We have already completed 5 days of class, and we have covered a lot of topics in this time frame. Here are my thoughts regarding some of those topics:

First regarding integers, operations on them, and how to use them for instruction:

Integers form the backbone of all future mathematics that our students will be dealing with as they progress beyond late elementary/early middle school, so how we teach integers is vital to give students any chance at all of succeeding in mathematics. That being said, it is (to me) best to utilize an instructional method that uses definitions of integers and operations on them in a context that allows for a good discussion of integers and the defined operations on them. What I mean is that focus instruction on addition, multiplication, and exponentiation [if exponentiation is a middle school topic?] of integers in a relocatable context that survives the odd rules regarding positive and negative integers. Personally, I enjoy a context that I found while reading on this same topic, and that context is using video games to explain positive and negative integers, as well as addition of these integers. As for multiplication and exponentiation, I think using money {interest?} or some context that they can easily understand [perhaps rates and labels discussion could be useful like: velocity, etc.]. From there, simply go “by the book” and explain the rules regarding each operation; personally, I think showing students a pattern as to why negative times positive is negative, and then build on that idea to explain why negative times negative is positive [use idea of negatives simply cancelling out]. That being said, to us, negative times negative equals a positive is a fact, but to them, it might be a WTF moment, and this might be an instance that we need to tell them that this is just the way it is. If there is a “good” explanation as to why this is and it can be translated to a middle schooler’s level, then please let me know and then patent it and become rich in the “mathematical education sense”.

Additionally, we briefly mentioned assessments relating to these topics and the idea of number families. Number families seem like an excellent way to promote rote memorization of some basic operational results of integers that students can then apply to harder operations regarding more complex integers. As for assessments, we must all be reminded that our assessments should not just be a “plug and chug” type set up; instead, assessments must go deeper to really measure how well each student grasps both the concept [definitions, etc.] as well as the applications of the relevant math in various situations/contexts. Personally, I believe using story problems that are funny and realistic [to the students] goes a long way in achieving both of these goals.

Finally, I would just like to briefly mention that everyone of the games/activities we have done in class all have one fatal flaw, and that is time. Time works against the teacher because we only have approximately 60 minutes or something like that per single class to get a set amount of complex information to the students, and while we might have an entire week/month/tri/se/mester/year to get lots of information to the students, time still ever works against us. That being said, I really thought the expert/beginner discussion/game/thing we did in Class 4 on 1/21/15 is a brilliant idea that allows the students to converse with each other about ideas going on in the lesson/unit; while, simultaneously, allowing us to informally assess individual student’s opinions/knowledge regarding a specific topic.

Alright, that should conclude this post. I hope that something is of use to someone if you took the valuable few minutes of your time to read this.

Thanks

Interesting to me! This seems like a useful post, trying to sort through your position on what we’re talking about. The time thing is a big question. The longer I teach, the more I’m interested in those big moments that stand a chance of sticking with students. Those can be the anchor lessons.

clear – could be structured a bit more to showcase your ideas. Directions or a few details on the game in the last paragraph would help for people not in class.

consolidated – needs a bit of summary. What do you see as the theme running through, or why is this important?, or what is next, given this?

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content, complete, coherent +

🙂

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I agree that whenever we teach students a certain concept, like integers, there needs to be a context associated with it. Or else, it’s just a bunch of rules in a vacuum. And remembering rules has little to do with understanding, just memorization. Also, I agree that time is a huge consideration on how teachers design their lesson plans. We will just have to be more selective picking the exploration activities we do in class, and perhaps give some explore activities as homework so students could explore using their own time.

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I’m with you on the time consumption of the games Matt. Time is the mortal enemy of teaching. Consider as well that we are all ‘well behaved’ college students who are interested in the games. Fitting these can become increasingly problematic with more unstable audiences. However, for some kids, this provides another avenue to connect with mathematics and may reach them in a away that traditional lecture/notes cannot.

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