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.
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.
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
Enjoy our four consecutive days of investigation lessons, plus one BIG question: “Why the investigations? Are they worth the time invested?”
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!
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.
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:
It’s time to look at recent quizzes and evaluate the progress we’ve made this year. Why is it we teachers remember the slips, the failures, the lessons that didn’t work? We’ll try to be honest with ourselves here, and evaluate our outcomes so far for the year. We’re evaluating the three concepts we feel are VITAL, non-negotiable skills for 5th/6th grade.
We’re still having students draw their fractions as much as possible. Some students lean towards not wanting to draw – to use their algorithmic shortcuts instead. Which is fine! We do approve of algorithms — they’re excellent shortcuts based on centuries of refinement. Except that we want BOTH! Algorithmic and conceptual knowledge. So we’ve switched from computation-style problems to word problems in Level 1 on quizzes. Here’s the outcome: (we decided to use all female pronouns today)
Sorry we’ve been incommunicado for a while! In the last month, we’ve had one week of outdoor education (camping), one week of spring break(yay!), one week of standardized testing(no comment) and a week of school-wide theme-based learning(fun).
The trick is not to stress about curriculum 🙂 All those other things matter! If we are measuring LEARNING as our main goal, then each of those (except the standardized testing – yuck!) involves lots of learning.
So this week, we had to start by spending a couple days reviewing the unit we started last month – Angles. Here’s what we believe:
We are surprised every year (re-surprised?) at the most common mistakes fifth graders make around angles.
What’s NOT surprising:
- The difficulty of choosing WHICH of the 2 numbers you encounter on the protractor… Is is 60º or 120º?
What IS surprising