What you'll find in this post is not a one size fits all notion of how to teach number facts. If I knew one of those I'd embrace it and be announcing it to the world. But that is not what I have found. At University I was taught that if you teach number facts the way they showed us all children would learn their number facts to automaticity. I'm starting to doubt that.
We have used a plethora of different number fact products and no one product has been a great single fit (perhaps there's a great fit for us out there somewhere just waiting to be discovered but until then we have to use the products we have available). Some products have been better than others but we have gained something from most products we have used. I think the most important feature of any number fact product, is to use it consistently (daily is what I feel is best) over a good period of time.
The other key thing I have learned on our number fact journey is not to rush the journey. Make your first goal the ability to "solve" a number fact problem and start by using concrete things to move around and add. Later you can move to adding using only written pictures on a page and after this you can introduce written symbols (words and numerals) which resemble a number fact as we know it eg. 5 + 6 = . Automatically calculating an answer to such a number fact is a difficult skill which needs to build upon the concrete and conceptual experiences your child has had. (You know I knew all of this stuff before I started teaching my eldest but I did not take my own advice and rushed ahead to expecting mental computation from an early stage. Oh deary me, no wonder it's now an uphill battle
Below is a list of products and techniques that we have utilised on our number fact journey to date. I've also included my ah-ha moments which aren't necessarily backed up by research and mountains of proof but have come from my gut instinct and the ponderings I've had along the way. My hope, in sharing this with you, is that you may be able to fill your "number fact bag of tricks" with a few extra options on your own number fact journey. Of course if you have a number fact product or technique I haven't included please feel free to share it with me. Automaticity or even a "sometime this month would be nice" type length of mental computation is not yet on the visible horizon with one of my boys and I fear getting him there could turn me grey
These books were books that I bought direct from the author Calvin Irons at a Mathematics seminar I attended when I was a teacher (I was a Key Mathematics Teacher so why then am I struggling with number facts with one of my children????
. This can't be right
). These books used a number sense approach to teaching facts eg count on the small numbers, memorise the doubles and use these facts to help with near doubles etc (these ideas are used in the Australian textbook "Go Maths" and possibly others). The idea was great I thought, however I either introduced it too early, before enough real life and hands on type experiences were had or it just wasn't a good fit for my child or perhaps both. Recently I have returned to some of these ideas and am reintroducing the concepts to see if time may have helped.
After attempting something that may have failed due to a lack of concrete experiences I returned to basic approaches to cement the concept of addition and number combinations.
Counters (store bought or homemade collections) were invaluable. Fun counters like the dinosaurs were helpful in inspiring us while we made up number fact stories.
In hindsight I know I rushed this period in my haste to achieve my goal of automaticity in number facts. I didn't just want him to solve the problem and give me the answer which is all that was necessary at that point. I wanted him to be able to solve the problem with barely a thought - using automatic mental computation. Our foundations were shaky and our number fact building has suffered as a result of my haste.
Of course I couldn't settle for just using counters for long and I was back to looking for a way to speed up the process. Above you can see the nifty door facts I created for my hands on learner. He loved these and enjoyed using them which certainly made number fact practise a breeze...until I tried to introduce more complex facts without concrete aids.
Please oh please don't rush or skip the hands on solving stage of number facts. Wait until they are making the leaps for themselves before moving on.
I relented again and pulled out the manipulatives and allowed my learner to "figure out" the answers to his problems. Unifix blocks were what I used when I was a child and my boys love them. (See they were giving me all the clues I needed to know that this activity is what they needed and yet I was in a hurry and ignored their nudges.)
By this point our textbook was requiring a lot of number fact practise and I was feeling the pinch to move forward so I began printing these wonderful number fact worksheets off the internet. This particular one from the photo is no longer available. It was a free software download that has since become a purchasable product but there are lots of other places on the internet that you can find them. Any quick search will locate a stack of options.
Since I was slowly learning that concrete experience are very important, I allowed my learner to utilse whatever manipulative he chose to help him solve these problems. Towards the end of this period he was starting to find manipulatives tiresome and cumbersome and was perferring to use his easily accessible fingers or quick drawn dots or dashes on the page.
Long pages of number facts to solve were boring after a time and my learner began to dread the sight of them. So this called for some different approaches to number fact practise. Above you can see two ten sided dice. You can buy these from teacher supply stores. Instead of number fact worksheets we began rolling two dice and adding their numbers to find the total. If you have four ten sided dice you can play a version of Number Fact War where you use dice instead of cards. Each player rolls their two dice and adds the numerals to find the total. The player with the highest total wins the round. You can even keep a tally of the number of rounds each player wins.
If your learners still need concrete reinforcement then you could use six sided dot dices. I'm not aware of any ten sided dot dice but that would work even better.
Another alternative just came to mind. Instead of using dice you could put your dot dominoes upside down in a dish or into a bag. Each player could withdraw one domino and add the total of dots to determine who is the winner of the War.
Slowly, on my child's timetable and not mine, my learner was starting to move to mental computation using dots and finger counting as his fall back to concrete aids.
Above is a quick game I made on the computer to help motivate my learner to practise his number facts. At this point my child desired incentives to stay focused on number facts so I looked to include more novel ways to approach our practise.
This is a Learning Wrap Up which is a fun tool for practising number facts. It's not a good tool to use while your child is relying on manipulatives to solve their number facts though as it requires two hands to handle it. Some children might find the wrapping process frustrating and tiresome particularly if they wrap the string loosely and the answes fall out of place. But once they have mastered the technique they will be able to practise their numbers facts independently as you turn over the device to reveal the self-correcting feature.
Children who are auditory learners might enjoy this product. It's the number facts sung and then each number fact set is sung but a pause is left for you to include your answer. It's a nifty concept but it didn't work at all for my boys. Listening isn't high up there on their strengths.
For a time we tried chanting and memorising our number facts just like I did as a child. This works well with our skip counting and memory verses but it wasn't a huge hit for our number facts. There were just too many things to chant and memorise.
For this technique to work you would have to break it down into manageable sets but we had found a product that I was sure would be the answer and moved on.
Addition the Fun Way utilises pictures and stories to help a child memorise number facts. It is a great program and one that did work well for both of my learners. There are various products that you can buy to accompany the "Addition the Fun Way" program - cds, workbooks, flashcards, posters etc. I bought several of the pieces of the program but essentially you only need the story book to run the program. The other items are just the icing on the cake.
For the majority of number facts (excluding +1, +2 and +9 as there are easier techniques to use) there is a fun story and picture that is attached to a number fact making it easier for a child to recall. My own children love these stories. When we first received the book they were asking for the stories to be read at bedtime. Okay they aren't top notch literature and would never replace your read alouds but the stories do appeal to children and they ask to do number facts as a result. That is a GREAT thing.
I also bought the flashcards and used them as part of our
Ding game. My boys love this game and the flashcards help them recall the stories.
I know some people are cringing at the thought of using a program that seems to leave number sense out of the process. I have found, with one of my children for who number facts are a breeze (Praise God I have one of those children...rest assure he's turning me grey in his own way
) that he tends to rely on several different strategies to mentally solve his number facts. "Addition the Fun Way" is just another technique in his bag of tricks, alongside number sense and number strategies. It doesn't replace it but rather gives him an additional tool. That has to be a good thing I say.
However I would suggest that this approach should be used well after a child has built a firm concrete and conceptual understanding of number facts.
Over time I have also collected several toys / tools that help make number fact practise fun without noticing that we are practising and working. These items are left out within reach of my boys. I try not to include all of these items as part of school otherwise my boys attach a stigma of "work" to them. Some things are best left perceived as an awful lot of fun.
Monkey Math is a good exploratory toy. My boys like to lie on the rug and explore equations with their friend the monkey. When his arms don't balance his eyes don't look straight at you but rather at one of his arms. He's lots of fun.
Hot Dot sets are another fun tool my boys enjoy exploring on their own. You use the pen to press on the correct answer dot. If you have the correct answer the pen makes a sound to indicate that you are right. Alternatively it may indicate with a sound that you need to try again.
There are lots of board games on the market that reinforce number facts. Here are just three I pulled out of our cupboard. "Sum Swamp" is one of our favourites and as it hasn't been used for "school" the boys enjoy playing it for fun.
Card games are another option for number fact reinforcement. This is a game we bought
recently and have enjoyed.
I'm finding that my boys prefer a short written number fact practise (okay "prefer" is a strong word in this case and "tolerate" might be more accurate) and I can use games like this one to beef up our daily amount of practise.
Another thought I had, in regards to the ease of memorising number facts, was the amount of facts that are presented at one time to learn. We expect an awful lot if we expect them to memorise all of those facts quickly. Imagine being presented with 100 foreign words to memorise...wouldn't we flounder with a task like that?? Wouldn't it be easier to break the task down into bite sized manageable pieces?? With this thought in mind I hit the internet as I often do, looking for something that suited this approach. I stumbled on Rocket Math (which was financially right out of my reach) which led me to
Dadsworksheets.com.
At this
website I found a treasure trove of worksheets that were already prepared that followed this idea of breaking down our expectations into bite sized pieces. Instead of offering twenty of so different number facts, three or four numbers facts are practised over and over again until they become second nature.
My boys baulked a little at having to complete a whole page of facts that were mostly the same so this led me to create my own version that would better suit them.
Our
Daily Calculations book was created out of a need to have a book that contained a few sequentially progressive number facts to be completed each day. Instead of repeating the same facts on one page I opted for including turnaround facts.
By the end of the book the facts are a mish mash of facts reviewing all that they have learned. I plan on repeating this same book with the boys when they finish this one.
Just ten quick facts a day is an easy feat for the boys and because they aren't battling me about doing the task it's something that is rarelyskipped as a dreaded activity. It's quick, easy and painless and it's repetitive and consistent nature is really helping cement the facts.
I have saved this device for last because it's absolutely fantastic!!! You can not beat it. It's called a
Flashmaster and it's an electronic number fact review device. It can do just about anything you can imagine...short of hooking it up to your child's brain and programming the number facts into their grey matter electronically.
Now it looks complicated but it's not. Just turn it on, then pick a yellow button, a white button and press start.
You can practise any number fact (+, -, x, / ) either in order or out of order. You can practise them in a timed situation (with several time options) or wihout. You can select whether you want them to type the answer or figure out the missing addend ( e.g. 4 + __ = 9). You can even input your own problems into the device and have your child practise those. The device even recalls your errors and presents them more often to practise. Oh yes and, as if it doesn't have enough features already, it also displays your results from your previous sessions.
Okay so it doesn't have a gaming element but we have enough of those on the computer and did not need another edutainment device.
My eldest uses this device every day. He enjoys it and it's great for number fact practise. Once again it's not the best choice of device for very early learners but it is a wonderful tool for students working towards cementing their number facts into their brain.
So there you have it...our plethora of number fact tools and paths we have travelled on this long journey. Many of them have been instrumental in getting us to this point and the obstacles have taught me things that have helped me avoid the same pitfuls for my second son. But the one thing that I think has been vital on this journey and that will get us over the finished line is ...
time.
Provided we stick to a path, and follow and practise it daily...time will eventually lead our children to an automatic recall of their number facts...at least I live in hope of that
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