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Unit Using Writing to Assess Students' Problem-Solving and Critical Thinking Skills in Mathematics
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
- Attitude
Needs Analysis
- 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.
Performance Objectives
- 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.
Task Analysis
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.
Curriculum Map
Media:Writing_Curriculum_Map.pdf
Instructional Guide
Lesson 1: Writing in the Mathematics Classroom
Lesson 2: Identifying Student Skills
Lesson 3: Creating Word Problems
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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Unit Using Writing to Assess Students' Problem-Solving and Critical Thinking Skills in Mathematics