Teaching Secondary Mathematics

5th Edition

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Chapter 3 – Equity, Shame, and Anxiety in the Mathematics Classroom

Mathematics is still the most feared and disliked content area in the curriculum for children (and adults). It is socially acceptable to be terrible in mathematics and hate the subject, but it is not socially acceptable to be illiterate. It is important to focus on research that examines this phenomenon as well as strategies to reverse this trend in the secondary mathematics classroom. This chapter explores anxiety and shame in the mathematics classroom. Teacher behaviors and teaching strategies that alleviate the impact of these negative emotions are critical. The goal is to promote healthy associations with mathematics starting with young children that carry into adulthood. An emphasis on timed tests, high-stress techniques, and correctness has been shown to increase the levels of anxiety in the mathematics classroom. Promoting authentic, developmentally appropriate mathematics tasks that emphasize problem-solving and construction of concepts is the first step in battling math anxiety and shame.

Exercises

Exercise 3.1  Looking at a problem graphically- start with the equation y = 2x + 3

  1.  Use a graphing calculator, app or software to explore what happens to a linear function in slope-intercept form ( y = mx + b ) as you change the constant b.
  2. What happens when you change the slope m?
  3. What if you use negative numbers for m and b?
  4. Now try fractions
  5. Now try 0 for m and b, what happens?

Exercise 3.2  Looking at a problem numerically

  1. Use one of the equations of a line you graphed above and make a table by inputting x values and solving for the corresponding y values
    1. This x and y pairing will be an ordered pair.  Look on the graph from exercise 3.1 to verify that the point in on the line
  2. Make sure to try plugging in negative numbers and fractions for x and solve for y
  3. Try plugging in numbers for y and solving for x
  4. Try plugging in 0 for x, this is called the y intercept.  On your graph verify this is where the line crossed the y axis
  5. Try plugging in 0 for y, this is called the x intercept.  On your graph verify this is where the line crossed the x axis

Exercise 3.3  Looking at a problem algebraically- start with the equation 2y – 8 = 5x

  1.  Solve the equation for y to put this into slope intercept form
  2. Use what you know about slope and the y intercept, graph the function
  3. Try to create equations in non-slope intercept form that will describe lines that have a negative slope
  4. How would you write an equation for a horizontal line?
  5. What about a vertical line?

Some students fear asking questions in large groups.  A small group setting can be much more manageable for students and they might be more comfortable making mistakes and asking questions.

Exercise 3.4  Group Work

  1. What are some ways to ensure that all members of a group are an active part of the learning process?
  2. How can a group dynamic be different than whole group instruction?
  3. What impact might assigning roles to students have on the learning experience?
  4. How does group work help both high and low performers if done well?
  5. What are some hurdles to group work about which teachers and students need to be aware?

Exercise 3.5  Lessening math anxiety

  1. Students sometimes find the prospect of being wrong daunting in a math problem.  What are some ways to lessen the “shame” of being wrong?
  2. Students with math anxiety often have trouble demonstrating their understanding on tests, what are some strategies that might help with this issue?
  3. What are things that teachers can do in class to lower the stress level of the classroom?

Exercise 3.6  Equity

  1. What types of differences might exist in math abilities in the classroom?
  2. How and why do these differences exist?
  3. What are some equitable practices that could be applied to the math classroom?

Problem Solving Challenges

Problem 1

Your grandparents give you and your sibling two gift cards.  All that you are told is that one of them has twice as much money on it as the other.  When you look at the balance of the first card you see that is has $200, should you keep that gift card or switch to the other?

Hint: No Hint.  This one is up to the reader!

Answer

Solution;

Option 1- you keep the $200

Option 2- you have a 50% chance of getting $100 and a 50% chance of getting $400, so the expected value of the card is 100(.5) + 400(.5) = 50+200 = $250

Problem 2

Ask a friend to choose a number between 1 and 10 and keep it in their head without telling anyone.  Tell them to multiply that number by 9, and if it is a two digit number to add the digits together.  Then have them take that sum and subtract 5.  Now ask them to convert that number to a letter where 1 = A, 2 = B, 3 = C and so on.  Lastly ask them to think of a state that begins with that letter.  Now think of an animal that begins with the last letter of that animal.  Once they have that in their head you can inform them that there are no elephants in Delaware.

Hint:  Try this problem with 2 different values.

Answer

Solution:

The digits will add up to 9, and then when subtracting 5 the 4th letter of the alphabet is D, and Delaware is the only state beginning with D.  When asked for an animal starting with E, most will go to elephant, but beware the eel or the emu.

You can do similar things with countries that start with D, most will name Denmark, although the Dominican Republic is also a possibility.  If it is Denmark kangaroo is most likely the animal beginning with K that they think of, but beware the Koala bear messing things up.

Problem 3

A man was asked to be a substitute teacher in a classroom for a month.  The principal offered $100 a day.  The man asked if instead he could be paid 1 cent for the first day he worked, 2 cents for the second day, four cents for the third day and so on until the end of the month.  What should the principal decide?

No hint

Answer

Solution:

Let’s assume that there were 20 work days in a month.  If he were to earn $100 per day for 20 days that would be $2,000.  If the principal accepts the man’s offer he would get paid double the day before, starting with one penny, for 20 days.  This is an exponential growth problem.  Where the initial amount is $0.01, the grown rate is 2 and the number of intervals is 20.  So the sum of the payment would be

.01(2)20  = $10.485.76 or you could do this the long way and add the 20 days pay up.

Additional Learning Activities

There is no Additional Learning Activities for this chapter.

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