Writing about Math and Documenting What You've Learned
Whether you call them math notebooks or math journals, writing about math and documenting math activities are a great way to cement mathematical understanding. And along the way, you're creating a wonderful record of your math studies that can be useful for portfolios or homeschool evaluations.
Grab a three ring binder and some paper. Let's start making math notebooking pages! Here you will find ideas for things to put into math notebooks, math journal prompts, free printable pages, and other math notebooking books and links.
What is Math Notebooking?
What you see in the picture above is math notebooking in action. My daughter is creating equivalent fraction diagrams with fraction manipulatives that we had just used to play a game. Because the manipulatives are made of paper, she can easily affix them to a sheet of paper, add her notes, and store this page in her notebook.
A math notebook is not just a notebook full of boring worksheets and math problems. It's far more than that! It's a notebook filled with a variety of math related ideas and experiences.
The possibilities are many:
- drawings to illustrate math problems or math concepts
- written explanations of mental calculations
- graphic organizers with math concepts
- math vocabulary lists
- math inspired art (such as tangram art)
- an interview of an adult who uses math in his job
- copywork related to the science of math
- newspaper or magazine clippings of math related stories
- photographs of children doing a hands-on project
- the actual hands-on materials or manipulatives (use sheet protectors to hold them or tape/glue them on)
- charts and graphs
- creative writing that features math within the story
- an explanation of how a problem was solved
- biographical sketches of mathematicians from history
Choose whatever kind of notebook you prefer. Some people like spiral bound notebooks, but most notebookers like to use 3-ring binders because of the versatility. With a three ring notebook, you can add in most anything simply by using a sheet protector.
For example, this sleeve protector holds a very long chart we made on fax paper.
Here is my daughter with another long number line that we used for learning hands-on about adding and subtracting integers.
When we're done with the chart, it goes back into the math notebook for storage.
You are limited only by your own imagination. Anything math related can go into your math journal!
Big Book of Math
Why Should You Keep a Math Notebook?
the benefits of a math journal
Marilyn Burns has written a concise article about the value of math journals (PDF). It's a wonderful introduction to the philosophy behind this instructional method.
Basically, writing about math stimulates a different part of the brain than simply working the arithmetic alone. By using multiple parts of the brain during the learning process, the understanding is deepened and retention is increased. In fact, the more ways you can learn math (through art, music, drawing, writing for example) the more pathways you create in the mind. Those pathways then become a network of various avenues for the student to travel along in doing math problem solving. It's like having four ways to get home from the grocery store instead of just one.
Also, writing about math may be a good lure for a reluctant writer who enjoys math. Use the topic he likes -- math -- for his writing assignments. Paragraphs and essays can even come out of math related topics! And for students who don't particularly like math but excel in verbal activities, math journals are a way to shine in math class! Creative students may also enjoy drawing diagrams and sketches to illustrate math ideas.
Amazingly, the process of writing and the process of mathematical problem solving have some similarities. Both require organized thought and logically presentation. So although the skills are different, there are some similar cognitive functions going on.
Besides helping cement a child's learning, you, the teacher can find out if the child really understands the mathematical concept. By reading a math journal, you get an inside view into your child's math understanding and can then address any errors that you find.
Things to encourage in a math journal entry:
- the use of correct math vocabulary
- the use of complete sentences
- the use of specific examples
- detailed explanations of results
Free Math Notebooking Pages
- Fractions Notebooking Pages
Several versions of blank notebooking pages with a fractions theme.
- Homeschool Launch Math Freebies
Homeschool Launch is a file sharing site especially for homeschoolers! Browse around the math section and see what goodies you can find.
- A Mathematical Coloring Book by Marshall Hampton
A coloring book of a wide variety of geometrical images in black and white, suitable for coloring or for notebook pages. At the back of the book is a description of what each image is.
- Pythagoras Notebooking Pages
A set of eleven pages for notebooking about Pythagoras and his discoveries about right triangles. These pages go especially well with the book Pythagoras, What's Your Angle?.
- Mathematicians are People Too, Volume 2
Betsy at Notebooking Nook shares a valuable freebie --PDF files, each with three layouts, for each of the fifteen mathematicians featured in Volume 2 of this great biographical resource.
- Order of Operations Notebooking Pages
Record what you learn about the Order of Operations on these pages.
- Factors and Multiples Notebooking Pages
Free printables in PDF format from The Notebooking Fairy. These factors and multiples pages feature two layouts in two line styles.
- Decimals in Place Value Notebooking Pages
(pictured at right) These pages go from hundred thousands on the left of the decimal to hundredths on the right.
- Pi Notebooking Pages
Another small set of varied pages I created for my daughter.
- Eratosthenes Notebooking Pages
These pages were especially created to go along with our study of the picture book The Librarian Who Measured the Earth.
- Positve and Negative Numbers Notebooking Page
This page features two graphics to demonstrate positive and negative numbers -- a thermometer along the left side and a number line at the bottom.
- Go Figure Book Review and Notebooking Pages
Along with a great living book review, Melissa shares two free math notebooking pages -- The Sieve of Eratosthenes and Pascal's Triangle.
- Plane Geometry Notebooking Page
A single page with the title, "What is Plane Geometry?"
- Solid Geometry Notebooking Page
A companion to the page linked above; this one is titled "What is Solid Geometry?"
Retail Notebooking Pages For Any Subject
I have this set of basic lined pages and highly recommend it for its versatility.
Blog Entries About Math Notebooking
Writing in Math Class
Marilyn Burns is the author of many wonderful math books: I Hate Mathematics Book, The Greedy Triangle, and Grandfather Tang's Story, for example. In Writing in Math Class, she gives lots of practical ideas for incorporating writing into math instruction. Be sure to look inside the book over at Amazon. Some really neat diagrams and illustrations are provided.
Writing Prompts for Math
Need some direction for what to write about? Here are some free online writing prompts that you can use for math.
- Mathwire's Writing Prompts
Mathwire's website is a treasure trove for math teachers! Go explore after you read their writing prompt ideas.
- WASL Math Questions
The questions are leveled by grade and mathematical concept. Click on the links in the left column for great math prompts.
- Catholic Mom's Journey Blog
A fantastic list of 30 math journal prompts written by a homeschool mom.
- Calico Cookie
A great math journal list for younger learners.
- Visual Math Sample Materials
Click on the link for "Philosophy, Questions, Reflections" for a nice 3 page PDF. The first page has statements about math that students could reflect on as writing prompts. The second page has writing or discussion prompts. And the third page has so
- 101 Math Journal Prompts
A doc file filled with more prompts than you will ever need!
Notebooking for the Pre-Writer
What about students who don't yet write proficiently? Can they still make math notebooks?
Yes! They can draw pictures or mom can act as a scribe to write down his words for him. Find out more at Notebooking with Younger Children. See examples at Mrs. Meacham's site.
Graphic Organizers for Math
Research in 1990 by Horton, Lovitt, & Bergerud shows that that use of graphic organizers (GOs) is effective for helping both middle school and secondary students to organize and remember academic concepts. To be effective, though, GOs have to be coherent. Make sure that the information is displayed clearly without any irrelevant details. The parts should be clearly labeled with relationships or sequences indicated by numbers, arrows, lines, etc.
Here are some free printable ones to use. First are some general ones and then some specific to math.
- Education World's Teacher Tools
Scroll down about halfway on this page to the Graphic Organizers section to find Venn Diagrams, Comparison Chart, Concept Maps, KWL Chart, Process Chart, and Spider Map, all of which would be suitable for math notebooking.
- Education Place's Graphic Organizers
More PDF graphic organizers: Clock, Cluster/Word Webs, Describing Wheel, Flow Chart, Four-Column Chart, Idea Rake, Ladder, Planning Chart, Problem-Solution Chart, Sequence Chart, Spider Map, Step-by-Step Chart, Tree Chart, and Venn Diagram.
- Math Graphic Organizers from UMass Medical
A variety of graphic organizers and other teaching resources in different formats all in a zipped file. For all grade levels
- Addition Facts Graphic Organizers
Attractive PDFs to record addition families for all addends from 4 to 12.