EDU 6380 Blog #2: TEKS Mathematical Process Standards and Algebraic Thinking and Reasoning

The TEKS mathematical process standards describe ways in which students are expected to engage with mathematics content to learn and demonstrate understanding.  For example, learning opportunities created to develop algebraic thinking utilize the process standard, “the student is expected to analyze mathematical relationships to connect and communicate mathematical ideas.” 

The creation of algebraic thinking tasks can begin with the identification of problems from classroom resources that are then extended to an algebraic task.   For example, consider the following problem inspired by a 2^nd grade textbook:

Mark took 8 pictures at the zoo.  Julie took 5 pictures at the zoo.  How many more pictures did Mark take than Julie?

This task can be transformed into an algebraic thinking and reasoning task by varying one of the quantities given, e.g., the number of pictures taken by Mark.  By developing a sequence of problems and noting the accompanying expressions (or number sentences), students can use these numeric examples to analyze a mathematical relationship.   Following the original problem with additional cases such as, Mark has taken 10 pictures, 11, or 45, provide an opportunity for students to generate their own meaningful expressions for analysis.  For example,  “8 – 5” followed by “10 – 5”, “11 – 5”, and “45 – 5”. 

In this algebraic task, the number of pictures more Mark took than Julie can be found by subtracting 5 from Mark’s number, “M – 5”, where M represents the number of pictures taken by Mark.  When students create a generalized statement such as “M – 5”, and discuss the connections to the mathematical relationship shown, they actively communicate these mathematical ideas and relationships. Furthermore, focusing attention to the connections to other strategies used by students on the same task, such as counting on, will further strengthen students’ understanding of the relationship between addition and subtraction.

Considering the constraints of an already full curriculum,  “a powerful benefit of using algebrafied arithmetic tasks is that students do many important things at once, including developing number sense, practicing number facts, and recognizing and building patterns to model situations (Blanton & Kaput, 2003, p. 73)”.

Blanton, M. L., & Kaput, J. J. (2003). Developing elementary teachers’ “Algebra eyes and ears”. Teaching Children Mathematics, 10(2), 70-77.

 EDU 6380: Due Tuesday, February 24, 2015 (5:15pm)

For the blog assignment #2, you will create an algebraic thinking and reasoning task situated in one of the STEM content areas.  Consider how will you assist teachers as they transition to teaching mathematics content through the mathematics process standards.  Begin with a problem or task that may be commonly used, but does not address the process standards.  How will you modify this problem or task to engage students as described in the process standards?  Create an example and support your instructional decisions using research-based strategies, research findings, or recommendations from established institutions. 

See course handout for specific Blog requirements.