Week of Inspirational Math
The week of inspirational math was to inspire us (the students) about math. In a way it was trying to make math fun and more interesting, sure the videos were cheesy, but that made it more interesting. It was almost like you wanted to watch them just to see how corny the videos were. The point was to try to help us to have an open mind about math, and explain that everyone could be a math student. The investigations showed us that it was alright to make mistakes and that whenever you made a mistake your brain grew. We learned that mistakes aren't bad, and that you should embrace them. We also learned to pursue every option and that there are multiple ways to get the right answer.
Week Overview
On day one we watched a video about brain growth and did an activity where we had a 13x11 rectangle. We had to try to divide it into the smallest amount of squares. On day two we watched two videos, one of them was about embracing mistakes. The second one was about having a growth mindset. A growth mindset, is having an open mind, you are open to your brain growing. We did an activity called squares to stairs. We were given a pattern and a few questions about the pattern. We had to figure out how many squares a given figure would have. On day three we watched a video that talked about how speed wasn't important to math. We then did an activity called hailstone sequences. For that we started with a number, then divided it by two, if it was an odd number we multiplied it by three and added one. This taught us about conjectures, a conjecture is a math term for educated guess. On the fourth and final day we watched a video about looking at math visually. We then did an activity where we had a 3x3x3 cube and dipped it in paint, the goal was to figure out how many 1x1x1 cubes would have 3 sides covered, how many would have 2 sides covered, how many would have 1 side covered, and how many would have 0 sides covered. We illustrated this using sugar cubes, we marked them with sharpies trying to figure out what sides would be covered.
Significant Messages
Each video we watched contained different messages, the two that really stuck out to me was the one about looking at math visually and speed. To this day I still use my fingers to help with simple math, I feel like that one really stuck out to me because I will always count with my fingers. I also feel like the speed video stuck out to me because I always rush through math and make small mistakes. All through elementary school we had timed math tests and were taught to rush.
Problem Extension
We had to take a problem and extend it, I choose to do the hailstone sequence. I extended it by looking at other formulas and trying to find patterns, i came up with three different formulas. Formula one was divide by two if even, multiply by three if odd. The second formula was divide by two if even, multiply by three if odd. The third and final formula was divide by two if even, multiply by three, subtract two if odd. I tested each former with a few numbers, and continues testing until I found a pattern with each formula. With formula one I found that if you got an odd number you were in an endless loop of odd numbers. I realized this because I noticed that it was multiplying odd numbers by an odd number without adding or subtracting anything to make it even. With the second formula it is much easier to get stuck in a loop. It happens because you are both multiplying and dividing an even or odd number. Therefore you would be doubling a number just to split it back in half. A challenge I came across was finding a formula that didn't quick get stuck in a loop. I realized that with the time I had that I wouldn't be able to find a formula that worked as well as the original hailstone sequence. The habit of a mathematician I used was "Look for Patterns" I used this habit to find loops and loopholes in the formulas I created. This saved me quite a lot of time, It helped me realize that the sequence was stuck in a loop much quicker.
Reflection
Overall this week helped me have more of an open mind about math. It showed me that there were many ways to find the correct answer. I learned much about brain growth, if you have a closed mindset your brain won't grow as much as if you have an open mindset. I feel like I put a lot of effort into each day, it made math seem fun. I enjoyed that it wasn't just sitting there doing math problems. We got to use our hands and build things like the cube in day four. I enjoyed activities like the squares to stairs activity, and the 13x11 rectangle. It was great to see everyone get the same answers in different ways, and the paths people took to get to the answer for the 13x11 rectangle problem. I enjoyed how the videos we watched directly applied to the activities we did. I would say that it was a quite enjoyable week, we learned a lot about not just math but group work and problem solving as well.