An Example of a "Learning Process" Journal (using the 2 colored box format)

Book: The Nature of Mathematics 10th ed by Karl Smith.

Source: Toronto Thomson Brooks/Cole, 2004.

It is 6:15 am (Monday). I am a little sluggish this morning, but let's see what happens.

Before I begin, the following thought just occurred to me: I wonder how this book could be integrated with Mathematica?

Chapter 1 The Nature of Problem Solving (pp. 1-52)

This is a lot to cover!

I don't believe it. I just begin skimming the first few pages and see a section about keeping a journal similar to this. Let's stay with the first skim.

Each of the four major sections has a problem set at the end.

I like the structure. It is organized into small chunks of only a few pages, with an opportunity to see how well one understands the material by presenting a set of problems of increasing difficulty.

Now let's try the first section.

1.1 Problem Solving (p. 2-16)

"... be willing to guess, experiment, estimate, and manipulate, and to try out problems withour fear of being wrong" (p. 2)

"You must make a commitment to daily work." (p. 2)

"The World of Mathematics by Newman is a gold mine of ideas." (p. 4)

George Polya's book, "How to Solve It" (1945, 1973) is considered a classic.

6:45 am I have finished reading the material in sub-section 1.1. Basically it consists of 7 different types of problems, the solution of which follows Polya's 4 steps:

1. Understand the problem
2. Devise a plan
3. Carry out the plan
4. Look back.

I have the Polya book. Good.

However I am unfamiliar with the Newman book. Let's try amazon.com. I now recall this 4 volume series from my undergraduate days. It is interesting to note that two of the reviewers mention that they refer to the book regularly (at least once a week!) and have been doing so for over a decade. It is now available as a reprint in softcover. I will file this fact away for the moment as I want to focus on the Smith book.

Now to have a look at the problem set.

Level 1

5. IN YOUR OWN WORDS At the beginning of this section three hints for success were listed. Discuss each of these from your perspective. Are there any other hints that you might add to this list? (p. 12)

1. You must make a commitment to attend each class.
2. You must make a commitment to daily work.
3. Read the text carefully.

I would add:

4. Have a playful attitude.
5. Keep some scrap paper and a pencil handy.
6. Use the Web and Google when an idea or question occurs to you.

Level 2

22. If an island's only residents are penguins and bears, and if there are 16 heads and 34 feet on the island, how many penguins and how many bears are on the island?

1) understand the problem. This is identical to the chickens and cows problem.

2) create a plan. Form a table that shows the pattern.

3) carry out the plan.

No. penguins	No. bears	No. Heads	No. feet
0	16	16	64
1	15	16	62
2	14	16	60
3	13	16	58
4	12	16	56

At this point it is clear that I can continue to extend the table and arrive at the answer. However in general this could turn out to be tedious is I had a few thousand residents. What is the formula that would give me the answer?

p + b = 16 (in this case)

2p + 4b = 34 (in this case)

Therefore 2(16 - b) +4b = 34

32 + 2b =34

b = 1

Answer is 1 bear and 15 penguins.

4) Check:

15 penguins have 30 feet and 1 bear has 4, giving 34 feet and 16 heads. Good.

 

I had no difficulty with this problem, but was surprised that I didn't "see" the answer immediately without doing the table or the algebra. I should have been able to estimate a value and then notice that I was dealing with an extreme situation.

I have been at this just over and hour. I want to spend at least one more hour on these problems.

That would imply 2 hours per sub-section or 8 hours for the chapter, which might be rounded down to one week on this chapter. That seems reasonable.

7:30 am

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