Thank you again for your patience! We have been very busy in our math classroom!
Our students have shown incredible communication in mathematics through our Number Talks.
During Number Talks, students are provided with a carefully constructed problem which allows them to share their strategies. We discuss which strategies are most efficient, why they work, and which ones work for all problems of a similar type. This allows our students to truly understand the WHY behind their math processes.
WHY is the WHY so important in Mathematics?
I always think of this example when I am asked why I care so much about students developing a deep understanding for what they're doing.
Consider the following problem:
1/2 + 3/4 =
Students are often told that to solve problems involving fractions with different denominators they need to do whatever they did to the bottom, to the top!
Is it really as simple as that? Could I really just do that? Let's say a student applies this method and decides to create common denominators by subtracting 2 from the top and bottom of 3/4. This brings us to 1/2.
Our new problem would be: 1/2 + 1/2 =
That's easy! 1/2 + 1/2 = 1 whole!
WAIT A MINUTE!
What if our students understood what 1/2 + 3/4 looked like? Ask your son or daughter how they would solve this problem. Most likely, they would connect this problem to what they already know - using money or a clock.
1/2 could be thought of as 2 QUARTERS (50 cents)
3/4 could be thought of as 3 QUARTERS (75 cents)
Well, we can borrow 1 QUARTER from 1/2 and bring it over to 3/4 to create ONE WHOLE. We are then left with one extra quarter.
THEREFORE, 1/2 + 3/4 = 1 1/4
We KNOW what this looks like, we can CHECK to make sure this is a reasonable answer, and we do not have to MEMORIZE, we can create solutions without being limited to only knowing how to solve specific problems. This helps our students generalize their skills to solving problems in the REAL WORLD!
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| You can see how some of our beginning thoughts allowed for errors in our methodology. Learning the money and clock strategies help us check that our answers are reasonable and ensure we can explain HOW we got our answers. |
Please stay tuned for my next post about the SUB PROBLEM!
