Zain Rehmtulla

 Reflection on course: After re-reading my blog posts and perhaps reconsidering some of my opinions, I’ve come to appreciate just how much math history has influenced mathematics today. In fact, as I was preparing a unit plan, I found videos that connect to today’s math curriculum and the entire video database includes math history. My first takeaway is how mathematics can be traced back to it’s origins and different civilizations to explain it’s use in society. For example, analyzing the weight scale problem helped me realize that mathematics can be used to solve problems when technologies like the weight scales today are not yet created. I’m certain that the idea of powers of 3 and powers of 2 have many applications beyond weight scale measurement. Secondly, looking at the different base systems, whether it is the base 60 system from the babylonians (sexagesimal), the base 20 system (vigesmal) from the mayans, helped me realize the benefit of looking at mathematics or probl...

  The Math History project taught me a lot about the connections to history and how to incorporate it into mathematics today. Before deciding on Shadow reckoning, I perused through various topics. I decided on shadow reckoning because of its clear and straightforward application to students. Given that the lower level maths (Math 9) are taught in every school and are often given to new teachers and the concept involved in shadow reckoning is related to similar triangles, I figured it would be a good topic to discuss. I first read an article that talked about the thinking of Thales a Greek Mathematician who travelled across the world. He wanted to find the height of pyramids and it’s intriguing how he used his height and measured the distance using pacing. I question how he was able to get the distance of his shadow as he would need some assistance to find the distance. I think there’s a great lesson here that math is not some abstract concept and can be applied into daily life ...

I think this concept of drawing in the sand and the idea of the constraint of their bodies is a brilliant way to make use of the land. I definitely believe that this idea needs to be more incorporated into a classroom. Classrooms have so many geometrical objects. For example, for a unit on surface area or volume, the teacher could make use of different constructions of the tables. I remember, when I took an undergraduate educational course on teaching and learning, the professor made two paper constructions and proved that the volume of a cylinder was greater than that of a cone even though the cylinder was much larger in height. She then filled the paper constructions with rice. What I thought was clever was that the proof tied nicely by taking the rice from one container and putting it into the other one which demonstrated it visually. I think this idea of using grains, whether it’s grains of rice, sand, quinoa, etc. is very useful as it’s inexpensive and can be used in various appli...

  The Pythagorean theoroem is a theorem that is an integral part of the BC curriculum today; yet, the history of the theorem is never considered. In fact, the gou-gu theorem was similar to the pythagoream theorem and is written in ancient chinese literature. Moreover, the Zhou Bi Suan Jing contains a method for fiding sides of right-angles triangles. I think there is much value in students’ learning the non-European sources of Mathematics. If we are examining the pythagorean theorem for instance, the Chinese were more concerned with practical measurements and geometric constructions, while the Greeks were concerned with abstract reasoning and formal proofs. Therefore, it would cater to certain learners to perhaps approach the theorem from a geometric viewpoint instead of a more algebraic/numerical one. Consequently, it would also encouarge students to think critically about their solutions and how there is more than one method to solve a problem.   Moreover, I think it...

  Why is Euclid and Euclidean geometry still studied to this day? Why do you think this book has been so important (and incredibly popular) over centuries? Is there beauty in the Euclidean postulates, common notions and principles for proofs? How can we define beauty if these are considered beautiful? I think that Euclid geometry has become popular over centuries due to it's capacity to touch of several key components of mathematics. For example, element 5 states that one and only one line can be drawn through a point parallel to a given line. I believe that many structures that were built in the old times and even today are built aesthetically and parallel structures are not uncommon. Therefore, these basic geometric ideas are essential and this is why the book is so incredibly popular. Moreover, determining the GCF as indicated in book 7 would have been very useful in ancient times as it would be important when trying to divide quantities among people. Many civilizations such as ...

  To solve the problem, I made a table of guests and dishes (attached) that worked my way up to 9 at which point I realized that there were 9 dishes served for 9 people. However, the lcm had not been reached yet so once we hit the lcm of 12 guests, then we will have 13 plates. So multiplying 13 plates by 5 we would get 65 multiplying 12 by 5 we get 60 guests. Interestingly enough, in our assessment course, one of the main reasons for cheating was that this assessments does not matter to me. Therefore, I think it’s important to create problems from students cultures or cultures belonging to their friends. It’s a way to make each student feel recognized. Moreover, it adds meaning to word problems where the anxiety of students may be removed as they can relate the problem to something they’ve heard, seen, or experienced in some way. Therefore, they will be more incentivized to give their best effort and thus it would be a productive class or assessment. Having a problem or puzzl...