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Using Writing to Assess Students Problem-Solving and Critical Thinking Skills in Mathematics
Intent of Project
This course will provide the following learning outcomes:
- Intellectual Skills
- Cognitive Strategies
- The Problem: Many mathematics students are unable to write about their problem-solving processes; this is especially apparent on Part II of the yearly standardized assessment in mathematics.
- What is to be Learned: Mathematics educators will learn how regular writing, incorporated into the mathematics curricula, will improve students’ critical thinking, problem-solving, and metacognitive skills while simultaneously creating students capable of providing written explanations of solutions to mathematics problems.
- The Learners: Mathematics teachers at all levels of education eager to enhance their instructional techniques and facilitate improved student performance.
- The Context: Teachers will read articles about the integration of writing in the mathematics classroom, discuss the articles in a forum, and apply their new knowledge to analyze examples of student work; teachers will also create problems to promote student writing.
- The Need for a Solution: Too often educators assume students are capable of applying their knowledge in many different ways. For instance, a straight-A student performs algorithms well, but when asked to provide a written response to explain the solution process they are not able to write a reflection of the process; this disconnect is the focus of this unit.
- The Goal: Mathematics educators will choose to incorporate writing into their mathematics curricula to enhance student understanding as well as problem-solving, critical thinking, and metacognitive skills.
- Learner will prove their understanding of how writing in mathematics utilizes metacognitive and critical thinking skills to portray student understanding by analyzing student examples
- Learner chooses to accept writing as part of curriculum by designing lessons utilizing various writing aspects
- Learner applies new knowledge and understanding by generating mathematical questions to assess students' metacognitive and critical thinking skills through writing
- Learner classifies students' written work by categorizing writing reflective of metacognitive and/or critical thinking skills.
Objective: Teachers will choose to implement writing in mathematics on a regular basis to assess student understanding and improve students’ problem-solving, critical thinking, and metacognitive skills.
Task 1: Teachers will read articles focusing on writing integration in mathematics classrooms and discuss how it can improve student understanding of mathematical concepts.
Prerequisite Skills: Teachers must have prior knowledge of how theory can inform practice.
Task 2: Teachers will identify examples of student understanding (or misconceptions) and identify problem-solving and critical thinking strategies by evaluating examples of students’ written responses to word problems.
Prerequisite Skills: Teachers must have strong foundational knowledge in mathematics and must be able to determine if students’ strategies are appropriate for the problem posed.
Task 3: Teachers will design three (3) mathematical word problems to integrate into their curriculum to assess students’ understanding and improve students’ problem-solving and critical thinking skills.
Prerequisite Skills: Teachers must be familiar with their students’ zones of proximal development to create questions that can stretch the skills of each of their students.
Resources and References
Connolly, Paul. "Writing and the ecology of learning." In Writing to Learn Mathematics, edited by Paul Connolly and Theresa Vilardi, 1-14. New York: Teachers College Press, 1989.
Huang, J., & Normandia, B. (2009). Students' perceptions on communicating mathematically: A case study of a secondary mathematics classroom. The lntemational Journal of Leaming, 16(5), 1-21.
Ntenza, S. P. (2006). Investigating forms of children's writing in grade 7 mathematics classrooms. Educational Studies in Mathematics, 61, 321-345.
Powell, A. B., & Lopez, J. A. (1989). Writing as a vehicle to learn mathematics: A case study. In P. Connolly, & T. Vilardi (Eds.), Writing to Learn Mathematics (pp. 157-177). New York: Teachers College Press.
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