# Dialogue in Mathematics Research

The purpose is to provide a forum to discuss research related to mathematics education.

## Wednesday, August 22, 2012

### Assessment

Describe how you will assess at least one of your instructional activities. What tools will you use to assess your students? What will you create to collect data for this assessment? How will you know if students have mastered the concept?

## Tuesday, August 7, 2012

### Language and Mathematics Learning

Week 2: Language and Math

From problem solving to procedures, the idea that mathematics learning is linked to language acquisition appears inherently true as so much of what we do in mathematics is embedded in language. With that being said entering the classroom with strong content knowledge maybe just one facet of your instructional practice, another piece that practicioners must consider is how to provide students with the linguistic proficiency that is needed for mathematics achievement. Language is a tool that organizes one's thinking about a concept and is essential when it comes to mathematical reasoning. How can one explain their thinking or check the validity of their work when they lack the language to make sense of what they are doing. Whether a student is monolingual, billingual or semilingual (lacking first language proficiency) language proficiency is essential for achievement and this component of instruction must be addressed.

Using the lens of Cognitive Theory the idea that information is stored in schemas implies that meaningful learning is essential for students to recall and remember information that is conveyed in the classroom. For the English language learner this can be a more complex task as students often do not have the background knowledge to support them in learning mathematics content and skills.

Scaffolding is an essential part of the process and requires thoughtful planning and individualized instruction. Furthermore teachers need to give students the opportunity to practice and rehearse their new learning otherwise the information will decay or be forgotten. The information processing theory reminds us that students must practice and rehearse new learning in order to recall it. Invariably the idea of multiple representation must be embedded in a teacher's practice as this approach will allow the learner to expand their foundational knowledge, develop more indepth understanding and expand their schemas which will enable students to meet lower lever cognitive demand tasks such as recalling and understanding. When this is achieved students will have the capacity to meet more challenging tasks and persist when they encounter disequilibrium.

From problem solving to procedures, the idea that mathematics learning is linked to language acquisition appears inherently true as so much of what we do in mathematics is embedded in language. With that being said entering the classroom with strong content knowledge maybe just one facet of your instructional practice, another piece that practicioners must consider is how to provide students with the linguistic proficiency that is needed for mathematics achievement. Language is a tool that organizes one's thinking about a concept and is essential when it comes to mathematical reasoning. How can one explain their thinking or check the validity of their work when they lack the language to make sense of what they are doing. Whether a student is monolingual, billingual or semilingual (lacking first language proficiency) language proficiency is essential for achievement and this component of instruction must be addressed.

Using the lens of Cognitive Theory the idea that information is stored in schemas implies that meaningful learning is essential for students to recall and remember information that is conveyed in the classroom. For the English language learner this can be a more complex task as students often do not have the background knowledge to support them in learning mathematics content and skills.

Scaffolding is an essential part of the process and requires thoughtful planning and individualized instruction. Furthermore teachers need to give students the opportunity to practice and rehearse their new learning otherwise the information will decay or be forgotten. The information processing theory reminds us that students must practice and rehearse new learning in order to recall it. Invariably the idea of multiple representation must be embedded in a teacher's practice as this approach will allow the learner to expand their foundational knowledge, develop more indepth understanding and expand their schemas which will enable students to meet lower lever cognitive demand tasks such as recalling and understanding. When this is achieved students will have the capacity to meet more challenging tasks and persist when they encounter disequilibrium.

## Thursday, July 26, 2012

### Reform in Mathematics Teaching - Carmel, CA, United States, ASCD EDge Blog post - A Professional Networking Community for Educators

Reform in Mathematics Teaching - Carmel, CA, United States, ASCD EDge Blog post - A Professional Networking Community for Educators

Please respond to the Blog Post on ASCD EDGE. You should post your response on the EDGE website. You should also respond to at least one other post.

Please respond to the Blog Post on ASCD EDGE. You should post your response on the EDGE website. You should also respond to at least one other post.

### Mathematics Pedagogy

Week 1: What do we know, want to know, or have learned about teaching mathematics?

Teaching is a craft, a skill that takes time, patience, reflection and experience to acquire. Content knowledge is domain specific where as pedagogy is the way we approach instruction. We need to think about how we approach instruction to engage and motivate learners.

Throughout this course we will examine different aspect of instruction that the teacher must take into consideration: language, assessment, representation, and culture. We will build three instructional activities that incorporates each of these aspects and incorporates a conceptual approach to instruction.

Let's begin by discussing what we know and want to know about Mathematics Pedagogy.

Teaching is a craft, a skill that takes time, patience, reflection and experience to acquire. Content knowledge is domain specific where as pedagogy is the way we approach instruction. We need to think about how we approach instruction to engage and motivate learners.

Throughout this course we will examine different aspect of instruction that the teacher must take into consideration: language, assessment, representation, and culture. We will build three instructional activities that incorporates each of these aspects and incorporates a conceptual approach to instruction.

Let's begin by discussing what we know and want to know about Mathematics Pedagogy.

## Friday, June 29, 2012

### Web 2.0 Tools in Mathematics

What are some ways that you can incorporate Web 2.0 tools into mathematics instruction? Could you use these tools with CGI or Algebra? If so how?

## Monday, August 22, 2011

### Culturally Responsive Pedagogy

In the article Culturally Relevant Mathematics Teaching in a Mexican American Context (Gutstein et al., 1997) the idea that teachers use their knowledge of students' culture to advance learning of mathematics is highlighted through a rich dialogue of classroom examples, field notes and teacher reflection. In this article you really get a sense that students knowledge, culture and beliefs are valued.

For the past few weeks you have been working on three instructional activities that engage learners from multiple perspectives. After reading this article which approach would you most likely implement into your instructional activities and how will you achieve a culturally relevant pedagogy?

For the past few weeks you have been working on three instructional activities that engage learners from multiple perspectives. After reading this article which approach would you most likely implement into your instructional activities and how will you achieve a culturally relevant pedagogy?

## Tuesday, August 9, 2011

### Performance Assessment Tasks

Performance assessment tasks are commonly used in mathematics classrooms to provide students with an opportunity to engage in challenging tasks that require mathematical thinking. According to O'Daffer and Thornquist, (1993) mathematical thinking "involves using mathematically rich thinking skills to understand ideas, discover relationships among the ideas, draw or support conclusions about the ideas and their relationships, and solve problems involving the ideas" (p. 43).

What are the potential benefits and/or drawbacks of using Performance Assessment tasks ? Share an experience from the perspective of teacher or student.

What are the potential benefits and/or drawbacks of using Performance Assessment tasks ? Share an experience from the perspective of teacher or student.

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