Welcome Back! Here we go – Year Two of our blog. (You can read more about us here.)
We’ve had a great summer, and approach our second year of blogging with the hope that we can improve on what we’re doing. Of course, that’s the thing about teaching — you never feel like you’ve ‘solved the puzzle’, like you get it completely right. There are way too many moving pieces: needs, circumstances, learning styles, personalities. But we all keep trying, improving, tweaking. There is plenty of data documenting the difficulty of our jobs: here, here, and here.
So we’ve promised ourselves that we’d keep teacher morale in mind:
Reminding ourselves of our goals:
- Higher achievement for all by slowing down the curriculum.
- Aiming for visualization and conceptual understanding over memorization.
- Providing challenge for fast learners, by going into more depth.
- Making math interesting and even fun.
1. Starting With Logic Puzzles
We started the year with several days of logic problems, much like last year — see our instructions from last Sept: WEEK ONE – A Logic Problem and WEEK ONE – The Lady and the Tiger , and an early classwork/investigation: CW 9_4
Basically, you can use any logic problems – the internet is full of them. Liars and truth-tellers, brain teasers, riddles. IMPORTANT: Try them yourself, first. They should be easy enough to do, after some head scratching. You’ll run into problems that are too hard or too easy, so caveat emptor. We use a think-pair-share approach to solving these, but other formats would work, too.
We’re hosting Back-to-School night tomorrow. Here are our editable slides that can be either projected or printed out for parents. Break a leg!
Enjoy our four consecutive days of investigation lessons, plus one BIG question: “Why the investigations? Are they worth the time invested?”
Raise your hand if you remember hating homework as a child … Raise your hand if you have children and hate it when they have homework … Raise your hand if, as a teacher, you have ever received homework submitted with teardrops on it 🙁 If you haven’t raised your hand yet, you were born under a lucky star, or you have a faulty memory.
On the plus side, homework
- offers a chance for students to independently consolidate skills they learned in a group setting
- builds skills of responsibility and time management
First of all, we’re glad we did this new unit. It uses Cuisenaire rods extensively.
However, it was hard! There were pitfalls and things we would do differently next time, but aren’t there always?
So, here goes.
According to this article by Jo Boaler — professor of mathematics education at Stanford and co-founder of www.youcubed.org — math memorizers scored poorly on the international PISA test, and the U.S. has more memorizers than most other countries in the world. The highest achieving students internationally were those who thought of math as a set of connected, big ideas.
Here’s what we see:
1. A visual approach to fractions gives students better number sense, and better access to word problems.
When we require drawing, every problem becomes a word problem. In the problem below, all students recognized that 1/2 is 6 out of 12, visually. This is a “12-peak Toblerone”, so a total of 17 twelfths (by simply counting!) . Then this student imagined moving one 12th from the top row to make the 2nd row equal to one, leaving 5/12 on top. This shows number sense! Our students can do fraction addition and subtraction mentally. More importantly, visualization helps facilitate the transfer to word problems, as below.
Word Problems – YAY!
Our intensive use of Cuisenaire rods came to fruition now as we attempt to transfer fraction visualization to word problems. Here are the 2 lessons we spent on this so far:
CW Frac to WP1 and CW Frac to WP2
We used a format called “Builders and Scribes”.
We found Lego-type blocks at the Dollar Shop!
REVIEWING MADE FUN!
We found on our second quiz that many students were still struggling with word problems. (Correct student quiz answers here.) So we adapted some of Steve Wyborney’s “Esti-mysteries” to continue reviewing word problems, and students seem to enjoy these ‘mysteries’ and look forward to them.
Try these engaging warm-ups:
Important: Take TIME when you show these. We try to slow down the process as much as possible (without totally ruining the tension!), in order to allow more students to spend the time they need thinking through the problems. Number 3 can be used as a “Number Talk’ to see how many ways students can see the problem 7 x 13.