Of course I told them that they needed to know their tables off by heart, but their parents and teachers had already told them this. If it was that easy they would have learnt them already. So this year I have made it my mission to get all the children I tutor to learn all of their times tables.

To start with I created a desire to learn them. I made a colourful chart to show progress, and offered rewards of stickers for each of the tables that they learnt. But not just any old stickers – exciting, shiny ones that made their eyes light up when they saw them. The boys especially liked these football ones from Superstickers .

Now I had children who were desperate to learn their times tables. What next?

We took the tables one at a time and started by chanting them. When we had chanted them forwards a few times, we did them backwards, then odd numbers only and even numbers only to get used to the idea of knowing them out of order. After that it was a case of practise, practise, practise. The trick was finding enough different ways to practise the same thing so that the children didn’t get bored with it.

I made some sets of cards with the questions and answers so that we could play pelmanism, and these proved very popular. I encouraged the children to read aloud the question as they turned each card over, and to work out what answer they needed to match before turning over the next card. We also used the same cards to play snap, and a race against the clock game to match all up all of the question cards with their answers – trying to be faster each time.

Although the children loved all of these games, I was very aware that I couldn’t rely on the same sets of cards forever without the children thinking “Oh no – not those again!” and losing motivation. I looked around for some new ideas and found some lovely products on Sue Kerrigan’s let me learn website.

The turn table cards were recommended to me by the trainer on a dyslexia course I attended. They are designed for multi-sensory learning and are really good fun to play with. On one side of the card they have a question eg 2×3 and a picture of an array to show children what 2×3 looks like and to give them a visual clue. On the other side is the answer. The children say the question and answer aloud (hearing their own voice) and then turn over the card to see if they are correct. There is a video of how to use them here . I usually use them with one child at a time, focusing on one set of tables at a time, using them as shown in the video, and then doing races against the clock to beat their own personal time. However I have also used them with a group of children each working on a different set of tables. One group of girls I worked with recently, who were all working on the same set of tables, made up another game to play with these cards which they found great fun: all of the cards were put answer-side-up in the middle of the table. I called out a question and they had to grab the card they thought showed the correct answer. They turned the card over to see if they were right, and if they were, they repeated the question and answer and kept the card.  If they were wrong they replaced the card. The winner was the girl with the most cards when they had all been grabbed. All of the children I have used these cards with have really enjoyed it, and I’m sure there are many more games that can be invented using them.

I found the maths wrap while I was browsing the site, and just thought I would give it a go. It’s used for learning tables “in order”, but is great for kinaesthetic learners. Across the top is a strip with numbers 1 to 12. At the bottom is space to put a strip of one of the tables, each of which contains all the answers but jumbled. You have to chant the tables aloud, hunting for the correct answer along the bottom strip and then wrapping the string around the correct number each time. When you have finished you can turn it over to look at the pattern marked on the back. If the children have got all the answers correct, the pattern made by the string will match the pattern printed on the back of the card. When I bought it, I thought it might be one just for the girls, but actually the boys have enjoyed using it just as much. One of my Year 5 boys said “Every child should have one of these. They’re really cool!” I even had texts from two mums, because their sons had been talking so much about how much fun it was that they wanted to know where I got them from so that they could get them as stocking fillers.

As we progressed through the tables we looked at how few they had left. By using counters to demonstrate that for example 2×3 was the same as 3×2, we were able to colour code each new set of tables to show which ones they already knew and which ones were still to be learnt. They learned the easy ones (2x, 5x and 10x) first, which made the chart look less bare, and earned them some shiny stickers pretty quickly. Then they did 4x (easy because it was double 2s). 3x came next (tricky but the colour coding showed that they already knew 2, 4, 5 and 10 x3, so there where only half of them still to learn). Then 6x was easy because it was double 3s. By the time we came to the tricky ones like 7x, the progress chart was looking quite full, and the colour coding showed that they already knew 2, 3, 4, 5, 6 and 10x 7, so all that was left was 7×7, 8×7 and 9×7. Suddenly the sevens didn’t seem so scary and the motivation continued.

Of course it took a long time, although considering the fact that I only see these children once a week it took less time than I expected. In September two of my boys didn’t know any of their times tables, not even 2x or 10x. They now know all of them. Not only do they know them off by heart, but they are able to apply them in all areas of maths, for example working with equivalent fractions. They immediately recognise numbers that are in their times tables which means their skills in division have improved. Their mental arithmetic skills have improved because they can multiply 6 by 7 straight away, instead of having to count up 7 lots of 6 on their fingers, so they have more time to think about what the questions are asking them to do with the information. They have both moved up a maths group at school and their confidence is higher. One of them said to me recently that he used to hate maths, but that he really loves it now. And that’s why I really love my job!

For maths and English tutoring in the north Birmingham, Sandwell and Walsall areas, visit www.sjbteaching.com. For links to other interesting education related articles, come and Like my Facebook page.

Related post: Teaching Number Bonds    A Multisensory Approach to Reading

“I’m your lab rat,” said the confident young voice at the other end of the phone line. I introduced myself and explained the concept of the literacy project. I thought he got the idea so I asked him to think about a topic in biology or chemistry that he might be interested in but that he found difficult. The next day I got an email from him saying that his ideas were, “chemical reactions and catilysts eg explosions.” In a follow up phone conversation I asked him if he had difficulty with these topics and he replied, “not really, I just haven’t really been taught any of it before.” I asked him why he chose these topics; he said that he was curious about what makes chemical reactions occur.

Then came the difficult bit, finding a text about chemical reactions that would challenge him. I was expecting the lab rat to suggest a text that he was already having trouble with rather than a topic to which he had never been exposed. Thoughts that occurred to me included only showing him a graph or a chemical formula. I was a little concerned about whether I would be able to find content that he would have difficulty with. Imagine if he simply reads and understands the text I give him with ease.  In the end I settled on two pages on the collision theory from a Year 9 workbook. It included a description of the collision theory, an illustration of particles colliding, and a graph showing the activation energy of catalysed reactions. I chose this text because it uses scientific terms that I think the lab rat may not be familiar with and because I want to see whether he uses the illustration and graph to help interpret the text. Fingers crossed.

Cycle 1 Analysis

I slid the two pages of text over the table to the lab rat and he began to read. I had explained to him that I was going to closely observe him and that I was not going to assist him during this first session. He concentrated carefully as he read with his arm crossed on the table. I watched him intently and noticed that he had started at the very beginning of the two pages. Every now and then he would nod to himself as if he was clear on what he had just read. To my surprise he did not make any notes, underline any words, or highlight any text. After around five minutes he looked up at me and said, “okay” to indicate that he had completed the reading. This threw me off guard a bit as I was expecting him to perhaps ask me questions or to need clarifications on things he didn’t understand. To initiate a discussion I then asked him to explain to me what he had just read. I was slightly amazed and bemused as he eloquently and fairly accurately paraphrased the content of the text. The purpose of this project was to help a student with a text that they would find challenging, not one that they would understand with relative ease. Keep in mind that this was a year 8 student reading a year 9 text on a topic for which he had very limited background knowledge. I then decided to change tactic slightly and moved straight into the second session of the project.

Cycle 2 Reflection

As I had decided to move into the second session rather quickly, my reflection was rather brief but focused. The lab rat was fairly confident in explaining the text to me in the first session. I had feared this situation from the outset and was hoping that he would struggle a little with the task. However, I had an ace up my sleeve. I purposefully selected a text that was ill structured. When I first read it I noticed that it didn’t paint a whole picture and was a little confusing for various reasons. So, although the lab rat understood and could explain what he had read I knew that he didn’t have the whole picture. I decided quickly that the first aim of my second session would be to assist him to identify the holes in the text and to help him fill them in. My second aim was to gain a better understanding of the strategies he used to read the text because they were not evident from my observations.

Cycle 2 Analysis

I asked the lab rat to read the text again and to raise anything that he did not understand. He spent a few minutes concentrating on the text and then said that he was a little confused about the collision theory because, “the text says that particles have to collide with sufficient energy to overcome activation energy, but the illustration shows the opposite.” I though he was mistaken until I took a closer look, the illustration was mislabeled and contradicted the text. This was something that I hadn’t even noticed because I had a strong understanding of the collision theory. I took this as a very important lesson. There are many mistakes in high school scientific texts that teachers may not notice but which can mislead students. Another thing he was unsure about was what the word ‘thought’ meant in the text, “a catalyst is thought to decrease the activation energy for a reaction.”  He was confused as to why the text would include such an uncertain term. I asked him to consider the word thought in reference to a theory. He considered my question for a few seconds and then answered, “Because they don’t really know.” “That’s right,” I said, “much of science is based on theories that best fit the current knowledge of a topic. They are subject to change as we learn more about these topics.”

Something he did not notice and that I pointed out was that the text did not include a definition of activation energy, which was crucial to understanding the collision theory in chemical reactions. I asked him what he would normally do if a text did not include an important definition and he answered sheepishly, “I’d Google it” and that is exactly what we did.  This was the beginning of our discussion on reading strategies because we had just used online resources as a strategy to support the reading and understanding of a text. Additional strategies he said he used included reading titles to gain a better understanding of the focus of each section in the text, skipping over sections that he had previous knowledge about, and double reading key words. From this discussion he also rightly pointed out that the text lacked a sub-heading that would have made it easier to understand. I agreed with this suggestion and asked him to write in the sub-heading he thought was appropriate. Many of the lab rat’s peers would have struggled with this text and I was impressed with his ability to utilize strategies that were advanced for his year. I will remember the strategies he used and endeavor to provide assistance to my students who are having difficulties in reading scientific text.

Cycle 3 Reflection

After completing the second session I wanted to change tactics slightly. Science is based on testable explanations and predictions about the world. The lab rat and I had worked together to gain a strong understanding of the scientific theory in the text. Now I wanted to see if he could apply what he had learned to explain and predict what might occur in an experiment.  In essence, I wanted to assist the lab rat to ‘read an experiment.’ This is a large part of scientific literacy, and honestly, conducting experiments is far more fun and interesting than simply reading about science. A fellow Grad Dip student recommended an experiment called Elephant Toothpaste. Elephant’s Toothpaste rapidly converts hydrogen peroxide to water and oxygen with fantastic effect. This was also a great experiment because I could change certain variables that would alter the rate of the chemical reaction in the experiment. My plan for the final sessions was to ask the lab rat to predict what might occur when certain variables where changed, conduct an experiment, and then ask the lab rat to explain what he observed based on his knowledge of the text.

Cycle 3 Analysis

Being the first day of the school holidays, I was impressed to see that the lab rat was excited about conducting an experiment in his back yard. Before we commenced I explained to him that I wanted him to use his knowledge of the text to explain what he observed and to predict how the rate of reaction might change when we altered certain variables. As I set up the experiment I asked him to review the text one more time. Standing in the middle of his back yard I placed a 600 mL plastic bottle on the ground. I then asked him to pour 150 mL of hydrogen peroxide into the bottle. Once he had done this I asked him to observe the liquid in the bottle and to tell me if he thought there was a chemical reaction occurring, he answered, “I don’t think so.” It was a bit of a trick question. I explained that the hydrogen peroxide was slowly decomposing to water and oxygen, but that there were no obvious signs that this was occurring. I then asked him to relate this observation to the text and he correctly answered, “so a chemical reaction is occurring but it is a slow rate of reaction.” Next I added a good amount of dish washing liquid before asking him to pour yeast into the bottle. I stood back a fair distance for dramatic effect as if to suggest that something might explode. This had the desired effect and he paused temporarily as if considering the dire consequences of adding this ingredient. Curiosity eventually got the better of him and he poured the yeast into the hydrogen peroxide. Something quite unique occurs when you add these two ingredients together; the rate at which hydrogen peroxide decomposes to water and oxygen accelerates dramatically. The oxygen causes the dish washing liquid to froth and the resulting effect is that foam quickly fills the bottle, gushing out in a tubular shape resembling very fat toothpaste.  After the reaction had stopped I then asked the lab rat to explain what he had observed based on the text. He correctly observed that the rate of reaction had increased and accurately referenced observation to the collision theory. He was unsure, however, about what had caused the rate of reaction to increase. I suggested that he ask questions of the text based on what he had observed to see if he could figure out which one it might be. He did this and, with a little assistance, he was able to determine that the rate of reaction must have increased because the yeast acted as a catalyst.  Over the next hour we repeated the experiment altering different variables. Each time we predicted what might occur, observed the experiment, and explained how different variables affect the rate of reaction by asking questions of the text.

To this day my chest tightens remembering how Joe looked when he told that story. He was embarrassed and sensitive, and his problem with literacy wasn’t that he couldn’t decode the words, it was that he couldn’t comprehend the concepts. He could not get it, and telling him to “pay attention” or “think when you read” didn’t help him. It hurt him.

As Joe read or listened to language, he processed “parts”—the in-one-ear-and-out-the-other syndrome. He could sometimes remember a few details, but he couldn’t get the big picture. He had always had the problem, and it wasn’t just when he read. It was also when he tried to follow directions and could not remember all of them, and then got in trouble for not paying attention. It was when he tried to express himself, verbally or in writing, and it came out disjointed and out of sequence. It was when he listened to language, conversation or classroom presentations, and it went by him before he could get it. It was when he tried to participate in conversation and could not make salient points because he spoke to the “parts” he processed. It was when he tried to think critically or problem solve, a constant frustration for him. Though Joe could read and spell words, he had a language processing problem, and IT permeated the quality of his life and eroded his self-esteem.

Joe’s symptoms could be traced to his difficulty in getting the gestalt, the whole—necessary for processing language and thinking. Most importantly, his difficulty in getting the gestalt could be traced to his weakness in the sensory-cognitive function of concept imagery—the ability to visualize the whole.

Numerous years ago, while researching the relationship of imagery to comprehension and trying various steps to develop imagery, I discovered an interesting phenomena. It wasn’t that individuals couldn’t image, it was that they couldn’t image the gestalt. They could not connect the parts to form an imaged whole. Instead, they got “parts”—bits and pieces—and thus could not get the main idea, draw a conclusion, make an inference or evaluate.

This processing of parts instead of the gestalt contributes to a range of symptoms, most of which Joe had experienced:

• Weak reading comprehension
• Weak oral language comprehension
• Weak oral language expression
• Weak written language expression
• Difficulty following directions
• Difficulty with critical thinking
• Difficulty with problem solving
• Weak sense of humor

Unfortunately, weakness in concept imagery can be a hidden problem in the field of reading. It is often misdiagnosed, and it interferes with processing both oral and written language. Those of us who do not have the problem cannot know how painful it is. Individuals have told me that it means that you feel foggy, like when you go to sleep in a movie and then cannot put it altogether. They tell me that they have hidden the problem behind good social skills, noting when to smile appropriately in conversation or when to laugh at jokes they really didn’t get. They tell me that they go to tremendous lengths to cover this problem because most people just think they aren’t as bright or aren’t good listeners or communicators. A graduate from MIT told me that when he was in class trying to grasp a lecture, it was as if someone was going along with an eraser and erasing the language before he could get it.

The critical role of this function to cognition and the quality of life provokes some questions. One frequently asked me is whether or not this function can be developed and applied to higher order thinking skills? The answer is yes. Just as phonemic awareness can be developed and decoding and spelling established, an individual’s sensory system can be stimulated to image and process the gestalt—enabling the higher order thinking skills of main idea, conclusion, inference, prediction to be improved. Reasoning, logical thinking, problem solving, and perhaps even creativity can be developed.

Another question often asked me is whether or not weakness in concept imagery is increasing? Unfortunately, the answer seems to be yes. Scores from the National Assessment of Education Progress (NAEP) show continuing deficiencies in higher order reasoning skills. The NAEP found, as have other recent assessments, that problems in reading and expressing ideas in writing stem mainly from difficulty with verbal reasoning.

What might be contributing to this apparent decline? One answer is television, not because of the content television brings, but because of the process television denies. Since individuals do not have to image when watching television, imagery is not being stimulated, at least not like it was when story-telling, old radio shows, and reading for pleasure were our recreation.

As we process information through our sensory system, concept imagery brings the sensory information together enabling us to create the gestalt. And, the gestalt is a necessary piece for cognition. Furthermore, there is little question that imagery is directly related to cognition. Aristotle said, long before phonemic awareness was thought about, “It is impossible to think without a mental picture.”

Lastly, as I speak nationally and internationally to professionals about the role of sensory-cognitive functions in language processing, I am heartened by their enthusiastic response and improved awareness about reading. I have hope that we are entering the era of gestalt thinking in the field of reading, and consequently may be entering a time where we institute solutions—solutions that might eradicate learning problems for all individuals. No more Joes. No more IT.

For information on developing concept imagery, contact Lindamood-Bell Learning Processes: http://www.lindamoodbell.com or 800-233-1819.