# Category Archives: Review

## Building back up confidence in math throughout Summer

I find it somehow arduous to follow what my daughter, Rosie, 8, learns in math on a daily basis during the school year. But in Summer, I usually am committed to catch up with what I have missed, especially as we usually have quite low key Summer at home.

• Two years ago, I decided to use the Common Core Math Standards (here) to come up with weekly activities to review with Rosie what she had learned in K. We had a fun Summer of learning, but it was quite time-consuming to plan it.
• Last Summer, I tried to take the same path, but could not keep up with the M.Ed. Summer courses I had to take in paralell. Rosie was a happy child in 1st grade, seemed confident in her math skills, so we ended up doing math mostly informally throughout Summer.
• This year, I decided to try something new with my now rising 3rd grader. I had to, as Rosie came home one day, the last week of school, claiming “I know I am not smart, I don’t even know my multiplication facts *”. Sigh**. I have 10+ weeks to build back up her confidence.

So here is what we have been doing:

1. Every day, Rosie explores a word problem “in any way that makes sense to her”, as recommended in Carpenter et al, 2014. We have been using the pool of word problems discussed in one of our previous posts (here).
2. She also works on a daily worksheet from Summer Bridge. I rarely give worksheets to my kids, but I was curious to connect our Summer learning with some of the math activities that Rosie does at School, and see if she needed any kind of reassurance on that front.  There are dozens of books to review Standards throughout Summer, I picked one that does encourage children to explain their reasoning in math. So far, I have liked it.
3. Once a week, we go to the library to pick up books related to math that we read informally throughout the week (click here for more details) .

And so far, it has been working quite well ! You may want to give it a try, it is not too late !

• It is short. Within 15-20 min, Rosie is usually done with her “formal” learning time and has the rest of the day to keep learning… through free play!
• The exploration of word problems has been quite nurturing. She started Summer with trying to remember the procedure she was taught at school, doubting of herself when she could not, to reaching out a new level of confidence, making sense of the problems on her own. As always, I mostly listen, asking questions from time to time to make sure I follow her reasoning.
• Observing Rosie filling up worksheets has been quite instructive as well. Most of the Summer Bridge activities encourage math thinking. Still, a few do not.
• I could see Rosie’s face change the first time she had to solve a dozen addition or subtraction problems in a row (see picture on the right), her eyes begging me to let her skip the few pages providing such a repetitive task. “Let’s just try to make it a little bit more exciting, Rosie. If you had to pick 5, which ones would you pick?”. Now she does not solve them like a machine, she thinks first. “I will do 688+102 because adding 102 is like adding 100 and then 2 more, so I already know it is 790!”.  I understand that practicing a skill develops fluency, but fluency  should not come with… a lack of thinking. At the CGI conference I attended last month, we were shown a video of  a high schooler, enrolled in advanced math courses,  solving 4001 – 3998 … with a standard algorithm (see representation on the left). He was so used to using the procedure that he did not notice that the subtraction could be performed mentally (believe me, it happens to the best of us… See one of our previous posts “When I got swallowed into the symbolic level“). En garde !
• I also noticed how being invited to solve a problem in a little square puts Rosie back in some kind of school tracks, away from freely showing her way of thinking. She did mention though that I should feel lucky, she could have just written 34 or 32, without any units or equations.
• Exploring math book has also boosted our math talks, as discussed here.

We shall see what the rest of Summer may bring, but so far, combining word problems, worksheets, and math books has provided us with a good balance of learning. Indeed, I even found a little fairy waiting for me on the kitchen table last week. A math fairy. She seems rather happy and confident, don’t you think? I just hope she does not fly away at the end of Summer.

* It is by the end of 3rd grade that students are supposed to know their multiplication facts, so obviously, Rosie, you still have plenty of time.

CCSS.MATH.CONTENT.3.OA.C.7
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

** T.J. Zager, the author of Becoming the Math Teacher You Wish You’d Had, shared a similar experience on Twitter last week. Wondering how many 8 year old girls feel that way.

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.

## 2016 – Here we come !

In the country I come from, France, we have until the end of January to send our New Year wishes so here I am, not that late : Happy New Year, dear readers !

It is time for us to get back to math. Here is a brief snapshot of what you may find here in the coming weeks.

• Remember Time 4 Fractions? I will start posting weekly word problems on all 4 operations this time (and fractions from time to time, not to forget what we did last Fall). Still, differentiated in 3 levels. Still, an opportunity for children to explore problems. Stay tuned, I should be able to start on Wednesday.
• Click“, our quick picture-posts spotting that Math is indeed all around, will take us to France for a little while. Conversion of euros to dollars, liters to gallons, etc.
• Drawing math” will include, from now on, questions that can be asked to young children, in addition to inviting him/her to create  a problem that could match the picture. I do not know about you, but my kids and I are having fun with just talking about math from a drawing.
• Finally, I am excited to take a course on Algebra this semester ! I may have a lot to share on how preparing young children to this branch of math !

Off we go !

## 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.

Anno’s Counting Book

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).
• 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.

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).

“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 !

To sum up: Anno books, I am hooked !

## Reviewing ordinal numbers with Anno’s book

I recently discovered math books from Mitsumasa Anno, a Japanese illustrator and writer of children’s books. As a book worm, eager to explore them further, I ordered a bunch of them online and I will write a special post once I get them.

But I cannot resist to share a quick preview.

The book “Anno’s Math Games” is full of short stories beautifully illustrated, and associated with math-related questions. Perfect to have some impromptu math discussions when we read books at night !

I have been looking for fun ways to use/discuss ordinal numbers with my daughter Rosie  for the past 2-3 weeks and this book was perfect to do so. Looking at the picture below, I would pick a window, and ask Rosie “who is at the second appartment on the right on the fifth floor?”. Then, Rosie would pick a window, and I would have to find the apartment following her instruction.

More to come about Anno’s books, but check them out ! They may have them at your library !

## Math education: could we all be part of the solution?

I thought I should dedicate a whole post on a book I am reading, “Teach like your hair’s on fire” by Rafe Esquith. Although it was suggested to me as a student pursuing a Master in Math Elementary Education, I find it quite inspiring as a parent as well. I highly recommend it.

The author, a 5th grade teacher, provides his vision, rather straightforward, of the US education system, what has changed in the past 20 years, the pressure teachers may have from testing, how they struggle with finding the time to just teach. But for every problem he mentioned, he provides tips, techniques to solve it, as a teacher, as a parent.

His statement on teaching Math is quite heartbreaking, though.

“Kids are taught ‘tricks” to help them compute. They have no idea what they are doing but can get the right answer. Their scores are decent and everyone is happy. But this should not be our ultimate goal in teaching numbers. We want our children to understand the power of numbers, to appreciate that mathematics is both relevant to their life and fun.”

Indeed, even with Rosie attending a quite nurturing school environment, away from tricks, away from EOGs, I can see that, sometimes, she does things without fully understand why. Quick example.

• Before Rosie started Kindergarten, we did some word problems such as “There are 4 ducks on a pond. 3 more ducks come. How many ducks are on the pond?” And intuitively, she would draw the ducks, talk, raise questions. Yes, they can be “rainbow ducks”. Sure, you can add some flowers around the pond if you want to. And Rosie would come up, naturally, with an answer of 7.
• During her Spring break, I asked her a similar problem. Just to see where she was. She read the problem, wrote some dots, an equation, and came up with an answer. A right answer. Intrigued by her dots, I asked her why she solved the problem using them. “Well, it helps me count”. Yes, but how does it help you? She couldn’t say. She could not say that, instead of drawing ducks, she wrote dots. That it was faster to write dots than drawing ducks. And I have no doubt she was told at School why she could use a dot. But at one point, somehow, she lost the connection. So we went back an inch. We drew some ducks. Colorful ducks. Silly ducks. We represented them with dots, squares, hearts, tally bars, anything that would come up into Rosie’s mind. We added numerals, we wrote an equation. Until she fully saw, again, the connection between the number of ducks, the numerals, the symbols.

I am just starting this blog, not certain where it is going to take me, but if there is a problem with math education in the US, I am ready to contribute to the solution. With Rosie. With you. Even if it is just a drop in the ocean, I am willing to try. Like my hair’s on fire.