Find the Right Math Method

I read a great article from Almost Unschoolers on using art to teach the concepts of Greater Than and Less Than. She has some very creative ideas for alternate learning methods.

What struck me as I read this is that it is so important that we find a method that reaches each child. For instance, I did learn with the method she wrote about and sadly, it did not work for me. For some reason I could never understand the concept that the open-ended symbol was supposed to eat the larger numbers. I have no idea why the memory trick did not work, but for years I would look at a problem written correctly, memorize it before a test and that is how I got by. The concept of eating numbers was a huge distraction. My brain would panic trying to remember if it ate larger or smaller numbers and then I was lost. I obviously understood that 3 was smaller than 4. However the symbols < or > eluded me unless I focused on memorizing the order, 3<4 or 4>3.

Many years later, I took a graduate course in teaching math to children and the professor discussed ways to reach different learners. This topic came up and several people pointed out that the arrow pointed to the smaller number. I was stunned. That visual concept had never occurred to me. I suspect my teachers had never noticed or they might have mentioned it. I have not had trouble remembering since then. When I taught this lesson to my students, we discussed ways to remember the symbols. Some went with the eating the larger number memory cue. Others chose the arrow pointing at the smaller number. They discussed different stories that helped them remember.

My point in mentioning this is that it is so important to help your child find his/her path to understanding math. In this case, it does not really matter if how they remember the symbols merely that they can use them correctly and identify when others have presented them correctly. It is important if one memory cue does not work to find one that does work. Do not make them wait until graduate school.

Use Real Math

There have been a number of math programs marketed with the concept of “real world math” as the core selling point. Few were ever really that close to the real world most of us recognize. As families continue to struggle with the economy there has never been a better time to teach real life math skills. This is never about frightening or burdening children with adult problems but teaching them to understand how math works in the real world.

As children get old enough to spend money they are old enough to start learning how money works. The older they get the more they can understand about money and budgets. While it is important not to scare or burden children with the worries of adult employment issues, failing cars, or shaky jobs, it is important in good times and bad for children to understand finite resources and the cause and effects that come with spending and saving.

When you are creating a master budget do consider how to have your children work with you on handling issues that impact their lives. I’m not advocating allowances or arguing against them. I’m discussing the money you spend on clothes and other items. As your kids get older work with them to understand how budget choices do have long term effects. For instance the impulse buy for the “must have jeans” can mean no other clothes for a period of time. While you may not actually make the purchase try journaling it and the purchase you actually make and see if the child still agrees in a month that the jeans were a better buy than the purchase you decided on. Kids do need to be taught not just impulse control but the consequences of having no impulse control.

Work on savings with children. Habits are hard to teach but once established are much easier to keep going in adult lives. Children who have never developed the habit of going to the bank and watching their savings grow often do not have that skill established going into adult life. Make the habit a life one which balances savings and expenses. If children are taught that all money has a balance between expenses that must be paid, charitable giving that is a responsiblity, optional spending, and savings, they have something to build on for the future. Most children do not have many expenses but saving for something they wish to purchase can be considered an expense that is separate from the other savings that are putting away. This can prepare them for the day they have real expenses that have to be paid before spending.

Emphasize the math used at home. All too often I hear even adult friends who are trained, skilled people who own their own businesses tell me they were never very good in school and they can’t do …. Well in fact to be successful in the businesses I know they are in they are very good at the subjects they claim not to have been good at school in, but they were never taught in the manner that made sense naturally to them. Math is found in the home everywhere. Make sure your kids are aware of the math they are doing every day even though it isn’t in a math book. Cook with them, work on craft projects, teach them to use tools, and your kids will absorb an amazing amount of math. Now just make sure they know what they have learned.

While doing more writing research I came across this free education site I thought people might find interesting. I will put it in the math resources as well.

Math in Daily Life

Picture Credit woodleywonderworks flickr.com

Back to School Math Warm Ups

Athletes know that it is hard to start running hard from a “cold start.” One should stretch and warm up before beginning any athletic exercise. Getting kids ready for school is really no different. Sending them back into school with a cold start can be very hard on many students. Give them a positive start to the school year with some warm ups.

Find age appropriate natural ways to reintroduce or continue to practice summer math activities. There are many household activities that require math. Shopping, cooking, cleaning, and house repairs are the most obvious. Many children’s games quickly fall into math practice. Children can be helped to remember math facts, measurement, fractions, geometry, and yes even algebra with some creative approaches.

Consider using math websites or other games to give children a chance to review or preview next year’s coming math attractions. This isn’t about drill and kill but more of that athletic stretch and preparation. The mind is reacquainting itself with old material and previewing new material that is coming. This is a chance for parents to find sites that will be useful in the coming year should your child need additional practice or challenges to stay motivated in learning.

This need not be a long procedure but a short time spent can produce dividends.

The following links are to areas on this blog that have math links sorted that you can use with your child to review, preview, or teach new math lessons.
Math Links

Multi Age Sites

Early Childhood Sites


Photo credit: whgrad flickr.com

File Folder Games and Activities

Parents and educators are looking for easy inexpensive ways to promote alternate learning styles. Independent learning is another value and frankly required element of learning. Neither parent nor teacher can be with a child at all times assisting and monitoring. Activities that provide solid educational learning and independent structure are valuable for child and teacher. Computers do provide many with these activities but there still are some old but good strategies out there that work.
As I was researching links for the blog the other day, I came across links for file folder games and activities which I added to the blog under Early Childhood and Math sites. I thought this would be an ideal candidate for article for a content site I write for as well as a chance to encourage people to try the strategy. It really isn’t complicated to do. File folders are cheap methods to make game boards and independent learning activities. You can create your own resources or use the pre-made options advertised here.

Want to find the file folder links on this site?

Early Childhood File Folder Links

Math File Folders

Fall File Folder Links

Halloween File Folder Links

Thanksgiving File Folder Games

Christmas, Hanukkah,and Winter Games

Money and Learning

Coins are a great manipulative to teach children a variety of math skills. Many kids have a natural love of playing with coins and valuable skills can be acquired playing with them. Practical chores can be accomplished and life skills learned.

Sorting coins
Many families have jugs or coin holders that hold their loose change. Even young children with supervision can be taught to sort coins that are similar. Pennies can be placed in a container with pennies, nickels, with nickels and so forth. Children can start to learn the name of the coins and you can play games trying to match coins in a pile. For instance in a pile of coins have them find pennies, quarters, or dimes.

Counting
Pennies make good counters for children. Family members often have quite a few they are willing to donate to the educational cause. Children can have practice sorting them into piles, setting up stacks up ten to practice place value, and using them to work through a variety of problems.

Skip Counting
Coins are a wonderful way to teach skip counting. Most people start skip counting with 2’s and 3’s and 5’s, and 10’s. Pennies, nickels, and dimes are a great way to demonstrate what they are counting. Pennies give the actual numbers and then nickels and dimes start to represent the skipped numbers.

Practical Applications
Teach your children how to roll coins. Many people have started to use the automatic coin machines to redeem their change. Some of these are free and some have fees. However, a great teaching moment is missed when you allow the machine to do the counting. While it is time consuming, if you commit regular time to rolling your change with your kids you will see benefits. Math skills improve and there is a personal understanding between work and savings. They can see how savings builds.

Educational References to Have At Home

While more references are available on-line and with software, students still do benefit by having their own hard copies of certain items available for study. Whether you are a home schooling parent who will be responsible for choosing your curriculum or a parent who is preparing for the back to school homework schedule, having these items on hand can make life simpler. You will see ads for products on this site but I encourage you to be frugal. I work from home so the ads provide revenue. However, I will suggest alternatives as I am in this article. You are not the first or last group of parents seeking these items which means the second hand market flourishes. You can find many of these items at library books sales, Church sales, used book stores, and yard sales. Also check any of your other favorite second hand shopping places. I have had great luck shopping for the notebook references in odd venues like Christmas Tree Shops and Office Supply Stores. So by all means I will be happy to have you check out the ads but this article is about finding reference sources to have on hand.

A simple one that arises early on is a dictionary. I could never get a school system to provide me with a complete set, but was able to upgrade through used book sales in the fall to complete the sets when I moved. Do to the use a dictionary gets, buying a hard covered children’s dictionary is a good investment. I have experimented with the paper versions and they do not last. There are on-line options, but children can lose quite a bit of time searching. My experience has been that the resources also are not as extensive as one would wish. I know I just recently bought a thesaurus after finding the on-line version limited and time consuming for my own writing.

I could not find the copy of the student thesaurus I used to purchase, on-line. The reviews on the others were questionable so I did not post one. I would suggest reviewing a few before purchasing. There is an American Heritage Student version that I flipped through that is due out this summer that looks more detailed than many of the other current versions available for purchase. One possibility is to get a simple version to teach the child the basics and then buy a more complicated one as the child understands the process. Home schooling parents obviously expect to teach their children these skills. I would suggest that all parents review dictionary and thesaurus skills with their children when they start using them. Valuable time is wasted when children do not understand how both these resources work. While it can seem a burden on limited homework time, making sure the child understands the basics can increase homework productivity for years to come.

These notebook resources are available from a few different publishers. The value is that they present the terms for the subject in clear, easy to understand terms. They define the vocabulary, use diagrams, and demonstrations to key concepts in the subject areas. I used to use the math and the science ones in my classroom and still buy both for family. Even if your school uses different math and science programs with different vocabulary, it gives you a starting point to work from when your child comes home and does not understand. Also, it sometimes presents a new way for your child to see something that is not in the textbook which can be the “light bulb” moment that kids need. I have given these to family members who home school as well. The general reference material is handy to have.

Another item you will want to consider adding to your home reference section is a writer’s guide. I like Write Source products. However, if your school has a preferred product and guideline for writing I suggest you buy it. Students are doing more structured writing at younger ages. Being able to check the guidelines and formats and see examples can be helpful to you and the child. Again for home school parents it is a great resource for both the format of writing and the grammar that supports that skill. Choose one that fits your home school format.

One last note for public school parents, during curriculum night do check to see what topics will be covered in science, math, and social studies during the year. Knowing your child, this may be a time to consider any additional resources you might want to add to your home resource library. You may want to research free resources you can access on-line or through your local library. Do check the curriculum resource links on this blog for help. For instance if this is the year your child needs to learn the states and capitals of the United States and your child struggles with memory, this would be a good time to start thinking about what you could do to help. While it is the job of the teacher to teach and you do not want to step on toes, anticipating problems and having resources you can access is not a bad option.

This also is a chance to integrate local areas of interest that support the curriculum. Many schools are cutting back on field trips do to expenses. However, libraries still are offering free passes to science and history museums that can help kinesthetic, visual, and auditory learners to process and integrate information in unique ways not available in the classroom. You can provide alternative learning strategies that support the curriculum your child needs to learn without busting the household budget

Visit Place Value With Software

In a previous post I discussed using manipulatives to help students construct a physical understanding of place value. Today I came across a free site on a publisher's website that demonstrates the concept better to parents who may want to try this. You can use the website or still use this concept with physical manipulatives but this gives you a visual representation of what I was discussing in the previous article.

I want to give full credit to the website and publisher Harcourt Publishing. I encourage you to check out their free resources.

Harcourt E Lab Understanding 1,000

The first picture shows the place value chart blank. When making my own I do draw lines.

I start with having the children build to ten to work in the ones column. Using this software you may want to choose problems that help you to reach ten first. (Just a note about the pictures, if you want to get a better look, click on the picture.) Those of you using blocks following this column process works just as well with physical manipulatives as it does on the computer.

Now you move to explaining what happens when you reach ten and all the blocks can no longer remain in the one's column. I suggest not having a problem that stops at ten. It is easier to start by leaving some amount in the one's column.

This program demonstrates that there are too many blocks in the ones column and asks the child to select regrouping. There is a benefit to using actual blocks in the beginning for many children to make the connection. However, this is the best method I have until I dig out my manipulatives and start taking digital photos to demonstrate the process.

The group of ten is now moved into the ten’s column and the one remains in the one’s column. I actually prefer the method of moving ten ones into the ten’s column, not substituting a different symbol for the ten’s and hundred’s as it decreases the connection for the kids. However, this is not my program. When using manipulatives, you can take your stack of ten connected cubes or Lego’s and just move the whole group into the ten’s column. There is no need for a new ten’s symbol.

This now moves us into the hundred’s column. This level was sometimes challenging with this software. I was having trouble getting the software to leave no values in the ten's column after regrouping if there were 0 tens. It worked sometimes and it failed sometimes. This was one area where having more control over your environment is useful. I chose a problem to demonstrate where I avoided the problem.

I did need to regroup more than once while experimenting with problems. If doing this myself, I am not sure I would use different symbols for different place value groups. It is one of the reasons I do not tend to use the traditional place value blocks that come with many math kits. They often do not accomplish what they are marketed to do. That was just the way I was trained and my experience from working with students. Do what works best for your child.

This software is free and available for your use.

Math Tip of the Day: Spend Time With Place Value

Spend Some Time with Place Value

We spend the toddler years endlessly teaching children to memorize numbers, counting them in order. The numbers are repeated over and over, songs are sung, toys are counted and the exercise is celebrated and rewarded. Most children come to school able to count, many to a hundred and beyond.

What we really need to encourage is an understanding of what those numbers actually mean. There needs to be a connection between number and meaning. In our efforts to push children into math, we have lost the understanding of how and why numbers actually work the way they do.

For instance why do we borrow, regroup, or any of a number of words we use in math texts to describe what happens when we are in the one’s column, for instance and the number on the bottom is larger than the number on the top? Why does that process work? I sat with a group of adult learners in a graduate course as the professor had us work through various place value games. There were many “aha” moments as adults who had been proficient in math for most of their lives, saw it in a whole new light, finally grasped the why’s, not just the how’s of what they were doing. It was a powerful moment to see people come to terms with something as basic as subtraction. Instead of memorizing a series of rules, this group of people had constructed valuable meaning that they in turn could pass on to their students about why math works, not just how to make numbers behave.

So, the tip for today is to spend some time with place value when working with students. There is a wonderful game called “Race to One Hundred.” Students use linking cubes, or I have even used Lego’s, and dice to play the game. Each pair, or individual, creates a place value chart, with columns for ones, tens, and hundreds. The dice are rolled and that number of cubes is linked together and placed on to the board in the appropriate column. When the ones column reaches 10, the students take the complete set of 10 cubes and move it into the tens column leaving and remaining cubes in the ones column. When the children have created an additional ten it is added to the tens column, until they are able to move ten, tens into the hundreds column. Some people choose to start with one die to avoid the need to move items out of the one's column immediatly. That is an option.

When students have played this game over a few sessions, try having them race back from one hundred. This is more challenging, but it builds the skills required to handle regrouping faced in subtraction. They will need to move a ten into the ones column when the number required to be removed is more than the number in the ones column. This will also occur when tens are removed from the the hundreds column when the tens column is short.

Eventually, this process can move to paper and support math on paper. Students can set up the math problems on the place value board using the blocks. The math is done with the blocks and recorded on the paper. The goal is to have students understand what they are doing, not just memorize the rules for doing it. I have them use the notebook paper sideways as described in the previous tip. After they have the ability to work through the problems with the manipulatives, we work on how to work without them. However, the strong basis is built.

Math Tip of the Day:Use Lined Paper More Effectively

How To Use Lined Paper More Effectively

Successful teaching of math is often a matter of finding small ways to get students to see math in a way that makes sense to them. Constructing meaning is the goal for all students. Yet, how often are we stuck on making the child fit the method and not the strategy fit the child. There are so many simple strategies that work, require simple changes, few additional costs, and are often ignored, as people continue to try to make the square peg fit into the round hole. It amazes me why they do not put square peg into the square opening right next to it.

Today, we are going to discuss an extremely simple change, using lined paper in math. Schools and tutors for years have struggled with ways to keep place value alignment when doing math problems. The most common math mistakes occur when students move numbers into the wrong column, squish numbers together, and result in performing the wrong functions with the wrong numbers. People have used graph paper, students have been taught to use special designed papers found in their workbooks, and teachers have printed specialized papers to help students keep numbers properly aligned. While none of these strategies are bad, none of them create independent strategies for students. They do not always have graph paper, or the specialized sheets that they practice with in school. Teaching them a method that they can always use, gives them independence.

The simple strategy is basic lined writing paper. I stumbled on this strategy while tutoring, after getting tired of drawing lines to help students keep their numbers in the proper place value columns. Looking at a piece of plain lined paper I realized that turning the paper side ways, created the same effect with no effort on my part. The lines provided natural colored differentiation between the place value columns without needing to draw them. When setting the paper up, instead of having the lines established for writing, you should see lines set up for column math. This creates a quick, easy, and inexpensive math sheet for students that they can almost always recreate for themselves, at school or at home. This is a great strategy for home school parents who are looking for an inexpensive, independent strategy for children to learn as well.

Notebooks of lined paper make great math journals. Students can turn the paper sideways, label the columns to get practice on understanding place value, and have greater success in working through math problems. In addition, when mistakes are made, it is easier to trace the origin of the mistake when the problems are aligned correctly. Lastly, students can recreate this format anytime. It is rare that they can not find a piece of lined paper when they need to do a math problem and should they be without, they can remember just to draw the lines.

When we look we can find simple strategies that improve our tools, create independent learners, and do not add significantly to our financial challenges.