|The spotlight in Q3 goes to Kristina Alekseyeva and her middle school math classes in Holmes County. In the Fall semester she completed a virtual course through Stanford University and designed by Jo Boaler. She then incorporated what she learned and is now sharing her results. The strategies she has implemented align well with our mathematics vision, especially in regards to computational fluency, solving complex problems, and making and critiquing mathematical arguments. I strongly encourage you to consider how these practices can strengthen your own classroom, and to reach out to Kristina if you have additional questions!
Read Kristina’s reflections below!
My name is Kristina Alekseyeva and I teach 6-8 grade math in Holmes County, MS. These nine weeks I was lucky enough to participate in an amazing online class dedicated to increasing student confidence and engagement in a math class. In this blog I would like to take this opportunity to share some of the course insights with you.
I would like to start off by saying that the information in this class was actually helpful to improving my class performance and attitude – something that differentiates this class from so many others that only seem applicable in places where students are mostly on pace. Some of the most dramatic results for my students were getting more confident in math and becoming open about sharing their mistakes. Another result was getting students to actually ask “Why?” in the classroom.
There were several themes in the course that I believe helped me achieve these results. In the next paragraphs, I would like to tell you about the ones I found most helpful. One of the main ideas that I have learned through this class is that simply saying that “I love mistakes” to my students won’t necessarily get the message across. What I need to do is to implement correcting mistakes and celebrating mistakes into my daily routine. For example, giving points back for correcting quizzes and making homework that asks students to look at questions on which they have made a mistake and resolve it. Similarly, I learned that the way we message mistakes to students matters a whole lot. For example, saying something like “Girls are usually bad at math, don’t worry” will not help the child’s progress. So, now I am prepared to always make sure that the conversation we are having is something along these lines: you have had different opportunities than your classmates to learn this in the past, so today, I want to make sure that you get your opportunity.
Next, I learned that students truly need to practice decomposing numbers and working with numbers in different ways to be able to gain number sense and better understanding of math across topics. Numbers are malleable. For example, if you are adding 8 and 7, you can think of 7 as 2 and 5. This is helpful, because you know you need 2 more to get to 10 and then you can just add 5 to 10 to get your answer. I have mostly just assumed that all students view numbers like that because I have always thought about numbers in that way without direct instruction to do so. And I thought that if I just show them how to do this one time, they will be able to recreate the strategy. Now I think I will be doing math talks on a regular basis. Idea number two is the idea of relational equity that you talked about at the end of the session. I think this is a very easily overlooked point by instructors but I think that overlooking it is dangerous for student development. In my classroom I too often notice students deferring to another student they think is smart because they do not value their own contributions. I think that math talks have the potential to change that and give them energy to carry throughout the class.
Lastly, I have learned that students most often do not understand that persistence and effort is what makes a good mathematician, not quick recall of a procedure that they need to use to solve a problem. I forget that the process of questioning, estimation and revision that comes so easily to me probably does not even occur to most (if not all) of my students. I will try to be more systematic in my classroom about getting students to really think about what their answer means and why it does or does not make sense. In order to do that, I will cut down the number of problems that we do in our class each period and focus on discussing the problems and the concepts that underlie the problems
As I have stated above, implementing these ideas has tangibly improved my students’ performance. Besides the broad changes in attitude that my students have towards math, they also have had specific improvements in several areas. First, my students are now much better at mental math because of the number talks. Secondly, my students are more focused on explanations and less on whether they are getting the right answer. Lastly, my advanced students have gotten very good at looking at problems in different ways and being able to come up with various methods of solving the same problem. Below, I have attached some samples of the student work, which showcase their focus on explanations and creative solutions!
The first example shows my students getting invested into better explanations:
Next, we see students trying to conceptualize and actually understand the problem by drawing pictorial representations. This strategy really helps them understand how to write equations for more complex problems.
In the last example, you can see students making the problems their own. In the sample, a student wrote her own problem to model the equation – which helps invest her in the task and also shows good conceptual understanding of percent.
|For more from Jo Boaler, Professor of Mathematics Education, Stanford University…
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