Category Archives: Kindergarten

Misconceptions in math

If you have visited this blog for a while, you may have noticed my continuous quest in helping children deepen their understanding in math. I share here what I do as a parent with my own children, hoping that it could help other parents as well. At home, I use games, math discussions,  explorations of word problems, etc. But I also try to identifying any misconceptions they may have in their learning.

Example.

My son Tom, 5, has learned how to count by Fives and Tens, while playing hide-and-seek with older kids.

– “Ten, Twenty, Thirty, Forty, Fifty, Sixty, Seventy, Eighty, Ninety, One hundred ! Ready or not, here I come !”.

I was quite surprised, initially, to hear him count by Ones, Fives, and Tens, as it is not a concept often mastered at a young age. So one day, as he was playing with his cars, I asked him if he could count them.

– “Sure !”, he said, pointing one car at a time, “One, two, three, four, five, six, seven, eight, nine, ten !”.

– “Could you count them by five?”, I asked

– “Sure !”, and pointing one car at a time as he did while counting by Ones, he counted : “Five, Ten, Fifteen, Twenty, twenty-five, thirty, thirty-five, forty, forty-five, fifty !”.

– “Could you count them by Tens ?”, I asked

– “Sure ! Ten, Twenty, Thirty, Forty, Fifty, Sixty, Seventy, Eighty, Ninety, One hundred !”, pointing again one car at a time.

He could root count by Ones, by Fives, by Tens up to a hundred and more. But he did not understand that counting by Fives means counting by groups of five, counting by Tens means counting by groups of tens. For him, it was just three independent ways of counting. You have ten cars when you count by Ones, fifty when you count by Fives, a hundred when you count by Tens. But since you “usually count by Ones”, you have ten cars. Seems logical in Tom’s world.

With Tom, 5, a discussion is usually the best way to assess his understanding, with a “tell me about what you are doing”, or “what does it mean to …”. With Rosie, 8, I like to use pretend-playing : she is the teacher, I am the child. I do not do it often during the school year, but Summer break is a fun time to do so. And since Summer break starts tomorrow… you should hear more about it pretty soon.

Stay tuned !

 


How I support my child exploring word problems at home

I don’t really teach my daughter math. Well, sometimes I do, informally, when  the perfect opportunity to strengthen and connect a math skill to real life comes up, but most of the time, I don’t. I trust her teachers.

But there is one thing I try to make sure : that she has plenty of opportunities to explore math concepts at her pace. Away from peer pressure, or time pressure, she can model, draw, write equations. Few minutes here and there. Once a week.

I recently made a video of how we do that, with the example of my child exploring one of the Time 4 Fractions problems (Problem 10) in a meaningful way for her as recommended in Carpenter et al., 2014. And her Mom following her reasoning. Now, bear with me, it is quite unnatural to me to speak English to my child, but I thought the video could help you see what our journeys, such as Time 4 Fractions, or WedWoPro are about.

Enjoy !

Reference:

  • Carpenter, T., Fennema, E., Franke, M., Levi, L. and Empson S. (2014). Children’s Mathematics, Second Edition: Cognitively Guided Instruction. Portsmouth, NH: Heinemann. ISBN-13:978-0325052878.

Click # 8 – Numeral recognition

Spotting anything related to Math, and take a picture of it : “Click” is a quick picture-post to help you show our kids that Math is indeed all around.

When numeral recognition does not help much :-)

Click#8

 

 

 


Click # 7 – On the French highway

Spotting anything related to Math, and take a picture of it : “Click” is a quick picture-post to help you show our kids that Math is indeed all around.

Welcome to France where the metric system  is used everywhere !

How many feet before the left lane ends ? How many yards?

Click#7

 


Exploring coins

My daughter has been expressing interest in learning more about coins. I thought I should share what we have been doing !IMG_4118

We started the exploration with the book Dollars and Cents for Harriet, from B and G Maestro. It is one of the books listed as highly recommended in The wonderful world of mathematics ( Thiessen, D., Matthias, M., & Smith, J. (1998), see here ). Indeed, I like how the concept of money is introduced through the story of Harriet, a young elephant who wants to buy herself a gift (suspense until the end of the book !). Through small jobs, she collects a variety of coins until she has enough to purchase her gift. My child loved the book, and have read it on her own several times since (on a side note, there are more Harriet concept books, including some on Time. I am going to check them out, as my child is studying this concept this year at school. Stay tuned…)

Then, we looked at the coins my daughter has been gathering around for years, and sorted them. We identified them in the book. We discussed the value by using the base Ten blocks (not familiar with the base Ten blocks? Click here). For the record, you can use paper clips or Legos®, as long as the child sees visually that different coins have different values, it should work as much.IMG_0617

After that, we played ! My child decided to sell tiles. How much for 5 pink tiles? How about this precious lonely brown tile? And so on.

And finally, we went on a field trip. And a hunt for items that would be less than $1. I must admit I was surprised, we found more items than I thought (made sense once I realized that many fruits were sold by the unit). 19 cents for a banana, 79 cents for an orange, 29 cents for a lime. We could not find a box of cereal for less than a dollar, but we did find a pretzel stick for 99 cents i.e. almost a dollar. We noticed that it was cheaper to buy a sweet onions than a red onions.IMG_0637IMG_0636

We ended up paying… with my credit card. That’s what you get, kiddo, when you have a mom who grew up with Francs, switched to Euros when she was 26, and switched again to Dollars when she moved to the U.S.  :-)


Hooked on Anno books

A few weeks ago, I wrote a quick post about my recent discovery of Anno books (here). Now that I have had a chance to look at several of them, I can definitely claim, loudly and clearly, how instructive and entertaining they are.

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The book starts with an empty landscape, with the numeral 0. The next page, numeral 1, includes a house, a cloud, a bridge. One child, one grown-up. On the next page, a second house can be seen, two trucks. And so one until the page with the numeral 12.

I have always enjoyed counting book, but I would put this one on the top of my list.

  • The drawings are quite appealing to me, and to my children.
  • Page after page, you can see the landscape changing with the seasons, filling up with all kind of items, full of little details that my kids love exploring.
  • There is a neat connection, on the left, to the counting blocks children use at School (e.g. 3 blocks on the left, the drawing in the middle, and the numeral 3 on the right).thumb_IMG_0381_1024
  • Similar items are not always all together, providing support to discuss not only counting, but also adding. For instance, on page “4”, there are 3 birds on one corner, and one more on another corner. My son Tom, 3, would count them one by one, while Rosie, 6, would see it as  adding 3 to 1.

I just wish I have found this book a few years ago, when I started reading books to Rosie or when I was teaching PK and K. A must have for young kids, in my opinion !

Ann’s Math Games and Anno’s Math Games II

These two books include a series of activities to strengthen mathematical skills.

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Ann’s Math Games relates to comparing, adding/subtracting, ordering, and measuring. Ann’s Math Games II goes further, deeper. I found the chapter on Counting with circles quite interesting, showing that a group of children to be counted, can be represented from a complete drawing with all details, to something simpler, to a circle. A helpful transition to modeling and symbolics, that Rosie would have benefited from a few months ago (see here, first and second bullet point).

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“Parents, Teachers and Other Older Readers” can also find additional information about the math concepts presented in the book at the end of each book.

Anno’s Magic Seeds and Anno’s Mysterious Multiplying Jar

These stories relate to more advanced concepts (multiplication and factorials). However, I like to give opportunities to my kids to informally explore math concepts on their own before learning them at School. Anno’s Magic Seeds is a fun way to do so with multiplication. I just need to remember to come back to it when Rosie is in 2nd grade !

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To sum up: Anno books, I am hooked !