Story time in math class!

I love teaching math with stories. Not only do I value the authentic nature of solving math problems from books, I love how quickly they can engage a whole class. I find it so rewarding when a child makes the connection between the story and the math involved. I taught with a book the other day in kindergarten and all of us laughed when one kid yelled out, “hey, this is just like math!”, not making the connection that I was there to teach math!

My pet peeve, is that sometimes it is so difficult to find a book that teaches what I want to teach, when I want to teach it,  in the way that I want to teach it!

I give you Exhibit A!

book-req

Even after exhaustive on-line searches, a plethora of librarian requests, asking all my mathy friends on twitter and begging Marilyn Burns to write another book…I still find it hard to get that picture book that would explain the concept I want, perfectly. I’ve even considered asking my friend, who says that she has always wanted to write a kids book, to help me! (Shar expect a phone-call!). I could tell her the concept, she could write the story, and we could get someone else to do the pictures so we don’t scare the children!

I give you Exhibit B!

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This is a dog…in case you were wondering!

So when I do find the perfect book, I have to share it with everyone! Last week, I began a kindergarten class with the book called: “One is a snail Ten is a crab – A counting by feet book”, by April and Jeff Sayre and the kids loved it! I was getting so tired of all the books that predictably count up by one or down by one, and although this book does do that, it is a great book to use for showing different ways to compose numbers.

I give you Exhibit C!

onesnail

One is a snail, ten is a crab by April and Jeff Sayre

I would read a page, and then ask the students so, “What is 6”. Here are the responses I got:

“An insect!”

“ Six snails!”

“ A dog and a person!”

And the really clever individual: “3 people!”

Without knowing it, I had generated a number talk and every time someone offered a different way of making 6, all the kids were amazed! What’s great about the book, is the authors mix up their ways of composing the number too! Sometimes it is just one thing (i.e. a spider), and other times it is a combination of things (i.e. six snails)! This is a great book for those kids who are ready to step beyond the predictable patterns normally found in books.

Here’s Rory and Oliver trying to figure out what comes next. They obviously need more exposure with crabs!

Next week, I am going to use the same book for grade one in order to demonstrate equivalence. “Oh – so a dog and a person (4+2) is the same as six snails (1+1+1+1+1+1).” Since our school just bought a whole bunch of cuisenaire rods, I’m going to have the students use cuisenaire rods to record their responses.

I give you Exhibit D! (In class, we will use the concrete rods and a white board to record our work).

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Using cuisenaire rods to demonstrate equivalence.

If the teachers have time, I think we’ll extend it even further by having them make mobiles where one side is equal to the other side! I’m so excited! And what inspired me? A book!

Needless to say, I’m not the only one who appreciates this book. I stopped at page 10 (“ten is a crab”) for my K and 1 classes, but the book continues and could be used for many number concepts in K-2. Even Rory wanted to continue reading and as a result, got to demonstrate his new math milestone: counting by tens to one hundred!

If you search the net, you will find a lot of resources to help you use this book in your classroom as well.

Click here  for some suggestions!

Meanwhile, do you have other great books for the math classroom? Let me know in the comments section below!

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Digits versus Numbers

Rory was playing the Osmo Numbers Game (he was pretty spoiled by Santa this year!), and he was getting really frustrated because the game wanted him to make the number 12, and he kept doing 1 and 2 (instead of 10 and 2) and not getting it right. This led me to wonder how I could help him understand the difference between digits and their place in numbers.

osmo1

Oliver learning numbers with Osmo.

Rory is in kindergarten and has no understanding of place value yet, although he should start learning about numbers greater than 10, in school soon. To help him realize that 12 is different from 1 and 2, he needs help conceptualizing the idea that one 10 is different from one 1.

“They must be able to conceptualize place value; the understanding that the same numeral represents different amounts depending on which position it is in.” Charlesworth, 2012.

osmo2

Rory trying to make 14 with the digits 1 and a 4; then making 14 by adding 10 and some more.

Knowing the difference between digits and numbers is a developmental milestone and comes with a strong understanding of place value. I often have primary teachers ask, if I have any ideas on how to make this difference more apparent, and I do!

There are 3 main strategies you can use to develop this understanding:

1) Concrete representation of numbers

Use manipulatives to build the numbers. Showing the difference between 1 and 2 and 10 and 2 using a rekenrek, counters or unifix cubes clearly demonstrates that the digit in the ones position is different from the digit in the tens position. (If this doesn’t make sense, watch the video below!) Grouping or bundling things into groups of 10, or using base 10 blocks, is the best way for students to visualize the difference. Make sure you give lots of time for them to practice counting objects and grouping them into bundles of 10.

“A set of ten should figure prominently in the discussion of the teen numbers” Van de Walle, 2014.

2) Patterns

Write the numbers vertically and ask the students to notice any patterns they see. You will be surprised at your student’s or child’s ability to see that numbers repeat from 0-9, or that all the teen numbers have a one in front of it. Bring in the 100 chart! Now you’ve got a starting place for inquiry…why do they all have a one in front? Your goal is to have students come away with the understanding that digits mean different things when they are in different places.

3) Addition

In order to build number sense, you want students to think flexibly about numbers. In other words, can they decompose a number and can they do it in more than one way? When introducing numbers greater than 10, you want your child to decompose them into 10 and some more. This is another reason I love the rekenrek, for its amazing ability to show a number as 10 and some more.

“Mapping the teens number names to a ten and one structure is an important idea.” Van de Walle, 2014.

Counters are great too because they give students practice creating that group of 10: count out 13 ones, but if you group your tens…you have one ten and 3 more. Representing this as an addition sentence is another great connection for your kids to make and is the beginning of learning signs and symbols to represent math problems.

Here is a video of Rory and I learning about numbers greater than 10. Watching it back, I would have done a few things differently (like have my husband look after Oliver!), but I still think it gives you an idea of the 3 strategies in action (concrete manipulatives, patterns and addition)!

Do you have other suggestions of how to build the understanding that digits are different from numbers? I’d love to hear them! Please share them in the comments section below.

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What the heck is a rekenrek?

Never heard of a rekenrek? You’re not alone, but I’m here to tell you, it is one of the best manipulatives for developing number sense in early primary, and you can make it yourself! Originally developed in Holland, it looks like a mini-abacus, but functions quite differently. Although you can have many rows in a rekenrek, it usually comes with just 2 as seen below.

 

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There’s an app for that!

 

Why do I think it is the best manipulative out there? Well, let’s start with pre-school. It is a great instrument for working on one-to-one correspondence, counting and cardinality. Watch how Oliver (3 years old) easily subitizes a group of 5 on his first try with a rekenrek!

Not convinced yet? This math model offers teaching opportunities ranging from pre-school all the way to grade 2! Here’s a list of the other math milestones you can use it for:

  • Counting strategies: count all, count on, see groups.
  • Visualize numbers 1-20.
  • Develop benchmarks of 5 and 10.
  • Commutative property.
  • Number conservation.
  • Decompose and recompose numbers.
  • Subitizing.
  • Addition – subtraction relationships.
  • Math facts to 20.
  • Visualize doubles and doubles plus one, one or two more and one or two less .

Here is a video of Rory and I exploring some of these things on our home-made rekenrek.

Are you still thinking to yourself: “I can do all of this using 10 frames or unifix cubes” so what’s the big deal?” I’m definitely not saying: ditch the others; children should be exposed to many different manipulatives, but here’s a few reasons why rekenreks should be one of your first choices:

Rekenreks are concrete. There is often this push to move students to think abstractly too soon despite Piaget’s theory which states: children may remain in the pre-operational stage, and thus not able to mentally manipulate information, until the age of 7! Rekenreks are a concrete model that children can use to do their work, to communicate about their work, and to assess their work. Worksheets should be a method to RECORD their work. If you move too quickly to worksheets without giving the developmentally-appropriate materials to complete them, you may be hindering the development of true understanding. Rekenreks help develop the true understanding at a developmentally appropriate level.

Rekenreks have a 5 structure instead of a 10 structure; as a result this is a useful first step to learning place value. Young children find unitizing a group of 10 (seeing a group of 10 as one ten) difficult and this is what place value is. A rekenrek helps children unitize a group of 5 first, and then 10. In other words, it establishes those major benchmarks of 5 and 10, which will aid in subitizing skills (knowing the number without counting) and later in unitizing skills (seeing a group of 10 as one 10).

Rekenreks allow students to count in groups. When using unifix cubes or counters, children are manipulating one block or counter at a time in order to put them together. With the rekenrek, children can move a group of objects (i.e. 4) at one time. This means moving from a manipulative that requires counting all (counters), to one that encourages counting groups.

Rekenreks help in the development of pattern recognition. Pattern recognition is the basis of number sense and its development begins in the early years. Identifying patterns in pre-school leads to pattern recognition with numbers, which ultimately leads to greater number sense all around. By seeing what 5 is on a rekenrek, and then 5 and 1 more, and then 5 and 2 more, children begin to ‘see’ these patterns in their mind and thus master math facts. This leads to the next point…

Rekenreks help develop automaticity with basic math facts. This is the ability to produce answers in a few seconds by relying on thinking of the relationships among the operations rather than recalling answers. Because rekenreks support subitizing skills, they help kids achieve mastery of addition facts. Students begin to ‘see’ the answer, and don’t have to calculate the answer.

Rekenreks reinforce  the different relationships between addition and subtraction. There are three categories of problem structures for these relationships: change problems (join and separate), part-part-whole problems and compare problems (how many more or less). The rekenrek is an excellent manipulative to use to model all of those structures using rich real-world problems to support them.

Rekenreks allow students to think flexibly about numbers and construct their own strategies. They are an ideal tool for number talks. Starting a class off by saying: I made the number 11, can you guess how I did it, opens up the floor to hear and discuss alternate ways of making 11. For example, I made doubles of 5 and 5 and then added one more or I used 10 on the top and added one more on the bottom. “Not all children invent their own strategies. So strategies invented by class members are shared, explored and tried out by others.” Van de Walle.

Still a non-believer? Well believe this: evidence abounds!

Well…actually it doesn’t… but what little research I could find showed that there definitely was a difference between children taught with a rekenrek and those taught without.

“Results indicated that students in Group 1 (who were taught with the rekenrek) scored significantly higher on an addition and subtraction test with numbers from zero to 20 than did students in either Group 2 (taught without the rekenrek) or 3 (not taught).” Tournaki, N., Bae, Y., & Kerekes, J. (2008).

So what are you waiting for?! Start using rekenreks in your home or classroom today!

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The Facts about Facts!

Why bother?!

In this age of technology, do we still need to learn number facts? Absolutely! Thinking flexibly about numbers opens up thinking for more complex mathematical problems. Mental math is also a survival mechanism when you are out in the real-world! Think of how often you use it: How many km am I going over the speed limit?! Do I have enough money to pay for the groceries? How many points is Hillary Clinton up by?!

How do you teach mental math?

Traditionally learning math facts has always been focussed on drill, drill and more drill. In recent years, however; teachers are straying from this model and realizing that drill is not as effective as other methods for ensuring that deep understanding and number sense.

“Posing a story problem…followed by a brief discussion of the strategies that children used, can improve children’s accuracy and efficiency with basic facts.” Rathmell, Leutzinger, & Gabriele, 2000

In fact (no pun intended!), it has been found that these children actually master more facts than children in a drill program! In addition to story problems, number talks that expose children to multiple strategies goes much further than drill alone. A number talk is when you pose a question (ideally in a story problem) and engage the students in a dialogue about how they solved it.

Playing games has also been shown to increase students’ recall and accelerate their understanding of facts. This is only true, however; if the use of reasoning strategies is explicitly built into the games and reinforced through interactions with others. So, if you are a fan of worksheets, drills, timed-tests or Kumon – hopefully this post will change your mind!

Addition strategies

It may interest you to know that there is a huge difference between the way we present facts in North America, compared to China. In China they teach fact tables (for example, the 6 fact tables are all the facts with 6 as an addend: 6+1, 6+2, 6+3 etc.). In America, we teach fact families (for example all the ways to make the sum of 12: 1+11, 2+10, 3+9 etc.). The result? Using fact tables, there are 81 facts to learn (although if you know the commutative property that can be reduced to only 45!!!); using fact families, there are a whooping 153!! (W. Sun and J. Zhang, 2001) So I encourage you to rethink the way you present facts in the early years. Your child may thank you 153 minus 45 times!

Although students should be exposed to multiple strategies, it is important that they are allowed to invent and use their own strategy and not be pigeon-holed into a teacher-chosen one. That being said, there is usually one strategy that is more preferable to use for the given scenario. Discussions about efficiency should take up a lot of your time. You’ll find children are quick to realize that one strategy is better than another and your job is to make the opportunities for those discussions to happen.

The main mental math strategies are:

  • Counting all
  • Counting on
  • One more or one less
  • Two more or two less
  • Making 10
  • Doubles and near doubles

Does order matter? Kind of….the first few methods are counting skills so children should find those mental math skills easier to master. The next few are reasoning methods which require a lot more higher thinking. In order to master those, students must be comfortable counting on and back as well as familiar with composing and decomposing numbers. At school, we just started a unit with making 10’s, but only because they had just finished place value and it seemed like a natural progression. But even within that strategy, we can make it easier or more difficult for students that need it. To make it easier – start with the 9 fact table (easy to make 10 by counting one more). To make it harder – start with the 6 fact table (how many more to bridge 10?).

The important things to remember? Ensure repeat exposure with each strategy and have patience! “It can take between 2-4 lessons before most students really internalize the reasoning strategies discussed in class.” Steinberg 1985

Isn’t using manipulatives with mental math cheating?

I like to call it reinforcing! Child development naturally progresses from concrete to pictorial to abstract, so do that! Help build the mental picture in their minds by using concrete manipulatives. Here are some good ones to use for facts to 18:

  • Five and Ten frames
  • Rekenreks!
  • Abacus
  • Base 10 Blocks
  • Number lines
  • 100 chart
  • And one of the favourites! Fingers!  Read an interesting article HERE on the importance of fingers and mapping within the brain!

Here’s a video of me introducing addition facts to Rory using 5 frames. My first check is to see whether he knows what addition is; then I follow to see whether he has the ability to count on. If he doesn’t, then the only mental math strategy accessible to him at the moment will be counting all. I was super surprised and excited when Rory automatically made groups of 5 with his 5-frames and even more impressed when he made the group with the larger number (i.e. 4 instead of 3), especially since he has never seen this manipulative before. This just shows the power of a manipulative in learning addition strategies.

Keep in mind...

Kids need continual practice throughout the year. Look for ways to incorporate mental math into your day naturally. Even exceptional students benefit from conversations about the efficiency of each strategy. For example, when should we use bridging 10 instead of making doubles?

Can you expect your 4-year-old to master the facts? Not usually and not with full understanding. The ability to reason and achieve full mastery for addition and subtraction facts up to 18, usually occurs in Grade 2, but it is different for each child.

What can I do with Rory at the kindergarten level? I can expose him to problems of joining and separating and teach him the meaning of the words add (join) and subtract (separate). I cannot teach him reasoning strategies until he has the ability to count on and is developmentally ready, but I can see where he’s at. In Grade 1, I can use 5 frames and rekenreks to help him develop his facts up to 10 and help him achieve mastery of those before entering grade 2. And then in grade 2, expose him to different strategies so that he can think flexibly and easily, mentally.

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Feeling Peppy for Patterning!

The importance of patterns

Pattern

Peppy for patterning!

Young children are naturally drawn to patterns, but as a parent, you may wonder why exploring patterns is such a useful activity.

“Learning to look for, describe and extend patterns are important processes in thinking algebraically.” Van de Walle

Patterning is the process of discovering repetitions or regularities and can be explored used songs, movements, manipulatives, nature or behaviours. Patterns and relations are important for understanding the world around us. Much of our life revolves around a pattern: seasons, days of the week, set the table – clear the table, wash your hands – eat your snack, or my Personal favourite: the 3 P’s: Potty, Pull-ups, P.J.’s!

The stages of pattern development:

In pre-K: Children discover patterns (shapes, colours, routines, nature)
Grade K-1: Children learn about number patterns (odd vs. even, 2’s, 5’s, 0’s, the 100 chart)
Grade 2: Children extend patterns into operations (skip counting, adding 10 each time)
Grade 3: Children use patterns as a strategy for multiplication and division
Grade 4-5: Children use patterns to prepare for expressions, equations and functions
Grade 6: Children see algebra as the study of patterns and relations!

Repeating vs Growing Patterns

Now obviously your 3 year old isn’t about to study functions and relations, but the more exposure he or she has to interpreting patterns the better. Marilyn Burns suggests that even in the kindergarten years, we should be exposing our students to repeating and growth patterns to help students develop flexibility in their thinking. By mixing up the type of pattern you present, you are introducing them to problem-solving experiences that will aid in their development of numerical reasoning.

Having taught growing patterns to Grade 6 for years, I couldn’t imagine a 4 year old identifying a growing pattern. (A growing pattern happens when something is added each time).

I decided to present Rory with a growing pattern that could be represented by x+1. I was quite curious to see whether Rory would see the pattern, and was really impressed at his innate ability to solve it after only a few hints! Notice how I use the key questions listed below to engage him. I also use my voice in a rhythmic way to help him identify the growth pattern (“one fish, one bunny, two fishes, one bunny, etc.). Watch how he does!

How to start

Ideally you want to expose your child to as many different types of patterns as possible. This means use song, movements, nature, the world and of course manipulatives. For teachers, Van de Walle stresses the use of manipulatives instead of work sheets or drawings. Manipulatives allow for trial and error and reduce the fear of being wrong. If you are using worksheets to keep a record, you could always have the students record their work after.

When introducing your child to patterns, there are a few key questions to ask:

  1. Did you see a pattern?
  2. Tell me about this pattern (describe it)
  3. What is the pattern? How do you know?
  4. Can you predict what comes next?
  5. Can you extend the pattern for me?

Here’s a video of Rory being introduced to patterns. I started with an easy one using colours, then I tried a different modality (sound) and showed how it could be related to manipulatives. After some discovery time with repeating and growing patterns, I had him create his own. With each exploration, I kept those 5 questions in mind.

Feeling peppy about patterning? Click here for some activities!

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Pattern blocks for pre-schoolers!

Say what?! Melissa and Doug make pattern block toys?! Of course the lead manufacturer of educational toys would make something appropriate for the pre-school generation and I thank them for it!

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What are pattern blocks? Pattern blocks are a type of manipulative made up of different shapes (triangle, trapezoid, hexagon, square, parallelogram, and rhombus). As the name implies, they are a great tool for exploring patterns, but they are beneficial for so many more reasons as well!

“ Using pattern blocks … helps students “see” mathematical patterns and differences and develop abstract mathematical strategies.” D. Rigdon, J. Raleigh, S. Goodman

For Oliver, pattern blocks help him develop fine motor control as well as reinforce his knowledge of shapes and colours.  For Rory, the same learning applies, but I can also introduce a level of problem-solving while he’s playing with the patterns. There are 10 key strategies for problem-solving and pattern blocks can be used to develop at least 7 of them:

  • Modelling
  • Guess and check
  • Look for a pattern
  • Use logical thinking
  • Draw pictures
  • Make a list
  • Make a table

Pattern blocks also encourage the investigation of relationships among shapes (how many ways can you cover the hexagon using different pattern blocks?); they introduce children to fractional relationships (how many triangles do you need to make a parallelogram?); and are perfect for discovering algebraic reasoning (2 trapezoids = 1 hexagon).

Young children are naturally drawn to patterns: seeing them, creating them, playing with them. So why not introduce your kids to this fun tool that they will be using often in their elementary years?

Here is a link to the set we used: Melissa and Doug Pattern Blocks

Enjoy!

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Sorting and grouping

The thing with children is they change so quickly and if you blink, you feel like you missed the moment when a major milestone was achieved. For example, Rory used to say he wanted a hangaber for dinner. Alan and I thought it was adorable, and did nothing to encourage the proper pronunciation of the word! But then one day, we noticed he was asking for hamburgers instead of hangabers, and the moment was gone.

This week, I was playing with Oliver and noticed that he now knows some of his colours! This is a very recent development and one we’ve been anxiously waiting for. Rory knew all his colours by 2 years old, and Oliver is almost 3 and was showing no signs of progress; but then, just like that, he got them all right! This is so exciting for me as a mathematician because it now opens up so many more informal sorting activities!  

“As the children’s vocabularies increase, they will be able to label and describe how and why they are sorting and grouping things.” (Charlesworth, 2012)

Here is an example of Oliver engaged in naturalistic play. Notice how I commented any time he knowingly (although usually unknowingly!) put things into groups. Also notice he learned a new word (rectangle!) and now has additional sorting power for next time!

Because Oliver is now ready for more informal instruction on sorting, I started looking for articles about this important stage of development and was surprised when I couldn’t find many. I couldn’t even find agreement on what strand of math sorting falls into! In some books, classification was stuck under geometry, but the content was directed at a higher age level. For example classifying polygons versus nonpolygons; or triangles with the same area versus different areas.  Another resource I looked at, clumped sorting under data analysis because organizing data into groups is important for graphing. I myself, would have linked classification with logic and pre-algebra, because sorting involves reasoning and logical thought. It is also the precursor to addition (putting groups together) and subtraction (taking groups away).

In addition to the controversy over what strand this falls into; sorting and classification only really appears in the pre-k to k curriculum, and as a result it is minimized in the teaching resources or believed to develop naturally. This surprised me because classification is such an important skill not only at school, but also in our daily life. This skill, although it may appear basic, is the basis for further logic and reasoning. It provides an introduction to graphic organizers such as Venn diagrams and to me, it is a life-skill that may even precede executive functioning ability! (New research project?!) Think of the importance of learning how to sort and classify in this day and age, with all the information we have access to.

Now that I have convinced you of the importance of this seemingly natural ability, I want to share with you how to nourish this skill in your child. In the early years, classification activities fall into three categories:

Stage: Your responsibility:       Example:
Naturalistic: Provide free time, material and space
  • Blocks, cars, farm animals, nature things
Informal instruction Provide comments or tasks that identify or encourage sorting
  • Your picture has lots of red.
  • Can you separate the forks from the knives?
  • Could you put your cars in the car bin and your balls in the ball bin?
  • I see you’ve arranged your dolls from smallest to largest.
Guided instruction Give specific objects and guide classification strategies
  • Find some things that are___.
  • Tell me why these belong together.
  • Sort these into groups, how did you decide?
  • Is there another way to sort these?

 Rory has a larger vocabulary than Oliver and a larger understanding of the universe. For his sorting activity, I used guided instruction. You’ll notice he came up with interesting ways to sort things: by function (button, sticker), by colour (red, blue, yellow, green) and by category (animal, vehicle, shape).  I guided him by encouraging him to think of different ways to sort his materials; however, it was ultimately his decision.

Next time, I might choose different objects that force him to make different decisions. For example, choosing all cars but different sizes, or choosing all art mediums (canvas, paper, felt etc.) and let him sort by texture, or all natural objects and have him sort by common features. I would also provide objects that relate to different content areas. For example, objects that float or sink (science), pictures of workers and different materials (social studies), or sorting plants into edible and non-edible. The possibilities are endless! The only thing to keep in mind is that classification activities should follow the same progression as manipulatives (see my post on this here), so start with 3-D objects and then move to cut-outs and then to pictures.

Although I couldn’t find much on how to teach classification, I found bucket-loads of activities that involve sorting.

Click here  and sort through these for starters!

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Making Math Meaningful with Manipulatives!

If you’re not a teacher, you may not be familiar with the term manipulatives, but you can probably infer what they are. Manipulatives are models that help children think and reflect on new ideas in math. They include resources that allow children to explore, question, guess and check, but more importantly, to play with the problem. Counters, toys, linking cubes, abacuses are just a few examples.

Why use manipulatives?

We all know the old adage: we learn better by doing and math is no different! Manipulatives give students, of all ages, opportunities to have a hands-on approach and develop deeper understanding of concepts. Research has shown benefits to using manipulatives all through life! That means, don’t be in a rush to move your child into more abstract ways of solving problems. There is a natural progression to manipulatives and you need to assess your child’s readiness before pushing them to a more abstract level. When choosing materials, they should be sequenced from concrete to abstract and from 3-D to 2-D. See the chart below for more information.

Transitioning from concrete to abstract manipulatives (Charlesworth, 2000)

1) Start with real objects. Sensorimotor stage.
2) Move to real objects supplemented by pictures. Pre-operational stage
3) Once the first two are mastered, you can use cutouts of real objects. This is the transition from 3-D to 2-D, but the objects can still be manipulated. Pre-operational stage.
4) Now move to pictures. Transitional stage
5) Finally (and much later!) use paper and pencil. Concrete operations stage

So where do virtual manipulatives fit on this spectrum? Good question! I’m not sure! My guess is that they act like real objects because you can move them, but because they are 2-D, they might be more on par with the cut-outs level, in terms of concreteness (see step 3 above). Let’s see what Rory thinks. I’m going to get Rory to do a task with real objects and then do the same task with on-line manipulatives. Then we’ll see what he has to say! This task is an introduction to addition but it would also be great to use for lessons on one:one correspondence, decomposing numbers, counting on and  cardinality.

Well it looks like Rory prefers virtual manipulatives. It may have been the novelty of it or the fact that the computer images acted more life-like than the real objects! He claims that the boat was more real compared to my egg carton version and he liked that the bears kept looking at him (in case you couldn’t tell)! The important thing is that children are given the freedom to choose their own manipulative so that they aren’t restricted to one method. That way, they can discover their own way to reach a solution that makes sense for them. If he likes the on-line tool, on-line tool it is! But I’ll make sure he has the real objects on stand-by in case he’d like to use them as well.

Looking for manipulatives? Look no farther!

Click here for a list of manipulatives that teachers often use with this age group!

Are you a parent? The great thing is that anything can be a manipulative! You don’t need to run to a teacher supply store in order to help your child.

Click here for a list of great things to use at home!

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