Klingenstein Part 3: How Students Learn

One idea about how people learn that has resonated with me throughout the institute is the idea of metacognition and how it can help bridge the gap between the “taught” and “learned” curriculum. The testing effect stuck with me particularly. As a student, I found that I learned best by testing myself. Kelly Nich-Flynn’s sessions about how we learn reinforced this discovery. In those sessions we talked a lot about the testing effect and research that shows how effective it can be for helping students.

The image shows the result of the testing effect. (S=study and T= test). When students were tested in addition to studying, their results were not quite as good after 5 minutes but the retained the information much better after a week.

I help my students practice the testing effect by using frequent formative assessments. The students study a topic and when they “feel ready” the take a quiz to see where they are with that material. However, after our session with Kelly, I would like to improve this practices. The quizzes that I provide are highly cued and the students know exactly what to expect. I would like to implement more uncued recall; for example, have the students do a “brain dump’ of what they know. I can also improve this practice by giving better feedback on the assessments; feedback that asks them to find their own mistakes and determine their own misunderstandings before trying again. These improvements will help me and the student ensure that they truly are reaching the targeting learning goal.

Attending Kelly's plenary session

I also help my students practice metacognition. At the end of each class, my students think about their comfort level with the material that they explored that day. I do this in the form of math journals and tracking matrices. I would like to improve this practice by helping my students to confirm their feelings about success with the material or misunderstandings of the material. One way that I can provide this feedback is by giving them my own opinion alongside the one they record on their tracking matrix. I also think it would be beneficial for me to collect their math journals and provide written feedback to them more frequently. These improvements will help the student become better at thinking metacognitively so that she can assess her own gaps between “taught” and “learned” curriculum.

Another item that will stick with me about how people learn is the role that misconceptions have in the learning process. The video Kelly showed about college students from prestigious universities that still maintain misconceptions about photosynthesis and gases really struck me. This inspired me to change my teaching practice. We started a list of common math misconceptions during our curriculum group and I have been adding to that list. I want to address all of these by interleaving questions that address these misconceptions within assignments throughout the year in all of my classes. Through this, I hope to make the misconceptions visible to myself and the students, and give my students enough opportunities to grapple with them and construct new mental models. Identifying and addressing misconceptions is one of the most important aspects in bridging the gap between “taught” and “learned” curriculum.

I was encouraged by Kelly’s advice for helping students free up working memory. By freeing up space in working memory students will be able to execute more complex tasks and be more creative. Two of the methods that Kelly suggested were: helping students create mental models and actually encouraging some memorization. Memorization gives students easy access to information. I would not want my students to have to derive the properties of logarithms every time that they needed to take the derivative of an expression involving logs. These facts are even more useful if they are organized as mental models. Models help students organize knowledge and create meaningful structures. They can be abstract or a representation of an object. They facilitate encoding by providing contextual information that aids comprehension and focuses attention on relevant information. For example, if a student could have a mental model for graphing: identify intercepts, end behavior, maxima and minima, asymptotes. These identifiers could be applied to any function in order to create the graph. Kelly emphasized that you can get a complex idea much more deeply if you have a simple explanation for it. This will allow students to not only “learn” the “taught” curriculum but to be able to apply it in new and novel ways later.

Finally, I learned about how large an effect teaching growth mindset can have on our students, especially students that fact stereotype threat. I can make sure that I am praising students for the questions, for their effort and for the incremental progress that they are making. I believe that celebrating small progress is extremely important in helping students feel successful. Since the feeling is success is highly motivating, the practice of celebrating progress will encourage students to keep putting the effort in to learn. Learning is hard work!