Sunday, May 15, 2011

The Q

For the past three years I have been working with a diverse group of students to develop their mathematical skills. I work with students age 15 to age 20, from many walks of life. I am responsible for teaching all math content at my school, from pre-algebra through algebra 2. This is a true challenge because I may go from teaching fractions, decimals and percents to teaching composite functions or translations. This variation is difficult to plan for, but can be done. I love my job and what I do most days, the students I teach have had very little success before coming to my school. It is amazing to see the transformations that occur throughout the year with our students.

Saturday, May 14, 2011

Annotated Bibliography

Below you will find a list of reference materials, articles and various other pieces of information related to, and gathered from class.

1. Roth Mcduffie, A., Wohlhuter, K. A., & Breyfogle, M. L. (2009, May). Tailoring Tasks to Meet Students' Needs. Mathematics Teaching in Middle School, 16(9), 550-555.
Description: The authors in the article are making the case that four very simple and easy to implement changes will help all students achieve high-level reasoning skills.
1. Switch to a Familiar Context
2. Supplement Foundational Gaps
3. Incorporate Overarching Goals
4. Adjust for Reading Levels
Using these four strategies every teacher can help his ELLs and Special Education students achieve high-level reasoning skills.

2. Rider, R. (2007, March). Shifting from Traditional to Nontraditional Teaching Practices Using Multiple Representations.Mathematics Teacher, 100(7), 494-500.
Description: The author of this article proposed that her students were very good at going from symbolic representations of a function to tabular or graphical representations of the same function. However, when her students were asked to go from tabular or graphical representations to symbolic representations they struggled. What Rider discovered is that her teaching style and area of comfort had placed more emphasis on symbolic representations than others. To correct this problem Rider began to use all representations equally to describe a function and assess students knowledge of functions. While students wanted only "one way of doing it" Rider found that her students were able to better change from one representation to the other.

3. Melin, Axelsson, and Wedlund (2009). Project-based Learning - An Emergent Framework for Designing Courses. Information Systems Education Journal, 7 (34). ISSN: 1545-679X
Description: The authors of this literature review found through research that a project can be implemented and should be reviewed using the six methods below.
1. Overall Project Design
2. Project Task
3. Project Group
4. Examination
5. Feedback
6. Course evaluation and improvement
I would recommend this article to teachers interested in implementing project based learning. The authors develop an effective framework that could be used to easily evaluate and implement a PBL activity.

4. Skemp, R. R. (2006, September). Relational Understanding and Instrumental Understanding [Electronic version]. Mathematics Teaching in Middle School, 12(2), 88-95. Reprinted from the December 1976 issue of Mathematics Teaching.
Description: The author argues that there are two types of understanding 1) Relational Understanding: How and Why and 2) Instrumental Understanding: following the rule without knowing why. Skemp provides examples of both types of understanding and argues that instrumental understanding is not what we want students to be able to do. Students with instrumental understanding are only able to continually do the same type of problems over and over as long as the "instrument" is used. While students with relational understanding are able to take what they have learned and apply it to various situations. I would recommend this article to all math teachers, it made me reevaluate what type of understanding my students have.

5. Manouchehri, A., & Lapp, D. A. (2003, November). Unveiling Student Understanding: The Role of Questioning in Instruction. Mathematics Teacher, 96(8), 562-566.
Description: The authors of the article use a teacher's talk with her students as the launch point for discussion. What they found in the evaluation of the talk is that the teacher was using very focused, closed-ended questions to guide student thinking. The authors suggested teachers consider these three areas when developing questions.
Form: Do you want to ask closed or open ended questions?
Content: Does the question tell the teacher what you want the student to know?
Purpose: What do you want the question to do? (i.e. engage, mastery, explore)