EDCP 342A - Finding # Squares in Chessboard

Solution

Finding the number of squares in a 8x8 square chessboard is an interesting example of one's attitude towards Math or solving problems in general. The thought process isn't difficult, nor does it require hard core Math skills. The puzzle is about digging deeper and not giving up. It's easy to conclude there are 64 squares in total without thinking much and going beyond the superficial level. In other words, success in life is generally achieved by getting out of one's comfort zone and embracing the challenge. 

Another important aspect of solving puzzles like this is thinking mathematically and looking for patterns. Students that like solving problems, and are used to thinking mathematically would take it as a challenge and use all their tools to solve it. However, students that don't like solving problems would need to get comfortable with mathematical thinking, and we, as educators, can help them achieve the comfort!

EDCP 342A - Integrating Instrumental and Relational Understanding

While both instrumental and relational learning individually contribute their share towards understanding Mathematics, the union of both can produce fascinating results. For instance, relational understanding can limit our intellectual horizons while understanding the topic of limits in Mathematics. On the other hand, the topic can be thoroughly understood if approached instrumentally. 

Similarly, relational understanding is not to be underestimated, as it provides  a platform to make Math relevant. As educators, we need to instill in our future Mathematicians the importance of thinking mathematically. It is relational thinking that allows us to apply Math in other contexts.  For example,  thinking logically is as important for lawyers as for Mathematicians. Likewise, the revolutionary invention of MRI (Magnetic Resonance Imaging) that highly relies on differentiation in Bloch Equation is only possible when the students are taught both instrumentally and relationally.

EDCP 342A - Instrumental Understanding vs. Rational Understanding

I'm not surprised to hear about the popularity of instrumental approach in teaching Mathematics. It reminds me of my non-Math friends that would often advise me to 'just practice' to ace exams during my undergrad. There is clearly more to Mathematics than the famous quote 'practice makes a man perfect'. 

Richard's proposition of teachers teaching different subjects under the umbrella of Mathematics is really interesting. I've always believed some teachers teach Math better than others. Furthermore, I absolutely agree with Richard in that knowing why a method works is as crucial as knowing the method itself. It reminds me of one of my colleagues that hates Mathematics but loves Physics. Although Physics and Mathematics are closely related, he strongly differentiates the two. In his mind, Physics makes sense, while Math does not!

If future Math teachers truly and deeply take the challenge of adding rational understanding along with instrumental understanding, we'll produce a generation of Math Lovers.

Welcome

Hello EDCP 342A!