Monthly Archives: September 2014

Week 5 Assignments

Week 5 Assignments

** EXTENSION: WeBWorK Assignment #4 (due last week) has been re-opened and extended to Tuesday, October 7th, if you wish to continue working on it  (this was done because the final problem has some material on negating statements that we will cover early this week)

Written work¬†‚Ästnone
WeBWorK¬†–¬†Assignments #4** and #5, due Tuesday, October 7th, at midnight.
OpenLab РOpenLab #5, due Thursday, October 9th (at start of class).

The Question of why?

When I was in the 5th or 6th grade we started to learn about area. We first learned about the area of a rectangles and came up with the formula of (LXW=AREAsqr). When we moved on to triangles the teacher asked us how would we find the area, I thought it would be the same concept as the rectangle but then I realized that the triangle has three sides so how would the formula (LXW=AREA sqr)work. She gave us all a rectangular piece of paper, we were to make a doted line from one diagonal to the next, then fold the paper along the doted line and cut it. We saw that we had two identical triangles, she asked us to put it back together and find the area of the rectangle. After we found the area of the rectangle, we took it apart again she asked if the area of the each of the triangle is the same as the rectangle, no the area of the triangle is now half the rectangle.  So she let us make up our own formula for the area of a triangle based on what we just discovered. That is how i acme to understand why the area of a triangle is (1/2BXH).

The questions i would like to know why is.

Why is it that the answer is different when we switch from degrees to radians.¬† I found his question interesting because it was never explained to me why I had to make that change when doing calculus and what is the difference between to the two, I was just told that’s what is done.

Why does the quadratic formula works. I saw it in the examples and it made me think that I have no idea why it works I just know how to use it.

 

OpenLab #4: The importance of “Why?”

Kids love to ask “Why?”

If you’re like most people who attended public school in the U.S., most of the math you‚Äôve done in your life has been primarily¬†computational, or algorithmic – you learn a kind of problem, you learn a method to solve it, you practice it a few times, and you demonstrate that you’ve learned it by solving a problem on an exam. ¬†Maybe the solution involves memorizing a formula, or a set of steps (an algorithm). ¬†Very seldom are you asked to consider the reasons¬†behind the method – what I call the “why” questions. ¬†And if you ever asked these kind of questions, there is a good chance that you were not often given a very satisfying answer.

Questions you may not have spent much time on in math class:

  • Why does the formula look like¬†this,¬†instead of something else?
  • Why do we do these steps, in this order? How do we know this method actually works? ¬†Why does it work?
  • Why is this fact (“theorem”) true? ¬†I don’t believe it – can you convince me?
  • What’s the big deal about this fact (or formula)? ¬†Why is it important?

To begin¬†this¬†assignment, I’d like you to spend some time thinking about the different kinds of math you’ve learned in your life. ¬†Look at math textbooks or class notes from past and current classes. ¬†Think about the ¬†math skills you learned at different ages – from early experiences with counting, up through things like algebra or geometry, and on to Calculus or Linear Algebra or other recent courses. ¬† If you still have some old math work from your high school, middle school, or elementary school years that might help too (maybe your parents kept some of your childhood work?). ¬†If you’re in the Math Ed program, you can think about the math that you are working on¬†in your MEDU courses. ¬†As you consider these topics, think about the “why” questions – when you were learning this topic, did you spend time in¬†class talking about “why?” ¬†¬†Did you do activities or other work that helped you understand the reasons for the formulas and methods that you learned?

Assignment (due Thursday 10/2/14). The assignment consists of two parts.  Be sure to answer each part completely (they are equally important).

1. ¬†Describe a time that you DID learn about the “why” behind a mathematical idea (why something works, or where it came from, etc.). ¬†Tell us about it –¬†how old were you, what was the class (or did it happen outside of class?), what was the topic, and what did you learn?

One example that came up in a class discussion was the activity introducing the number \pi by having students measure the diameter and circumference of various circular objects, and showing that the ratio was always a little more than 3.

2. ¬†State¬†three questions about math that you do not¬†know the answer to (but would like¬†to!). ¬†For each question, tell us why you find it interesting. ¬†The questions…

  • …should involve¬†“why” or “how”
  • …should be about math topics that you are already familiar with – things you’ve studied (you need not be an expert)
  • …should come from different math topics, at different levels (some examples: ¬†arithmetic, fractions, algebra, geometry, functions, calculus, probability, … )

Some examples of “why” questions.¬†

  1. Why does a \times b equal b \times a?
  2. Why do we need a common denominator when we add fractions?
  3. How do we know that \sqrt{2} is irrational (not equal to a fraction)?
  4. Where does the quadratic formula come from?  How do we know it always works?
  5. The fundamental theorem of calculus gives us a way to evaluate an integral Рfor example, to find the area under a curve.  How do we know this actually works, and gives the correct answer?

 

Exam #1 – date change and review sheet update

Hi everyone,

As decided in class on Tuesday, we will be moving the date of our first exam to Thursday, October 2nd.

The Review Sheet and Answer Key have been posted to the “Handouts” page of the OpenLab.

IMPORTANT: Problems #7c and #7d on the Review Sheet have images of Venn diagrams which did not print well Рtake a look at the online version to see which regions are shaded in.  Same goes for the Answer Key #7a and #7b.

If you¬†get stuck or have questions about a problem, feel free to leave a comment in reply to this post – I’ll check it regularly and respond here.

Best of luck,
Prof. Reitz

Week 4 Assignments

Week 4 Assignments

HEADS UP: Next week Tuesday 9/23 is on a Friday schedule (so we do NOT meet), and next week Thursday 9/25 there are no classes.

Written work¬†‚Ästnone
WeBWorK¬†–¬†Assignments #3 and #4, due Tuesday, September 23th*, at midnight.
*NOTE: we do NOT have class this day!
OpenLab РOpenLab #4, due Thursday, October 2nd (at start of class).

OpenLab #3: “Sentences”

Due Thursday, 9/18/14.¬†¬†For this week’s writing assignment, take a look at the picture below called “Sentences.” ¬†Read every sentence in the picture. ¬†As you read, pay attention to your own stream of consciousness – what are the thoughts that pop into your head? ¬†For full credit, respond to all 4 of the following items.

  1. Record¬†two observations¬†about the sentences in the picture – what do you notice / what’s something you find interesting / what popped into your head / what stood¬†out.
  2. Choose one of the sentences in the picture (do NOT choose the same sentence as anyone else). ¬†Type the sentence out “in quotes”, and then answer the following questions:
    a. Is it a statement (as discussed by Prof. Park in class on Thursday )?  Explain why or why not.
    b. Is it true or false? Explain in everyday English why or why not.
  3. Make up a sentence that you believe would fit into this picture.  Tell us the sentence, and then tell us whether it is a statement, and whether it is true or false.
  4. What connection (if any) does this assignment have to do with the work we are doing in class?
“Sentences” by Flickr user Eldeem

Week 3 Assignments

Week 3 Assignments

UPDATE: WeBWorK #3 will be due Tuesday, September 23 (not September 16 as originally indicated)

Written work¬†‚Äď Sec 1.8*: 3, 5, 6, 8, due Tuesday, September 16th, in class.
* GRADING: odd-numbered problems worth 3 points, even problems 5 points.

WeBWorK¬†–¬†Assignment #3, due Tuesday, September 23th, at midnight.
OpenLab РOpenLab #3, due Thursday, Sept 18th (at start of class).

OpenLab #2: Mathography

This assignment is due Thursday, September 11, at the start of class.

Assignment.  Choose ONE of the following two topics.  Write a reply to this post, responding to the topic.  Begin by telling us which topic you chose. (1-2 paragraphs).

Topics.

  1. Sometimes people can recognize a time when their opinion of math dramatically changed either for the better or the worse. If such a time happened to you, tell us about it.
  2. Choose an experience you had in which you suddenly understood a math concept (it could be any kind of math, from elementary school up through college).  Describe what happened.  Do you think you could explain it to others in a way that they could have the same flash of understanding?

Extra Credit. ¬†For extra credit, write a response to one of your classmates’ comments. ¬†Do you feel the same, or different? ¬†Did you learn anything? ¬†Did you get any ideas about teaching, or about learning?

Why are we doing this, anyway?¬† We are following two ideas that have come up already in class — things that may¬†not¬†seem related to learning math, but research shows that engaging in these activities can¬†dramatically¬†increase the amount that you learn, and change the way you learn it. ¬†The first is¬†writing¬†‚Äď something not typically associated with mathematics. ¬†When you express your ideas in words, it forces you to think them through very carefully, detail by detail. ¬†A great way to check and see if you really understand something is to try to explain it to someone else, either out loud or in writing. ¬†Example: if you know how to add fractions, try teaching it someone who doesn‚Äôt know how. ¬†The second is called¬†metacognition, or ‚Äúthinking about thinking.‚ÄĚ ¬†This happens when you think about what was going on in your head while you were working on a problem or trying to learn a new idea. ¬†What train of thought did you follow? ¬†Where did you get stuck, and what did you do next? ¬†What were you feeling at the time? and so on. ¬†Combining writing and metacognition can be a tremendously powerful tool in identifying the ways we learn best and the ways we make mistakes, and learning to improve. ¬†However, like any skill, it takes practice. ¬†That‚Äôs why we‚Äôre getting started by writing a little about our past experiences with mathematics.