On my first day at the Transition Math Project's (TMP)
Summer Institute, I sat in on a session where TMP members (many of whom are teachers) explored strategies to help students engage in and understand math concepts. Each table was given math problems to solve. For example:
Tasty Oats has 12g of protein in 100g of cereal
How many grams of Tasty Oats cereal will give you 9 grams of protein?
I started to have 7th grade flashbacks. My first instinct was to cross multiply to find the value of x. But why? Frankly, it's just because that's the algorithm I was told to use back in the day. But no one ever bothered to explain to me why it worked. I just knew that it did, so it never occurred to me to ask.
As it turns out, there are many ways to solve the problem, which was clear when we shared answers around the table. Each person at my table solved the problem in a different way! With algebra, simple proportions, percentages. But what was most interesting wasn't just that we solved it differently, but that each of us reached for the way that made the most sense in terms of how we learn. And it made me think...if adults (and teachers no less!) all solved the same problem in different ways, shouldn't we also give students that option?
Of course, this is the ongoing debate around how to teach math. We need to figure out a way to ensure kids have options, but also know basic algorithms like cross multiplication. And as always, balance is key. It's the middle ground we need to strive for. One that includes rote methods but also teaches deeper concepts to get us all to 75 grams of Tasty Oats.
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Perfect example of the need for more teacher math training
Allison,
You don't say what the make up of your table of teachers was. Since they all came up with different methods, I'll assume that they all have more math in their background than the 'normal' elementary teacher.
How can we expect a teacher that only knows "the algorithm" to teach other methods and concepts? To really improve the math skills of our kids, we will need a major effort to improve the math knowledge of our teachers.
This was the major mistake in the adoption of what is derisively called "new age math". We put new text books, etc. in place without regard to whether our "rote trained" teachers had a clue on alternative solution methods. Did your workshop last week discuss this need?
Teacher training and student learning
Great comments. Yes, the TMP Institute did have sessions on "Professional Learning Communities," "Math Coaching" and "Using Math Knowledge for Teaching." Unfortunately, I was only able to attend the last two days of the Institute (my colleague, Melissa, attended two days earlier in the week) so I, personally, was unable to attend these sessions.
Good point about the teachers at this event. Yes, those at the Institute did have a higher-level knowledge of math in general. To be clear, TMP's focus is on helping kids successfully transition from high school math to college level math. Of course, the elementary and middle school years lay the foundation for high school math, but TMP's made great strides in opening up conversations between high schools and college/universities to better serve kids. Their successes have helped to fill what was once a huge gap in our K-16 education system.
But back to your main point. I completely agree. Professional development is hugely important, especially in "specialty" subjects like math, science, music, special ed, etc. This is a conversation we continue to support. Proper instruction of a balanced curriculum is what we seek. But we also want to stress that equally important is the other side of this complex equation -- making sure teachers also have a solid understanding of how students learn.