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Contents

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This is a literature review, but not the kind that comes up with a summary of findings. Instead, it analyzes implicit theoretical foundations, and gives examples. Remillard comes up with four categories that are not mutually exclusive:

\n\n

There's a suggested framework for future research toward the end.

\n

 

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\n

In order to construct their own knowledge, students need to talk.

\n

\"If students are to develop an understanding of and an ability to use mathematical applications in a variety of contexts, they should have meaningful and relevant experiences that will actively engage them in constructing their own knowledge..  Also, that active engagement needs to be accompanied by opportunities for students to talk about what they already know and don't knwo and what they are doing as they strive to extend or change their current level of understanding.\" (p. 88)

\n

 

\n

Teachers ask a lot of questions, students few.

\n

 

\n

Types

\n

Factual -

\n\n

Reasoning

\n\n

Open Questions not calling for reasoning.

\n

 

\n

 

\n

 

\n

 

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"note", "note": "

This article investigates the structure of secondary pre-service teachers' beliefs. That is, it is not enough to look at what teachers believe or even how strongly they believe it. We must also consider the connections (or lack of connections) between beliefs and their orientation towards their own beliefs or knowledge or authority. The article gives portraits of four teachers through open-ended surveys and interviews taken throughout their last year of coursework, during their student teaching, and during a seminar following their student teaching. How they come to know was a central construct, following Perry's study of college men and Belenky's study of women. Perry identified:

\n\n

Belenky et al. identified:

\n\n

Sally - Seemed to exhibit dualism and received knowing, but when she began to listen to the voices of others, it confused her and she re-evaluated her commitment to teaching.

\n

Nancy - Primarily a received knower. Many of her beliefs were aligned with productive \"reform\" beliefs - multiple ways to solve problems, etc. - but she typically looked to others for affirmation and knowing what was right.

\n

Henry - authoritarian, relied on authority of particular others, suggesting dualism, and mostly did not tolerate others' views. So, his belief initial belief about technology is different from Greg's initial belief, even though they were both against it at the outset.

\n

Greg - Greg valued the opinions of others, suggesting Commitment stage. He weighed others opinions and he adjusted his beliefs based off of whether those beliefs aligned with his core beliefs, preparing students for the world.

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"version": 130, "parentItem": "WZBDXTFT", "itemType": "note", "note": "

Notes

\n

AR= Algebraic Reasoning

\n

This article reports on an empirical study: case study conducted over one whole school year.

\n

 AR has to be developed in the early grades. However, pbs for the teachers: how to integrate it?

\n

 The goal of the study was to analyze

\n

-       HOW a teacher integrates algebra (in terms of frequency and diversity)

\n

-       The impact on the students (in terms of achievement)

\n

-       In order to develop a framework about how teachers develop AR

\n

 Rationale:

\n

 If we want to build classrooms that promote AR, we must provide the teachers with the appropriate professional support. BUT to do so, we must characterize the teacher’s practice that supports Algebraic culture

\n

 

\n

How the author conducts the study:

\n

 

\n

-       observations / recordings analyzed. Coding emerged from initial analysis but refined

\n

-       13 categories of AR instances emerged

\n

-       analysis of frequency of these instances

\n

-       use of standardized tests to evaluate the level of the students’ achievement (does the teacher’s practiced affected the students’ achievement?)

\n

 

\n

This study defines:

\n

 

\n

-       entry points to introduce AR in elementary grades

\n

-       evidence that teachers can engage in AR

\n

-       algebra as generalization of arithmetic seems to be the easiest for the teachers to implement

\n

 

\n

they define why it is important to teach algebra: to help students study algebra later (MS and HS)

\n

 

\n

They also insist that it has to be connected to other math topics

", "tags": [], "relations": {}, "dateAdded": "2015-03-11T20:59:51Z", "dateModified": "2015-04-03T20:07:46Z" } } ]