While we have been concentrating on developing our lesson plans for the Lesson Studies at the high school, we have begun to discuss the challenge of motivating students in the mathematics classroom. In class, the document that we glanced at was https://docs.google.com/document/d/1Ir1vjNiu8FnyoBiDD_jgEMC6S4DKAYnmigXOCQrj6iA/edit?usp=sharing
Where nine strategies for motivating students are discussed. The nine strategies are:
- Call attention to a void in students’ knowledge
- Show a sequential achievement
- Discover a pattern
- Present a challenge
- Entice the class with a “gee-whiz” mathematical result
- Indicate the usefulness of a topic
- Use recreational mathematics
- Tell a pertinent story
- Get students actively involved in justifying mathematical curiosities
In mathematics classrooms, motivating students can be a particularly difficult challenge. Students regularly struggle to see the point of what they are learning in their math classroom. Reading through this article prompted me to think about how I plan to motivate my students in my future classroom. Motivating students can have a ripple effect and subsequently help to work toward equity and access, as well as toward other pedagogical ideals we have previously discussed in this class.
The strategy that intrigues me the most is #8: Tell a pertinent story. In the description, it discusses solely using a story of historical events involving mathematics to motivate students. This strategy can be modified to creating lessons around these stories. For example, in the document is a link to a story about how Eratosthenes calculated the circumference of the earth. This could be modified to give students the information (or modified more so that the lesson would guide them less) that Eratosthenes had, ask them to make the calculations and deductions that Eratosthenes made themselves. This could incorporate the real world mathematics that can be lacking in the high school classroom, while simultaneously utilizing the eighth strategy of telling pertinent stories to motivate students. Going through the process of solving the problem gives students the opportunity to see the world as the historical figure(s) did— through a lens different than their own.
Based off of this document, I began to search for other articles that discuss different ways to motivate students in the mathematics classroom. From this search, I found a few articles from National Council of Teachers of Mathematics. One of the articles I discovered focuses on writing proofs using technology. As a high school student, I remember that writing proofs in geometry was one of the most tedious, and at the time, irrelevant tasks that I had encountered. I found this article interesting and relevant to the cause of motivating students in general because proof-writing gives rigor to mathematics. However, it is difficult for high school students to comprehend its usefulness— resulting in an unmotivated throng of students. This article works to make proofs more interesting for students by tying in technology. The link to the article: https://drive.google.com/file/d/1lHNLkkZ_Pav7Px5Rjsco2KZfSc9F-wgS/view?usp=sharing
Another article that I found examines motivating students through problem solving. The article focuses on creating opportunities for higher-order thinking to motivate students. This coincides with number four on the original list of ways to motivate students: Present a challenge. Many students have only experienced the traditional classroom where opportunities for higher-order thinking are few and far between. Higher-order thinking is challenging for students, and if a lesson is executed well, it can lead to motivating students. The link to the article: https://drive.google.com/file/d/13Ymn8oTFTY2cGIP-CPABbAw3xn9htvr3/view?usp=sharing
In our 7-12 Math Methods class, we’re talking about problem solving, so I decided to read an article about using problem solving techniques to teach. The article was “Teaching Through Problem Solving” by Cos D. Fi and Katherine M. Wagner. The article gives five steps for using a problem to teach. The first step is to give the entire problem to them. This means that the problem shouldn’t be broken up to make it easier for the students. This encourages productive struggle for the students, meaning they have to persist and figure it out on their own, which will help them in the long run. The next step is to let students discuss the problems and make predictions about the problem. Students should share their work and listen to other people share their work to build understanding. The third step in this is to “focus on the big idea of the mathematics.” This means that students should make connections to other ideas and explain how to use prior knowledge to solve it. They could also make predictions about where the mathematics is going. The fourth step is to show student work. This should include mistakes and successes. Showing where students made mistakes can increase understanding. It can also make students more open to sharing their ideas and get them feeling more comfortable around their peers. One method I’ve seen is after a test, a teacher will take pictures of problems on people’s tests and project them and talk about where mistakes were made. Step five is giving students time to reflect on what they learned. There could be assignments with this where either students do a journal article or something similar to discuss what they learned or they can do additional problems that show understanding.
I think that one general theme with every step was that students had to struggle a bit and share what they were thinking and doing while they were completing the problem. This makes the problems a teacher does much more valuable and understandable for the students. In our class, we would call these problems higher-level demand tasks, because they force students to dig deeper into the mathematics and learn why they’re learning the information and explain their reasoning. I can use these methods for teaching in my classroom by keeping these steps in mind every day. I doubt that I’ll use problems to teach every concept, but I will probably teach through problems for some concepts, and these advised steps can help me teach more effectively.
Teaching Through Problem Solving
The past two weeks in Math Methods we have been talking about problem solving. I really enjoy problem solving now as an Education major, but that has not always been the case. In middle school/high school I did not have teachers that assigned any problem solving problems until I was in pre-calc and calculus. Then when they did assign them we had no skills as to how to solve problem solving problems.
It always seemed like half of the battle! We had no idea how to start the problems, work our way through, or end the problems. Since we were never expected to do it earlier, we never learned methods of how to solve them. I do not want to subject students to the same feelings, because it is discouraging and frustrating. Whatever we were supposed to learn solving those problem was lost on me.
I wanted to find methods to teach students about problem solving. I found the article Problem-Solving on the website TeacherVision. (link: https://www.teachervision.com/problem-solving/problem-solving )
The article broke down problem solving into three basic steps:
- Seeking information
- Generating new knowledge
- Making Decisions
Which makes sense now knowing how to problem solve better. The article then goes onto explain what I really wanted to know: five-stage model method of problem solving.
- Understand the problem– Students need to understand the nature of the problem, and potentially reword the problem to make it better make sense.
- Describe any barriers– Identify what is creating the problem.
- Identify various solutions– Some recommendations they gave are create visual images, guesstimate, create a table, use manipulatives, work backward, look for a pattern, and create a systematic list.
- Try out a solution– Then students need to try a strategy and gave the ides of keep accurate and up-to-date records of their thoughts, proceedings, and procedures, try to work through a selected strategy or combination of strategies until it becomes evident that it’s not working, it needs to be modified, or it is yielding inappropriate data, monitor with great care the steps undertaken as part of a solution, and feel comfortable putting a problem aside for a period of time and tackling it at a later time.
- Evaluate the results– Students need to assess there strategies and answers to see what they learned.
I want to take these steps and integrate them into lessons and problem solving. That way my students will be able to get to a point where I can just give them a more intricate problem and they will be able to start solving problems on their own.