ||   ||   ||
 * 5* ||  na  ||  na  ||  na  ||
 * 6 ||   ||   ||   ||
 * 7 ||  na  ||  na  ||  na  ||
 * 8* ||  na  ||  na  ||  na  ||
 * 9 ||   ||   ||   ||
 * 10 ||   ||   ||   ||
 * 11 ||   ||   ||   ||


 * TRC represents the traditional class lesson group. GPT represents the guided play time lesson group.
 * cannot use this question, as it is unclear whether or not their reaction is because of the type of lesson or if it is just that it was presented again and that in itself helped the student**
 * These are filler questions that could be used to examine productive disposition about these students as well. J