Derivative Project

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Summer is here!

Monday marked the beginning of summer break for my students and myself. However, here I am one day later, at school working to further my education so that I can improve the learning environment of my classroom. I am not getting paid for this time, in fact, I must pay to have this experience. Why is it that everyone who has a problem with public education always states the fact that we get a "paid" summer break as a reason our jobs are so easy. If teaching were so easy why wouldn't more people do it? Oh, I think I know the answer to that. Is it the fact that teachers are required to be certified in a number of content areas. Is it the fact that at minimum you are required to have a bachelors degree and must continue your education throughout the course of your career. Maybe it's because we have to educate other peoples children no matter where they come from or what they know. Public education is an amazing tool that our society has. The biggest asset in public education is the teachers. The ones who log hour after hour, who sacrifice time with their families to improve the lives of others. Today instead of chastising a teacher for having the summer off thank him or her for all they have done to make the children of this nation successful!

Conquering my Arch Nemesis

Planning for some people comes natural, not so much for me. Planning is one of the most difficult parts of my job. Each day I must develop lessons for 4 different classes ranging from pre-algebra to algebra 2. The problem I have is I never feel like I have enough time to make each class the best it could be. Some days I spend an hour planning for one class, it is just not feasible to spend that much time on each class every day. Currently I am not really happy with the way I plan my lessons and units. I attempt to set a schedule/outline for each marking period (6 weeks) but I am not able to stick to the schedule because I am not sure while scheduling what type of background knowledge my students have. Perhaps next year I should create a test to determine what type of background knowledge/skills my students have. I currently use the method of pretesting but the problem is many of my students lack any sort of skills to show any useful information, the majority of them guess on all questions. I feel that the pre-req. test would provide more information about background skills than any standard related pre-test. Using this method I would be able to develop appropriate lessons based on the skill levels of my students. While lesson planning is not my favorite part of teaching I realize its value and strive every year to improve upon what I have done in the past and look forward to new ideas in the future.

Grading???

While grading I want to determine if my students have "mastered" the content. The problem is what is "mastery"? I define "mastery" as a students ability to demonstrate through verbal and algebraic means an in depth understanding of the problem. Mastery could occur in any classroom activity, however all assignments are not equal. Currently I use a 60-40 weighting, 60% assessments and 40% classwork. This has been a method I have used my entire teaching career without question. I have begun to wonder is this really the best way to measure "mastery"? Next year my school will begin to move towards project based learning where "mastery" can be seen in a final product. I love this idea, but I do not believe my current 60-40 system would work. Perhaps I will move to a total points system that will vary the weights each marking period, but will reflect the type of work being done in class. I believe the method and ways that you grade should based on what best reflects the work students are doing in class.

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.

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). http://isedj.org/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)