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:
- 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).
- 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.
- 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.
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.
- 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.