Assignments 1 and 2
I did these assignments together on three lessons (at the end of the entry)
Brief Description of Assignment 7-1
Find a reference on the subject of math anxiety.
Leave comments on the three tasks someone designed during weeks three through five. In your comments, suggest steps that will help prevent or cure anxiety in students and/or teachers. Tie steps to the particulars of the task.
The 2 references I used were:
The Causes and Prevention of Math Anxiety
by Marilyn Curtain-Phillips, M. Ed.
Here are some excerpts:
Studies have shown students learn best when they are active rather than passive learners (Spikell, 1993).
The theory of multiple intelligences addresses the different learning styles. Lessons are presented for visual/spatial, logical/mathematics, musical, body/kinesthetic, interpersonal and intrapersonal and verbal/linguistic.
Learners today ask questions why something is done this way or that way and why not this way?
Students today have a need for practical math. Therefore, math needs to be relevant to their everyday lives.
To learn mathematics, students must be engaged in exploring, conjecturing, and thinking rather than, engaged only in rote learning of rules and procedures.
Brief Description of Assignment 7.2: Leave comments on the three tasks someone designed during weeks three through five. In your comments, explain how tasks can promote these mathematical sophistication, adding twists or ideas to the tasks so they can promote the values better. You can focus on task design and/or assessment.
List of 9 traits of Mathematical Sophistication (from Seaman and Szydlik)
1. Seeking to understand (recognize and describe) patterns.
2. Seeking to find the same essential structure in seemingly different entities.
3. Making and testing mathematical conjectures.
4. Making mathematical models of objects.
5. Using precise definitions of objects.
6. Interest in abstract relationships among objects.
7. Use of logical argument and counterexamples.
8. Use of precise language.
9. Use of symbolic notation for objects and ideas
I really liked this lesson when I first read it a couple of weeks ago, and after researching prevention of math anxiety, I understand the lesson’s appeal better.
The first thing that strikes me when looking at it are the three images of pictures of shapes. The visual nature of this lesson should appeal to all students, including those susceptible to math anxiety. The hands on and fun natures of the lesson are further advantages in avoiding math anxiety (see http://www.mathgoodies.com/articles/math_anxiety.html). The addition of real world applications (which you are already planning to add) is also considered an anxiety deterrent. This lesson pretty well covers every anxiety prevention suggestion in the article cited above and would be hard to improve on.
This lesson already covers a good number of points in the article, and probably doesn’t need further changes. In any case, here are some suggestions for more material:
An exercise where students model real world symmetric figures by plane figures.
An exercise where students find diverse real world figures that can be modeled by the same symmetric plane figure.
Perhaps for the constructive response question, a guideline or example about the use of unambiguous language in mathematical argument.
This exercise has a very nice go-easy approach. Students slowly build up information about a subject by doing a series of problems based on real life situations that get increasingly more sophisticated and complex. This should be very good for minimizing math anxiety. The only suggestion I can think of is the possibility of adding some activities for kids with different learning styles.
1. Role playing the actual scenario, where someone is hailing a cab and needs to figure out which company to use, or have two cab drivers try to persuade the same student that their company’s rates are the best for his needs.
2. Art/Graphic Design. Give students who are interested the opportunity to diagram or draw some of the cab ride scenarios.
I liked the progression of questions the students have to answer and the way they led to understanding the mathematics of the situation. Perhaps it would be possible to insert a few questions that would prompt students to ponder and conjecture about mathematical rules along the way.
For instance, before question 6, insert a question like: Do you think there is a rule for deciding which company is best to use in certain situations? In every situation? If there is a rule, what might it be?
One idea used to combat math anxiety is to give more students a chance to “connect” with the lesson. One possible approach is to prompt them to develop an intuitive feeling for what the equations mean.
1. For instance 2x – y = 2 can be restated
as y = 2(x – 1). This equation can be interpreted verbally: get y by taking x, subtracting 1 and multiplying the result by 2. You could plot a few sample points:
There’s now some context in the problem for students who are more verbal and visual.
With the second equation x + 6y = 27, do the analogous thing. Rewrite as
y = 4.5 – x/6. Verbally, take one sixth of x, and subtract it from 4.5.
Plot a few sample points
Also, conjecturing and connecting to real life are considered antidotes to math anxiety.
2. With the visual information above, there is an opportunity for the students to stop and think about the situation.
Could be some point that the solution sets have in common?
Is so, where would it be likely to be?
Is there a way to find it exactly?
3. Real life applications: Give an example of a real life situation where knowing the intersection of two lines is helpful (though I’m at a loss right now to think of one).
Conjecturing is also considered a point of mathematical sophistication (point #3), so suggestion 2 above might be helpful with sophistication as well.
Leading the kids to conjecture a general rule about when pairs of linear equations have solution sets might also promote mathematical sophistication.