Math Cut Ups Edition, Volume 14 - January 2016
The Importance of Process Thinking
What's the difference between Processes and Procedures
The Process Standards
The current version of the Texas Essential Knowledge and Skills for Mathematics, adopted in 2012 and implemented in 2014 showcase standards for process thinking at the forefront, and then layer in specific content objectives using the process skills as a foundation of strong problem solving and reasoning. All of the knowledge statements that comprise the standards that follow the process skills begin with the phrase “the student applies mathematical process standards to…” illustrating a newfound emphasis on the use of these skills in working with all mathematical content to be learned. The process standards found within the TEKS, like those found in the NTCM Principles and Standards and the Standards for Mathematical Practice in the CCSS, describe ways in which students are expected to engage in learning and working with mathematics content throughout their courses of study.
Read more in my paper about the importance of these process skills and find a reference chart highlighting the process standards found within the NCTM Principles and Standards, the CCSS, and the TEKS.
Classroom Ideas for Promoting Process Thinking
- Provide students a series of problems that are already solved. Have them identify correctly worked solutions and those that are incorrect. For all incorrect work, have them identify where the mistake occurred and describe why that person may have made that error.
- Have students match representations together or to display there solution using more than two representations - such as verbal, graphical, tabular, algebraic, etc. Students should be able to explain how their solution is represented in all the views and explain why they selected each. Are some representations better than others?
- For a problem with a series of steps, or a proof with several steps, provide students all the steps or component parts and have them determine the order they should be in. For example, for order of operations problem solving, put each step in the solution on a separate strip of paper. Provide a few extra steps that are incorrect based on common errors. Then have students put the steps in the correct order and try to identify the extraneous steps. Have them explain their thinking as they made decisions about which steps were to be used and which were not - using mathematical justifications.
Thinking cards are an easy way to keep the focus on mathematical reasoning and process thinking. Thinking card sets contain questions that scaffold and support students to reason, explain, analyze, and summarize their ideas while they work. Each set of cards is designed be used within a small group of students but certainly you could provide each student their own set. As students problem solve with the concepts presented in class, they use the cards to ask and answer higher order thinking questions and prompt thinking about the task and how it might be solved. Promote the use by assigning students or groups to share out responses to certain card questions, or have different groups share out different thoughts using the card letters to identify which questions are to be explained.
Thinking cards come in 4 types. Process Thinking Cards focus on the mathematical process skills while Algebraic Thinking Cards, Functional Thinking Cards, and Geometric Thinking cards focus specifically on the mathematics processes and reasoning within narrower strands of the standards. Each package of Thinking Cards contains 10 sets of the question cards, ideal for small group instruction. All cards are pre-printed in color on cardstock and for just $5 a set, comes ready to laminate, cut, and use!
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