By Marsha Sutton
After all the hubbub about what some say is an excessive amount of teacher training in the Del Mar Union School District, I asked to sit in on a professional development session.
DMUSD superintendent Holly McClurg enthusiastically agreed and set me up with a session for the district’s kindergarten, first- and second-grade teachers on Feb. 10.
Led by Dinah Brown, the training session drew me in completely, from the first moment.
Brown, DMUSD’s coordinator of curriculum and instruction who was hired full-time by the DMUSD last year, discussed strategies that allow students to think differently than the “one right way” to solve problems.
About 30 teachers gathered around tables in groups of four or five each, generally organized by schools (the district has eight). The all-day training focused on mathematics, specifically subtraction (addition was done previously). The problem being discussed was 80-26.
Teachers shared how their students might approach the problem in various ways. Brown said kindergartners and first-graders might solve the problem by counting by ones.
“If you gave numbers that high and they don’t have that ‘ten-ness’ yet, they might count out 80 [pieces] and that’s not horrible,” Brown said. “They don’t know to use tens yet. They’re still making sense of it. But they can still solve those kinds of problems.”
They don’t have that “ten-ness” yet?
Brown said understanding the concept of Base 10 is “so very, very important.” At some point in their learning, young students will discover “ten-ness,” she said.
Brown elaborated: “How do your kids connect to Base 10? If I were to give ‘80-26’ to my first-graders, they might count by ones. Is that okay? Yeah, if they don’t have that ten-ness yet, that may be what they need to do. You may see different levels of their understanding. But this is very common.”
And on she went, involving teachers with activities, questions, ideas, strategies and videos showing young children doing math – some solving the same problem in different, and all equally valid, ways.
Prepared as I was to be skeptical, this was fascinating. I found myself immediately drawn into the presentation, which was informal, collaborative and engaging.
Brown impressed upon the teachers the need to allow children to develop their own strategies for solving problems, while at the same time providing them with algorithms that work.
“Algorithms were developed by mathematicians who know mathematics,” she said. “They already understood mathematics. But if we’re teaching this before I understand Base 10, I may be able to memorize this and produce it and do it, but I might not be building.”
Let them use the algorithm, Brown said, and don’t tell them it’s bad or wrong because it’s not.
“It’s a good strategy – it’s just not the only strategy,” she said to the teachers. “But it might not develop a Base 10 understanding that we’re looking for.”
Kids will invent their own strategies, she said, “and that’s okay, even good. You never know what strategy will make the most sense [to them].”
Counting up
Sometimes as adults we forget how the principles of simple math that come naturally were once taught to us at a young age. For example, we don’t think about how counting up to solve subtraction problems is different than counting down. We just … solve it.
Consider this: How many more do I need to get from 26 to 80? This as opposed to: What’s 80 take away 26?
“When I see a child start with the amount and count to, they’re going to be looking at the difference, versus subtraction as taking away,” Brown explained. “That’s a huge jump. Huge jump. I used to have sixth-graders who still didn’t understand why we used the word ‘difference’ for subtraction.”
The strategies Brown shared with teachers, she said, are rooted in what makes sense.
“What if it were 80 take away 10?” she said. “Do I want them to start at 10 and count up? Or would I want them to count back? I’d want them to count back. What if it were 80 take away 79? We want them to count up.”
“They’re starting to understand that addition and subtraction are related, and can use addition to solve subtraction,” she said. “That’s a pretty big ‘aha’ when your kids start to learn that.”
Take, for example, counting back change at a cash .
“I used to do a whole unit on money in fourth grade and none of my kids could count back change,” Brown said. “I used to think, what is going on?
“What happens is the minute I learn the subtraction algorithm, I no longer am flexible to think that I can count back. The only way to do subtraction is to line up, cross out, do this, do that …”
Once certain strategies are taught, kids often learn them without understanding the principles behind them. And they block out alternative ways of thinking. They do what they are taught without thinking about the actual problem and how it might be solved differently.
As an example, Brown wrote on the whiteboard the problem 1000-999 like this:
1000
- 999
Do students really need to work this out on paper, with borrowing? Some do, because they were taught to solve problems in a certain way, without thinking logically.
Or take this problem:
17
- 8
Does it make sense to “borrow” from the 10s column by crossing off the 1 and writing a little 1 to the left of the 7? Of course not, but many students will do that because that’s how they were taught.
Brown said when students learn algorithms and strategies and don’t know why they are being taught to solve problems that way, they use the rules but often don’t have a clear understanding of why.
It becomes a case of, “I just do it because that’s what I’m supposed to do,” she said. “So when we think about mathematically proficient students, we want kids to look at numbers and make the decision which strategy is going to be most efficient.”
Brown asked teachers to question their tried-and-true methods. “I want you to be curious, not only about your kids but about activities you’ve done forever,” she said.
“Is it just an activity they’ve learned to do because I taught them? That’s a question I always ask myself.”
Blown away
True confession: I was blown away. This is what the shift to Common Core is supposed to celebrate: each child’s individual creativity, imagination and ability to find solutions to problems in unique and original ways.
And if teaching teachers how to explore and embrace instructional techniques that give children the freedom to discover solutions on their own, then how is that controversial?
The problem in Del Mar, however, seems not to be opposition to the principles behind the professional development. Rather, the controversy has mostly been about the lost classroom time for students when their teachers are absent for the training.
Providing training outside of classroom time is the goal, McClurg said, but there are obstacles, mostly having to do with the labor contract which restricts when teachers can be compelled to attend meetings, training sessions or other district business.
The early-dismissal Wednesdays, a source of great frustration for many parents, became incorporated into the Del Mar teachers’ contract over a decade ago, well before McClurg came to the DMUSD.
Although she said the contract language could potentially be changed if teachers agree, most believe it’s unlikely.
Two Wednesdays each month, teachers are required to stay at school after the 12:30 p.m. dismissal for meetings and training sessions, while their afternoons are free the other two Wednesdays.
“Those are not work hours on [those ‘go’] Wednesday afternoons,” McClurg said. “That is part of the contract. We do try to schedule things and have trainings and meetings on those days as much as possible, but it’s not in their contract. … So other than encouraging attendance and paying them, we can’t require attendance.”
“When I was assistant superintendent we did schedule quite a bit on [those] Wednesday afternoons and paid teachers to attend,” she said. “But it’s still an opt-in situation.”
Former DMUSD parent Melissa Myrhum said her children’s teachers were often missing from the classroom not just for professional development but also to attend district committee meetings.
“Why can’t these meetings be held after school?” Myrhum said. “They work six hours a day. Where do you have a job that’s only six hours per day and you can’t have a meeting after school? Why are they having these meetings during class time?”
“We do try to do as much after school as possible,” McClurg said. “Ideally that would be great.” But committee meetings usually run all day, she said, so meeting from 3 to 5 p.m. after school would require four meetings.
“So that becomes a bit less efficient because obviously you have a reset for each meeting,” she said. And again, the labor contract prohibits compulsory attendance at meetings after school hours.
McClurg said she understands parents’ objections and is working with union leaders to find mutually acceptable alternatives that would provide the necessary training without disrupting the children’s class time with their teachers.
“We’re hearing it and addressing it,” she said. “Last summer we did initiate a math institute where our teachers had five days of in-service during the summer time, so we are trying.”
Next week: Final addendum, with associated costs, on Del Mar’s struggle to find a balance between the competing needs for professional development and classroom consistency.
Marsha Sutton can be reached at: [email protected].
