Unfortunately, I myself do not yet have an answer for this question. I already see this will be an ongoing investigation throughout this semester and beyond.
I began my investigation this morning, as a substitute teacher in a high school special education classroom. I subbed for two classes - pre-algebra foundations (9th and 10th grade) and consumer math (11th and 12th).
In the first class, we worked with exponents. The majority of the students were completely stumped on the last problem, and I had the chance to utilize some of the problem solving strategies we have been working on in this course. I utilized Polya's Problem-Solving Principles to teach students how to tackle the problem.
http://www.learnlogic.net/design/polyas-problem-solving-process/
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Here is problem:
Figure out the relationship between the numbers in the top and bottom rows of the provided chart. Then, write a variable expression to determine the bottom number when the top number is n.
1
|
2
|
3
|
4
|
…
|
n
|
1
|
16
|
81
|
256
|
…
|
?
|
1) Understand the problem: I encouraged students to first read the question thoroughly, as many of them hadn't yet done that. I explained terminology, including what it meant to write a variable expression. I explained what n is. I helped the students understand what we were trying to accomplish.
2) Devise a plan: I made it clear to students which relationship we needed to understand in order to solve the problem. I pointed to numbers in the chart provided to make this very clear. We chose guess and check as a strategy.
The students struggled to understand that n can be any number and that we can use the variable expression with n that we are trying to establish in order to find the bottom value for any top value. We decided to first establish the relationship between top and bottom, as this would essentially give us our variable expression.
3) Carry out the plan: Students looked for the relationship between the top and bottom numbers. We started with 2. Consistent with that particular column, many students suggested that the bottom number was 8 times the top number. I told the students to check the trend in the other columns. They realized quickly that this didn't work with the other top numbers.
I asked students what the worksheet focused on, and they answered exponents. I hinted that the relationship between the two numbers likely had to do with this topic. They tested out different exponents (2^2, 2^3, etc.) before discovering that 2^4 equals 16. They tested 3 and 4 in order to determine if this pattern held true, which it did. The top number to the 4th power gave us the bottom number. Therefore, if the top number is any number n, the bottom must be n^4.
4) Look back: We didn't look into different strategies we could have used, but we took the problem one step further. There was still some confusion over the function of n that had to be addressed. Some students filled in 4 for the question mark rather than n^4. I wanted students to understand that any number can be substituted for n, so I had them plug in 5 and calculate what the bottom value would be. Having them plug in other non-sequential values, as well, could help eliminate some confusion. I am not sure how much these students have talked about variables yet, either, so further discussion on their function would certainly help a lot.
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So back to my initial question - what does it mean to be math literate? Today's experience has led me to incorporate a few elements into my personal understanding of "math literacy:"
-Being able to use reasoning skills on a problem that is initially puzzling. Equipped with Polya's strategies, I was able to help students in the pre-algebra class explore this skill.
-Being able to APPLY skills to your everyday life. The consumer math class worksheet today focused on calculating daily wage using hourly wage and hours worked. This is most definitely a relevant skill, as many of the students in this class are seniors soon to experience the working world. This is way more important than just crunching out values.
I will write more about this subbing experience in a future post. I look forward to share my teaching experiences with my readers!
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