Empowerment and The Ideal Problem

Week 7: Effective Mathematics Instruction

The reading/video for week 7 dealt with effective mathematics instruction. The main idea defined low level and high level tasks and what constituted as a high or low level task. One part mentioned how we should start with high level, cognitively complex tasks, which I disagree with. You need to gauge topics based on the students in your class. Levels within the class vary. Yes, all students should be given the opportunity to reason and think. However, the level of the students’ needs to be taken into consideration. You don’t want to start with something that will go over their heads. They will get frustrated and give up. Also, you don’t want to give them something that is too easy, because the students will get bored. Rather, testing the waters and giving them a problem with multiple points of entry might be the best course of action. Most classes will have varying levels of students and it is up to the teacher to determine how far to take the challenges. You want to be able to offer something for every student in the class.

The PowerPoint defined low-level tasks as (rote) memorization and procedures without connections. High-level tasks were defined as procedures with connections and “doing” mathematics. The problem with using high level tasks is that the teacher does not completely follow through with its implementation. Student learning will be at its highest when a high-level task is carried out consistently, which seems to be the greatest challenge. In all, I believe that while we should provide different opportunities for students to learn math, we should also consider the level of the students within the classroom setting. It is not as simple as giving the students a challenging problem and expecting them to reason.

In class, we spoke about empowerment, which seems to be our greatest weapon. Essentially, it is giving the ability, or opportunity, to do something that you couldn’t do before. We also touched upon gaining investment in the problem. Some students, especially young ones, don’t care about learning things that deal with taxes. It does not interest them nor is it prevalent in their lives at that point in time. The best type of problem a teacher can offer is one that is engaging, empowering, and demanding. As a student and teacher, I have to agree with that. Most students lose interest in problems that they cannot connect with. Students in my classes have asked why they need to know certain problems, and sometimes, I can’t provide a concrete answer. To me, they are important because I need to know information about taxes and personal finance. As a twelve-year old, they are more concerned with who is going to the dance next week with Johnny or Susan.

Getting through to students is like going through a medieval city. You have to go over every wall before you can reach the center, and it’s not as easy as knocking and asking for entrance. The first wall is grabbing the attention of the students, peaking their interest. The next wall is presenting the complex problem in a way that they are able to approach it. Further into the city, you have to offer them something in order to pass through the next wall. You must give them something that allows for them to be empowered. You need to offer them something they were not able to do before while demanding that they try to figure it out on their own. You need to be sneaky enough to demand more while making it seem like you are giving them more. Only then can you imagine getting through to every layer of the city.

What do you consider to be the ideal problem?

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