This article was helpful in pointing out 3 main reasons why teaching algorithms is ineffective to true understanding. The first reason they submit is that students believe that doing math IS doing the algorithm, when in reality algorithms are just one route to get to the answer. The second problem with algorithms is that students stop to think about math critically, and just start asking for the "steps" as an assembly line method of solving problems. Lastly, algorithms are ineffective because algorithms have to be followed exactly, but many of real word situations don't work that way. I liked how the article doesn't say that algorithms are bad altogether, but should not be the end in and of itself. That is why I wanted to research and "scoop" many different methods of teaching division for my students that would not stunt their mathematical thinking, but enhance it!
This blog introduces two books that introduce the topic of division. Could definitely be used at the beginning of a lesson to engage sudents, as well as integrate literacy into your math lesson! This could also work well in engaging students who love reading but are slow to like math.
I liked these rhymes on divisibility rules because it could easily be made into a jingle or short song for students to remember the rules. Since there could be an added tune and it's already written to a rhythm, students would be able to remember then in a fun and engaging way. As you can see, there are a lot of rules to keep in mind! I also like how each number's "rule" is written as a couplet (just 2 lines), so if I wanted to teach each rule one-by-one over a long period of time, it would be easy to gradually teach them to my students.
This method of division makes the process of division as "visually obvious" because you can actually see the rectangle while you are solving the problem. Not only are the students able to see how the numbers are getting split up, but they are also able to see the inverse operation of multiplication in play as well which will improve their basic number sense. I also really like how the primary prerequisite math skill is for the student to count up to nine. This method would work especially well with my ESOL or special ed, since some of them are struggling with even their basic addition or subtraction facts. Lastly, the students are able to work with the math hands-on since they are using physical manipulatives.
I liked this method of "chunking" because it allows students to deal with dividing bigger numbers and whittling it down to smaller "chunks" to make it easier to solve. The lady teaching in this video also asks the question "what is the biggest and easiest number in the 3 times table that I can take away from 72?" She decides to use 10 x 3, but any student can use any number that they personally think is the "easiest" number for them. This allows student choice in how to solve their division problem using the chunking method.
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