Math! When you hear that word, do you feel all warm and fuzzy inside? Do you love to teach math? Are you exceptional at creating concrete problems for your children or students that really help them understand math concepts? Well, you can stop reading now!
Ok, now that all those math-teaching-geniuses are gone, let's talk.
Math has been one of the most challenging subjects for me to teach over the past twenty-something years. I know that math should be - can be - fun and engaging, but figuring out how to do that as a teacher has been challenging. I've spent more money on math curriculum and activity books and fancy manipulatives than I've spent on all the other subjects combined! If you're nodding your head (or shaking you head in discouraged agreement), keep reading. I have an idea - an inexpensive idea.
I finally found a math book I enjoy - a blank composition book, with the handwritten title on the cover, "Name's Math Journal". Let me share with you some of the benefits of using math journals.
Before I do that, let's review the 3 foundations children need before age 12 to prepare them for scholarly studies and a life time of learning:
- A love for learning
- Self-confidence in their ability to learn (anything and on their own)
- Basic learning strategies
Math journals help build up all 3 of these foundations.
A Love for Learning
Children develop a love for learning when their learning connects to their own lives. When they can learn about what interests them, rather than what will be on the test. When they can use learning to answer their own questions and make personal discoveries, they begin to love learning.
Math journals allow children (and you) the freedom to include math that connects to their own lives. You are free to put whatever math you want to in that journal.
Do they want to save up for a bike or a puppy? Create a math problem for that. Budget. Brainstorm ways to earn money and create a timetable.
Do they want to run a lemonade stand? Write out the expenses and projected profit in their math journal.
Do they want to bake cookies, but they need to double or half a recipe? Figure that out and put the new recipe in their math journal.
Are you buying a new piece of furniture for their room, or any room in your house? Make a sketch of the room in the journal, take measurements and record those on the sketch, and then make a plan for where the new piece of furniture will best fit. If your kids are a bit older or like an extra challenge, make the sketch to scale!
Figure out how many days until Christmas or a birthday by adding up the days from each month.
When you identify the math that naturally arises in their everyday lives by recording it in their math journal, you are showing them how applicable and lovable math can be! Don't limit your math journal to problems from a textbook. Put real life math in there! They can even include notes about anything interesting they learn about mathematicians (you're reading them stories about mathematicians, right?!).
Self-Confidence in their Ability to Learn
Children build up their self-confidence as they are allowed to explore their own interests. Most kids come pre-filled with self-confidence, and sadly that confidence is eroded by criticism or invalidation of their ideas. When any authority figure (parent or teacher) discourages a child from exploring his/her own interests, that child develops an internal dialogue that their ideas are wrong or worthless. This doesn't mean that we must indulge every crazy idea that pops into our kids' heads. But a math journal can be an outlet for them to plan out their ideas, experiment, and record results. They don't need to succeed at every idea to build confidence. Simply being encouraged to express and work out their ideas will build their confidence, because they will come to believe that the authority figures in their life value their ideas.
One of my son's favorite activities to do in his math journal is to create his own math problems. Sometimes he creates them and solves them himself, and sometimes he creates them for me, and I solve them. He considers himself a math genius, simply because I have never indicated to him that his problems are any less relevant than the ones I put in his math journal. Don't panic if their math problems don't make complete sense, especially if your child is under 10-years-old. They will figure it out with time, and they will look back at their journals fondly and laugh at their own early math reasoning. Correcting them will not ensure correct math reasoning; it will only erode their self-confidence. Don't panic about "forming bad habits", as their own math problems are only a small part of what is going into their math journal. You continue to model correct math procedure, and they will catch on.
Basic Learning Strategies
Math journals are a great place for kids to experiment with and record basic learning strategies. Help your child to make notes, maybe in the margins or below a problem, with tips that will help him/her remember how to do that type of problem. The tips should be what clicks for that child, so make it personal. In doing this, you are teaching them a few different learning strategies. Of course, you are teaching some basic math strategies. But you are also teaching them that everyone learns differently and that they need to use the best ways for them to remember or learn a concept. There is no right or wrong way - just the best way for them and their brain.
Simply teaching the strategy of using a math journal is beneficial to students for later, more scholarly math work. My oldest daughter still uses a math journal for her high school math. She takes her own notes, as she is learning a concept-notes that make the concept clear to her. She records sample problems and observations from her life and the world around her, and she makes connections between those observations and the math she finds in her textbooks.
Many homeschool parents express anxiety over what will happen when their children reach high school math, but my daughter teaches herself math, for the most part. If she gets stuck, we work together to find a solution - search online, search the textbook, or work with a tutor (not me, as she passed me up a year ago in math). Her math journal is the primary tool that enables her to learn math.
Using Math Journals with Textbooks
Yes, you can use math journals with textbooks!
If you are very confident in teaching math, and you understand how each math concept builds on the ones before it (for example, teach skip counting by 5s and then teach clock minutes and counting by 5 minutes for each number passed on a clock), and you are creative enough to come up with math practice problems, then great, you probably don't need any help in the math-planning department. However, if you are interested in some basic math scope and sequence, here are some of my favorite resources.
The National Council of Teachers of Mathematics is a group consisting of experts not only in math, but in teaching math (in how children learn math concepts and build on each concept). They have published a series of guides, Curriculum Focal Points. These are not workbooks or textbooks. There are no math problems in the books for your child. These books outline the order in which math concepts are best learned. They do break up the concepts by grade (mainly due to public demand), but you can ignore the grades and just pay attention to the order. Look at where your child is, based on the concepts he/she already understands and then choose a topic that will build on that from their list.
Once I choose a topic, another resource I love is AIMS. If you look online at www.aimsedu.org, you will find a lot of math activity books. Again, these are not workbooks. They provide ideas for hands-on activities for every math topic you can think of. I choose an activity, we do it together, and then we do some practice problems in the math journal. Other resources are: Math Wise! and Hands-on Math Projects, both published by Jossey-Bass Teacher, as well as many books by Marilyn Burns (just google her or search on amazon.com, and you will find several fun math books).
I also use an unconventional math series, The Life of Fred, with my children. This is a collection of books that cover math concepts from the very beginning, through Algebra, Geometry, and Calculus. They do this through a series of stories about the life of Fred, who is a math genius - teaching college math at the young age of 5-years-old. These books are funny and entertaining, while providing a solid foundation for higher math concepts. You can check them out at www.lifeoffredmath.com.
Using Math Journals with Public or Private School
If you prefer more structure, or if your child is enrolled in full-time public or private school and required to use a specific math book, math journals can still be beneficial. If your teacher will allow it, work out your textbook problems in the math journal. If that won't work, you can still include a few textbook problems in the math journal.
The problem with math textbooks is that students too often get the impression that math only lives inside a textbook. This creates the impression that math is disconnected from the child's real life, or from anything the child finds worthwhile. Remember, we don't want them to be disconnected from math. When you include math problems from their textbook in their personal math journal, alongside their own investigations and their own problems, you create a connection between what is in the textbook and the math in their own lives. Oftentimes, they will perceive a connection between the two as they notice that some equations or rules learned from the textbook can be applied to their life-math. Now, the textbook has become a resource, rather than a task-master. Aside from a coaster, the only good use of a textbook (in my opinion) is as a tool and resource.
Even if your child's school provides a math workbook, you can still buy him/her an inexpensive composition journal, and the two of you can spend just a few minutes each day working in the math journal.
If you are a public or private school teacher, consider a math journal for each of your students. Spend just 5 minutes of each class day having them record their own, personal math in their journal. What did they observe that day that was mathematical (seasons, patterns, shapes, arithmetic, etc.)? What questions do they have that are mathematical? They don't have to answer them - just record questions. What do they like or dislike about math right now? Record feelings too! Help them connect math to their lives.
Learning and teaching math should be an enjoyable activity! Yes, really! If you want to teach your children the joy of math, the first step is for you to find some joy in it yourself, so begin with getting yourself a math journal. Record your own mathematical observations and questions. Make notes. It can be messy! Enjoy yourself! Now, share your journal with your kids!