Archive for TEACHING STRATEGIES

Thursday, June 8th, 2017

Math in 3D!

Math in 3D!

3d

 

To many people, mathematics is seen as a topic of study, a course or content that they remember as problems they saw in textbook- A 2D experience – Flat and unrelated to their real world or daily lives. One of the paradigm shifts needed for many, is Math in 3D! What does that mean? Math in 3D has depth of understanding as it relates to  and  exists in the real world.

How can we help students see themselves as mathematicians using mathematics in the real world to many everyday decisions?

 

3 D Math

In this way, mathematics, should be seen as 3 D: a) mathematics conceptual understanding , 2) Procedural Understanding and set in a 3) real world context.

So for examples, 1) math concept of area—–> 2) relate to the procedure of A=L*W and is 3) used in the real world to figure out the square footage of houses. It is this third dimension, the context in the real world that takes the often experience mathematics to the 3D level!

Thursday, January 5th, 2017

Modeling Mathematical Ideas- Published in 2017!

modeling-math-ideas-book

Developing Strategic Competence in Elementary and Middle School

JENNIFER M. SUH AND PADMANABHAN SESHAIYER

Modeling Mathematical Ideas combines current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students’ common misconceptions in investigating and discussing important mathematical ideas related to number sense, computational fluency, algebraic thinking and proportional reasoning. In each chapter, the authors opens with a rich real-world mathematical problem and presents classroom strategies (such as visible thinking strategies & technology integration) and other related problems to develop students’ strategic competence in modeling mathematical ideas.

https://rowman.com/ISBN/9781475817607

https://www.amazon.com/Modeling-Mathematical-Ideas-Developing-Competence/dp/1475817592

Tuesday, February 16th, 2016

High Leverage Practices in Math

Pulling it altogether: How do all the research-based practices support effective teaching and learning of mathematics?

 

High Leverage Practices http://www.soe.umich.edu/academics/bachelors_degree_programs/uete/uete_hlp/

MQI MQI 4-Point to use for MATH MODELING

TRU framework trumath_introduction_alpha

NCTM 8 teaching practices PtA Effective Teaching Practices

 

 

Tuesday, February 16th, 2016

Principles to Action

PtA Effective Teaching Practices Band Concert

Tuesday, February 16th, 2016

NCTM 8 Teaching Practices

  1. Establish mathematics goals to focus learning.
  2. Implement tasks that promote reasoning and
    problem solving.
  3. Use and connect mathematical representations.
  4. Facilitate meaningful mathematical discourse.
  5. Pose purposeful questions.
  6. Build procedural fluency from conceptual understanding.
  7. Support productive struggle in learning mathematics.
  8. Elicit and use evidence of student thinking.

Monday, February 15th, 2016

Standards for Mathematical Practices

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

CCSS.MATH.PRACTICE.MP4 Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

CCSS.MATH.PRACTICE.MP6 Attend to precision.

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(xy)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

Saturday, November 1st, 2014

Math Happenings

Math happens all around us. One way to promote kids and parents talking about math daily is to introduce Math Happenings? As it’s important to read daily with your child, it’s important to find math in our everyday life and share how important it is to know and use math daily. Teachers can model this at the beginning of the year with a personal math happening and ask students to come to school and share their math happenings. Kids love to share about their weekend and events in their lives. Why not have them see it through a quantitative lens. For example, they love to tell you about the sport they played over the weekend with scores and statistics.

Zachary:: Ms. Jones, we won our soccer game 6-3. I scored a hat trick -3 in a row!
Teacher: Wow, you scored 1/2 half of the points for your team! Great job!

Share a math happening!

Saturday, November 1st, 2014

Recommended Readings in Math Education

Research Readings on Preparing Math Teachers

 Teacher learning
Cohen, S. (2004). Teachers’ professional development and the elementary mathematics classroom: Bringing understandings to light. Mahwah, NJ: Erlbaum.

Hammerness, K., Darling-Hammond, L., Bransford, J. with Berliner, D., Cochran-Smith, M., McDonald, M., & Zeichner, K. (2005). How teachers learn and develop. In L. Darling- Hammond & J. Bransford (Eds.), Preparing teachers for a changing world: What teachers should learn and be able to do (pp. 358-389). San Francisco: Jossey-Bass.

Moschkovich, J. (2007). Bilingual mathematics learners: How views of language, bilingual learners, and mathematical communication affect instruction. In N. S. Nasir & P. Cobb (Eds.), Improving access to mathematics: Diversity and equity in the classroom (pp. 89- 104). New York: Teachers College Press.

Putnam, R. T., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning? Educational Researcher, 29(1), 4-15.

Teacher knowledge
Hill, H. C., & Ball, D. L. (2004). Learning mathematics for teaching: Results from California’s mathematics professional development institutes. Journal for Research in Mathematics Education, 35, 330-351.

Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371-406.

Philipp, R. A., Ambrose, R., Lamb, L L. C., Sowder, J. T., Schnappelle, B. P., Sowder, L., Thanheiser, E., & Chauvot, J. (2007). Effects of early field experiences on the mathematical content knowledge and beliefs of prospective elementary school teachers: An experimental study. Journal for Research in Mathematics Education, 38, 438-476.

Stein, M. K., & Lane, S., (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2, 50-80.

Preservice teacher education (How might prospective teachers learn to teach in a way that they have not been taught?)

Darling-Hammond, L., Hammerness, K., with Grossman, P., Rust, F., & Shulman, L. (2005). The design of teacher education programs. In L. Darling-Hammond & J. Bransford (Eds.), Preparing teachers for a changing world: What teachers should learn and be able to do (pp. 390-441). San Francisco: Jossey-Bass.

Gutstein, E. (2007). “So one question leads to another”: Using mathematics to develop a pedagogy of questioning. In N. S. Nasir & P. Cobb (Eds.), Improving access to mathematics: Diversity and equity in the classroom (pp. 51-68). New York: Teachers College Press.

Mewborn, D. S. (2000). Learning to teach elementary mathematics: Ecological elements of a field experience. Journal of Mathematics Teacher Education, 3, 27-46.

Sowder, J. T. (2007). The mathematical education and development of teachers. In F. K. Lester, Jr., (Ed.), Second handbook of research on mathematics teaching and learning (pp. 199- 204 only), Reston, VA: National Council of Teachers of Mathematics.

Perspectives on professional development as a mechanism for reform
Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3-32). San Francisco: Jossey-Bass.

Davis, F. E., West, M. W., Greeno, J. G., Gresalfi, M. S., & Martin, H. T. (2007). Transactions of mathematical knowledge in the Algebra Project. In N. S. Nasir & P. Cobb (Eds.), Improving access to mathematics: Diversity and equity in the classroom (pp. 69-88). New York: Teachers College Press.

Little, J.W. (1993). Teachers’ professional development in a climate of educational reform. Educational Evaluation and Policy Analysis, 15, 129-151.

Thompson, C. L., & Zeuli, J. S. (1999). The frame and the tapestry: Standards-based reform and professional development. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 341-375). San Francisco: Jossey-Bass.

What do we know about effective professional development?
Garet, M. S., Porter, A. C., Desimone, L., Birman, B. F., & Yoon, K. S. (2001). What makes professional development effective? Results from a national sample of teachers. American Educational Research Journal, 38, 915-945.

Heck, D. J., Banilower, E. R., Weiss, I. R., & Rosenberg, S. L. (2008). Studying the effects of professional development: The case of the NSF’s Local Systemic Change through Teacher Enhancement Initiative, Journal for Research in Mathematics Education, 39, 113-152.

Sowder, J. T. (2007). The mathematical education and development of teachers. In F. K. Lester, Jr., (Ed.), Second handbook of research on mathematics teaching and learning (pp. 157- 199; 204-223 only). Reston, VA: National Council of Teachers of Mathematics.

Conducting professional development
Cobb, P., & Hodge, L. L. (2007). Culture, identity and equity in the mathematics classroom. In N. S. Nasir & P. Cobb (Eds.), Improving access to mathematics: Diversity and equity in the classroom (pp. 159-171). New York: Teachers College Press.

Desimone, L. M., Smith, T. M., & Phillips, K. J. R. (2007). Does policy influence mathematics and science teachers’ participation in professional development? Teachers College Record, 109, 1086-1122.

Stein, M. K., Smith, M. S., & Silver, E. A. (1999). The development of professional developers: Learning to assist teachers in new settings in new ways. Harvard Educational Review, 69, 237-269.

Wayne, A. J., Yoon, K. S., Zhu, P., Cronen, S., & Garet, M. S. (2008). Experimenting with teacher professional development: Motives and methods. Educational Researcher, 37 469- 479.

The intersection of mathematics education policy and practice
Spillane, J. P. (2004). Standards deviation: How schools misunderstand education policy. Cambridge, MA: Harvard University Press.

 

Issues for reform
Burris, C. C., Heubert, J. P., & Levin, H. M. (2006). Accelerating mathematics achievement using heterogeneous grouping. American Educational Research Journal, 43, 105-136.

Spillane, J. P., & Thompson, C. L. (1997). Reconstructing conceptions of local capacity: The local education agency’s capacity for ambitious instructional reform. Educational Evaluation and Policy Analysis, 19, 185-203.

Tate, W. F., & Rousseau, C. (2007). Engineering change in mathematics education: Research, policy and practice. In F. K. Lester, Jr., (Ed.), Second handbook of research on mathematics teaching and learning (pp.1209-1246). Reston, VA: National Council of Teachers of Mathematics.

Walker, E. N. (2006). Urban high school students’ academic communities and their effects on mathematics success. American Educational Research Journal, 43,43-73.

National Mathematics Panel
Borko, H., & Whitcomb, J. (2008). Teachers, teaching and teacher education; Comments on the National Mathematics Advisory Panel’s report. Educational Researcher, 37, 565-572.
National Mathematics Advisory Panel. (2008). Foundations for success: Findings and recommendations from the National Mathematics Advisory Panel (ED 00424P). Washington, DC: US Department of Education.
Sloane, F. C. (2008). Randomized trials in mathematics education: Recalibrating the proposed high watermark. Educational Researcher, 37, 624-630.
Spillane, J. P. (2008). Policy, politics, and the National Mathematics Advisory Panel report. Educational Researcher, 37, 638-644.

Professional Development
Elmore, R. F., & Burney, D. (1999). Investing in teacher learning: Staff development and instructional improvement. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 263-291). San Francisco: Jossey-Bass.
Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning to use children’s thinking in mathematics instruction. Journal for Research in Mathematics Education, 27, 403-434.
Hawley, W. D., & Valli, L. (1999). The essentials of effective professional development: A new consensus. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 127-150). San Francisco: Jossey-Bass.
Loucks-Horsley, S., Hewson, P. W., Love, N., & Stiles, K. E. (1998). Designing professional development for teachers of science and mathematics. Thousand Oaks, CA: Corwin.
Smith, M. S. (2001). Practice-based professional development for teachers of mathematics. Reston, VA: National Council of Teachers of Mathematics.
Wilson, S. M., & Berne, J. (1999). Teacher learning and the acquisition of professional knowledge: An examination of research on contemporary professional development. In A. Iran-Nejad & P. D. Pearson (Eds.), Review of research in education (Vol. 24, pp. 173- 209). Washington, D.C.: American Educational Research Association.

 

Teacher Change and Leadership
Burch, P. & Spillane, J. P. (2003). Elementary school leadership strategies and subject matter: Reforming mathematics and literacy instruction. The Elementary School Journal, 103, 519-535.
Drake, C., & Sherin, M. G. (2006). Practicing change: Curriculum adaptation and teacher narrative in the context of mathematics education reform. Curriculum Inquiry, 36, 153- 187.
Fullan, M., & Stiegelbauer, S. (1991). The new meaning of educational change. New York: Teachers College Press.
Miller, B., Moon, J., & Elko, S. (2000). Teacher leadership in mathematics and science. Portsmouth, NH: Heinemann.
Richardson, V., & Placier, P. (2001). Teacher change. In V. Richardson (Ed.), Handbook of research on teaching (4th ed., pp. 905-947). Washington, D. C.: American Educational Research Association.
Spillane, J. P. (2002). Local theories of teacher change: The pedagogy of district policies and programs. Teachers College Record, 104, 377-420.
Spillane, J. P., Diamond, J. B., & Jita, L. (2003). Leading instruction: the distribution of leadership for instruction. Journal of Curriculum Studies, 35, 533-543.

Strahan, D. (2003). Promoting a collaborative professional culture in three elementary schools that have beaten the odds. The Elementary School Journal, 104, 127-146.
van den Berg, R. (2002). Teachers’ meanings regarding educational practice. Review of Educational Research, 72, 577-625.
Wang, J., & Odell, S. J. (2002). Mentored learning to teach according to standards-based reform: A critical review. Review of Educational Research, 72, 481-546.
West, L., & Staub, F. C. (2003). Content-focused coaching: Transforming mathematics lessons. Portsmouth, NH: Heinemann.
York-Barr, J., & Duke, K. (2004). What do we know about teacher leadership? Findings from two decades of scholarship. Review of Educational Research, 74, 255-316.

Teacher Education
Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (4th ed., pp. 433-456). New York: Macmillan.

Cochran-Smith, M. (1995). Color blindness and basket making are not the answers: Confronting the dilemmas of race, culture, and language diversity in teacher education. American Educational Research Journal, 32, 493-522.
Conference Board of the Mathematical Sciences. (2001). The mathematical education of teachers: Vol. 11. Issues in mathematics education. Providence, RI: American Mathematical Society.

Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Educational Research Journal, 32, 465-491.

Sleeter, C. E. (2001). Preparing teachers for culturally diverse schools: Research and the overwhelming presence of whiteness. Journal of Teacher Education, 52, 94-106.

Steele, D. F. (2001). The interfacing of preservice and inservice experiences of reform-based teaching: A longitudinal study. Journal of Mathematics Teacher Education, 4, 139-172.

Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards- based mathematics instruction: A casebook for professional development. New York: Teachers College Press.

Wilson, S. M., Floden, R. E., Ferrini-Mundy, J. (2001). Teacher preparation research: Current knowledge, gaps, and recommendations (Center for the Study of Teaching and Policy Document R-01-3). Seattle: University of Washington. Available on-line at http://depts.washington.edu/ctpmail/ Click on Publications and then Research Reports.

Policy and Reform
Desimone, L. (2002). How can comprehensive school reform models be successfully implemented? Review of Educational Research, 72, 433-479.

Gamoran, A., Anderson, C. W., Quiroz, P. A., Secada, W. G., Williams, T., & Ashmann, S. (2003). Transforming teaching in math and science: How schools and districts can support change. New York: Teachers College Press.

 

Gold, B. A. (1999). Punctuated legitimacy: A theory of educational change. Teachers College
Record, 101, 192-219.
Knapp, M.S. (1997). Between systemic reforms and the mathematics and science classroom: The dynamics of innovation, implementation, and professional learning. Review of Educational Research, 67, 227-266.
McCaffrey, D., F., Hamilton, L. S., Stecher, B. M., Klein, S. P., Bugliari, D., & Robyn, A. (2001).    Interactions among instructional practices, curriculum and student achievement: The case of standards-based high school mathematics. Journal for Research in Mathematics Education, 32, 493-517.
Newmann, F. M., & Associates (Eds.). (1996). Authentic achievement: Restructuring schools for intellectual quality. San Francisco: Jossey Bass.
O’Day, J. A., & Smith, M. S. (1993). Systemic reform and educational opportunity. In S. H. Fuhrman (Ed.), Designing coherent education policy: Improving the system (pp. 250- 312). San Francisco: Jossey-Bass.
Pollock, M. (2001). How the question we ask most about race in education is the very question we most suppress. Educational Researcher, 30(9), 2-12.
Reys, R., Reys, B., Lapan, R., Holliday, G., & Wasman, D. (2003). Assessing the impact of Standards-based middle grades mathematics curriculum materials on student achievement. Journal for Research in Mathematics Education, 34, 74-95.
Rowan, B., Correnti, R., & Miller, R. J. (2002). What large-scale survey research tells us about teacher effects on student achievement: Insights from the Prospects stud of elementary schools. Teachers College Record, 108, 1525-1567.
Spillane, J. P. (2000). Cognition and policy implementation: District policymakers and the reform of mathematics education. Cognition and Instruction, 18, 141-179.
Spillane, J. P., Reiser, B. J., & Reimer, T. (2002). Policy implementation and cognition: Reframing and refocusing implementation research. Review of Educational Research, 72, 387-431.
Wood, T., & Sellers, P. (1997). Deepening the analysis: Longitudinal assessment of a problem- centered mathematics program. Journal for Research in Mathematics Education, 28, 163- 186.