My school decided to adopt the Bridges math program, and we’re in our first implementation year. Numeracy learning is so complicated that it feels impossible to unravel the web at times.
We know that conceptual understanding, knowledge and skills work together to form the basis of a child’s achievement in math. But “how” is the million-dollar question.
We know a lot of “don’ts” when it comes to numeracy learning:
- Don’t just focus on rote memorization of procedures and calculations
- Don’t drill and kill
- Don’t “silo” concepts and skills
- but also…Don’t focus only on conceptual understanding and leave out practice and reinforcement of skills in context
- Don’t expect students to jump directly to the abstract
- but also…Don’t expect students to “absorb” all the conceptual understanding, knowledge and skills they need from a constructionist approach (direct instruction is also necessary)
We also know a lot of “do’s”:
- Directly teach children important knowledge and skills
- Provide opportunities for students to connect to previous understanding and construct new concepts through exploration with manipulatives and in relevant, real-life scenarios
- Provide ample time for skill practice across many different contexts and scenarios
- Revisit concepts and skills often
- Make connections between concepts and skills often
- Assess understanding, knowledge and skills often (all three, not just skills)
- Make adjustments and use data to drive instruction
There are a lot of things I love about Bridges, and about other math programs I’ve worked with. There is some I don’t like. I think the “how” of achievement in numeracy, of combining the conceptual development, knowledge acquisition and skills practice in the right ratio is subjective. There isn’t a “right” answer, only the right answer for your students that year.
The answer for me and my students this year seems to be: go slowly.
It’s our first year with a new curriculum, and most students are coming into the program “below grade-level”. For those who need that extra support, going slowly, backtracking and filling gaps as we go seems to be the best and only approach so far. For those children who need a challenge, pushing them to express and communicate their thinking in more and more precise ways as well as applying their skills in complex, open-ended scenarios is pushing them to the next level in conceptual understanding.
One cautionary tale is… Be clear and intentional about your goals for students in any given lesson or task.
If your target is for students to learn a skill, TEACH the skill. If your target is to help students develop problem-solving strategies and flexibility in thinking, to practice application of skills, then provide opportunities for open-ended problem-solving or investigation. But do not confuse the two.
Don’t think students will absorb a deeper conceptual understanding or a skill because it’s embedded in a task or investigation. And don’t think students will know how to apply a skill if they’ve learned it in isolation.
Too often, rich, open-ended, transdicplinary tasks or investigations just muddy the waters because they require too much of an individual or a group in that moment in time. The necessary scaffolding is not in place. Students aren’t allowed to focus. Students aren’t allowed to consolidate, but are led in too many new directions.
Too often, direct instruction turns into monkey-see, monkey-do because the teacher says so.
It is shocking what kids will miss when instruction is not explicit. Of course, on the flip side, it’s shocking what kids are able to memorize without understanding it.
Some kids will need more targeted instruction, and some kids will need more time for exploration and application in open-ended investigations, opportunities to make deeper connections. They will always need both in some unique ratio.
As always, it comes down to: Teach your class, not your curriculum.