Vygotsky and 8th Grade Algebra

[Jalen Causey]

A time I learned while in my ZPD comes from my junior year of high school. I was taking Calculus AB, and the I was in only had nine people in it at the time (six juniors and three seniors). We were learning about derivatives and how to make an equation into its derivative and what we’re supposed to learn from that derivative and all those amazing math things. I remember learning the concept with the teacher, but I also remember the juniors in the class working with each other on classwork and homework assignments together, trying to figure out everything and checking each other’s work. That allowed me to gain confidence in my ability to do derivatives and I was able to do them forwards, backwards (which, for the record, are called integrals), side to side, and even now, years later, it’s still one of the most memorable topics of Calculus for me.

In terms of scaffolding in the classroom I’m observing, this week was great for seeing the application of Vygotsky’s theory. In the beginning of the week, we started with a new topic: we were learning about the simplification of expressions. We went over the general concept and key terms, but there were also model problems/examples for the students to see and understand how the problems were done. Then we moved into a group practice where problems were done by the teacher on the board with asking the students for the next step. Then the next class I visited the students had to practice the concept, but they were allowed to help one another! Being able to talk it out with a classmate or get help from a teacher on a question seemed to help. Then, on Friday, I noticed how the students doing their worksheets needed help less often, would use their calculators less, and talk to their peers less. They knew what they were doing and how to do it and so focused on the task at hand.

Being an MKO for these students has helped them, I like to think. The students have become comfortable with asking me for help and I personally love that I can be there to lend a helping hand. With me there, three adults can help students through their work. However, in terms of the help I give, it’s not much. Because simplifying expressions is a process that takes at max three steps to complete, more often than not I’m just asking students what the next logical move would be. And if they weren’t sure, I would repeat what has already been done and remind them what their objective was (which was to get the expression to its simplest form), and they would ultimately reach the answer without much poking or prodding from me. I would simply ask them questions to guide their thinking.

Some other things I noticed this week include Mrs. Hebz’s response to correct and incorrect answers: when calling on people she reinforced correct answers with something along the lines of “good job!” or “great answer!” – something to let them know that was the correct answer AND that was something to be proud of. And when the incorrect answer, she never dismissed them but instead would redirect the student’s thinking to help arrive at the correct answer. And the redirection would be patient and calm so the student would have time to think about where they went wrong and how they can move forward. And on top of that, she would focus on students that have not previously shared when trying to call on students.

This is also in line with Vygotsky I think, but I also noticed that when first explaining the newer terms that the class is learning, we first learn the more official definition of the terms, and then the teacher will try to explain it in a more culturally relevant way so that students will understand. An example would be – since on Wednesday we moved to combining like terms and the distributive property – the teacher giving a formal definition of what like terms are, and then being like “Another way to think about it is you can only combine friends that have the same variable – only x’s and go with x’s and only y’s can go with y’s.” I think this is Vygotskyan because the social-cultural context that is shared among student and teacher allow for a different way of explaining the content. Because they have a shared background, the teacher is able to use more culturally relevant language to convey more complex concepts to her students.

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