Learning Logs

A learning log is a written account of what we have done in class. As we will spend a lot of time working on problems on the whiteboard, your learning log will be the place where you summarize the ideas discussed in your groups and within the class as a whole.

Ideas should be written in your own words. There is a course book that has been prepared for you with detailed examples and information, but the intention of the learning log is not to copy what has been written in that book.

If you can put an idea from class into your own words, then you have really understood the material. If you can’t, you should be asking some questions so that you get help to understand the material before moving on to new ideas. A learning log is a chance for you to think about what you have learned in class and what questions you still have.

Why a learning log?

Developing your mathematical voice is a part of what is expected in a mathematics class. You are expected to communicate your mathematical thinking in many ways, and to use mathematical vocabulary and language to contribute to mathematical discussions.

Scientists "talk" to themselves as they work through problems as a way of clarifying their thinking. Your learning log is a way to create a conversation with yourself about the mathematics that is taking place in the class.

Most learning logs are written accounts of the concepts we are addressing each day. However, there are other ways to keep track of your thinking, and I am open to the possibility of a audio learning log in which you discuss the ideas rather than writing.

What Can be included in a Learning Log?

an explanation of all of the ideas in the unit (i.e. what is a polynomial function, what is a logarithm, how do you transform a trigonometric function) using English words
examples with completed solutions, and an explanation of why the example was included
practice questions, and a statement about what you've learned from the practice
explanations of why we do the things we do: ie, why is polynomial division useful?
diagrams and pictures that help make sense of the ideas
explanations of strategies that can be used to check your work
questions you have, and the answers you found (by asking the teacher, by researching in books or on the internet, by discussing with fellow students)
appropriate mathematical vocabulary, with explanations and definitions
an indication of connections that are found between different ideas of the course, and previous math courses
interesting things you have learned along the way
extra pieces of information that add to your understanding or experience in math class
observations from class, or snippets of any "ah-ha" moments you have experienced
explanations of how you can use technology to check your work; evidence that you have checked your examples
acknowledge the support you are getting: if a classmate says something you found really interesting, or helped you make sense of things, include this in your learning log
stop every once in a while to reflect on how things are going: what have you learned this week? what do you understand better now than a week ago? Give examples
use examples to make connections between ideas: leave room after you finish an example in case you can come back to it later and add more details
create a summary of common mistakes and what to look out for to avoid these mistakes
include "non-examples"
provide an overview of the sections at the end of each unit

Professional mathematicians spend most of their time writing: communicating with colleagues, applying for grants, publishing papers, writing memos and syllabi . . . It is ironic, but true that most mathematicians spend more time writing than they spend doing math.

But most of all, one of the biggest reasons for writing in a math class is that writing helps you to learn mathematics better. By explaining a difficult concept to other people, you end up explaining it to yourself.

Dr. Annalisa Crannel, Mathematics department chair @ Franklin and Marshall University

from Five Principles of the Modern Mathematics Classroom by Gerald Aungst, pp 63-4

Looking for some inspiration for your learning log?

Try the Feynman Technique:

Choose a Concept
Teach it to a Toddler
Identify Gaps and Go Back to The Source Material
Review and Simplify

The Feynman Technique: The Best Way to Learn AnythingThe Feynman Technique is a mental model that helps you learn faster and increases retention. Read this article to supercharge your learning.

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