Guest Post by Kathleen Whitney, Math Educational Consultant & Coach

It’s not about getting through the content- it’s about being intentional with your math instruction!

As a consultant for SIS4Teachers for the past six years, I’ve been in hundreds of math classrooms. I see the demands that are put on teachers to differentiate instruction for the varied levels of learners, to prove students are learning through constant data collection and progress monitoring, and to teach curriculum characterized by rigor that has reached an all time high. Teachers are so overwhelmed, stressed, and bogged down that it’s not surprising to see them blindly following the teacher edition of the math book, presenting concepts lesson by lesson instead of ensuring that children understand the concepts and standards they need to know.

In some cases, teachers turn to teaching math in small groups. However, I’ve seen teachers do the same exact lesson three times with different small groups without changing a thing about it. Everyone learns the lesson the same way, does the same problems on the same page and uses the same strategies- the “one size fits all” model of math instruction – just in smaller groups. Just because we are teaching in small groups doesn’t mean our teaching has changed. It’s just the old way of doing business with a new name and in the end, our students still aren’t getting it.

Math textbooks aren’t always helpful for our students either. I’ve seen so many children become frustrated because the book is asking them to fill in blanks on a practice problem set in a certain order and that’s not the way the child is thinking about the problem. But since that’s the way the book presented the equation, we make our students fill it in, causing them to be confused. I’ve heard so many teachers say “I hate the way the book sets this up. I wish they didn’t put in these blanks like this. it just confuses the kids.”

**The objective is to teach the concept, right? It’s not to fill in the blanks.**

## Intentional teaching is:

- knowing that the textbook doesn’t know as much as the teacher does about math instruction.
- understanding that different learners in my class need different approaches to understand the same concept.
- thinking about what misconceptions my students are going to have before I teach the lesson.
- accommodating the lesson so students don’t have those misunderstandings.
- thinking deeply about the lesson objective and the standard being taught.
- backwards-designing the lesson so I can teach it in a way my students will understand.

When we are intentional with our teaching we are not going day by day through the lessons. We teach concepts and strategies and using the book pages as practice problems.

**Strategies vs Lessons**

Recently, I met with a group of second grade teachers to work on backward design of some specific math units. We noticed that a big chunk of second grade math is adding and subtracting multi-digit numbers. I asked them: “What would happen if you stopped teaching lesson by lesson through your math book? What if you just taught the “3 Ways Plus the Traditional” strategies with the Math Mights for both addition and subtraction and used the workbook page as problems for practicing the strategies?”

It took a bit of discussion, but we came to the conclusion that we could teach the second grade standards to a better level of understanding, in less time, if we just concentrated on teaching the strategies. So instead of backwards-designing four chapters, we backwards-designed four strategies for addition and four for subtraction. We planned which math tools we could use for each strategy, what the pictorial model would be for each, and how to scaffold to the abstract (CPA).

We designed three levels of instruction for each strategy and decided what the expectation of performance would be for each level. We looked at “must do” problems and “can do” problems, as well as depth of knowledge (DOK) levels for each group. The remedial group would solve problems at a level one DOK, while the content based group could do level one and a few level two DOK problems. The accelerated group could do more DOK 2 and perhaps a DOK 3 problem. We decided which of the strategies would be taught in the beginning of the year, and which strategies we would hold off until second semester.

By the end of the collaboration, the teachers actually felt like addition and subtraction of multi-digit numbers was going to be doable instead of a huge weight on their shoulders all year long. Backwards-designing each computation strategy allowed the teachers to step away from the lesson-by-lesson routine of teaching math and be really thoughtful about what the students needed.

### Differentiation on Display

Another example of intentional teaching comes from a third grade teacher in one of our project districts. She naturally backwards-designs her math instruction. Every student has a daily assignment, but not every student has the same daily assignment. She teaches her class in small groups and practice problems are assigned based on how she is teaching the standard to that specific group.

I visited her classroom last fall and the class had been working on model drawings. She had four guided math groups and each had its own version of the same story problem. One group only had to draw the bar model that day because they were focusing on drawing a unit bar that matched the story. Another group did all the steps except the explanation. This group was working on scaffolding to independence all the way up to the explanation. Another group was given the bar model and asked to figure out the computation to solve, trying to analyze the drawing and decide what operation was necessary to solve. The last group was given just an explanation of the problem solving and had to go back and create the drawing and figure out the computation to solve based on the strategy mentioned in the explanation. All groups worked on the same story problem, but in different ways based on level of readiness and depth of knowledge level appropriate for that group. Every student problem-solved that day, but it definitely was not “one size fits all.”

I just visited that same third grade teacher recently. Her math block was being taught in a workshop structure. Each guided reading lesson was tweaked to accommodate the level of readiness of that group. She again differentiated her problem solving on this day. This teacher assigned the same problem-solving context and just modified it so each group could be successful in solving it.

This teacher knew that problem solving was the objective of this activity, so she adjusted the story to make it solvable for each group. She recognized that not all students are ready for the same level of computation at the same time and she chose to honor that by giving them equations at levels that are achievable so everyone could feel some level of success. Here are some samples of the simple adjustments she made to the same story problems that made them accessible to all students.

With this intentional teaching, she has avoided the situation that every teacher faces where a certain group of students can’t keep up with the whole group lesson. The teacher works through the problem thinking the students are understanding the concept, but what actually happens is that our struggling students wait to see what the teacher writes down and then copy it. The student gets credit for completing the work, but has the student made any progress towards mastery? Intentional teaching takes this into consideration, adjusts accordingly, and avoids teaching the learned helplessness that so many of our students have mastered.

**Intentionality – From Theory to Practice**

How in the world does a teacher have time to be that intentional? It takes collegial planning and collaboration. Teachers need time to meet and work together to backwards-design their math instruction. Together, grade level teachers could look at and modify assessments, figure out what standards are addressed in the unit of study and what actually needs to be mastered. Then teachers could plan the instruction at the concrete, pictorial, and abstract levels for their remedial, content level, and accelerated groups of learners. Without time to look deeply at the curriculum and figure out what would meet the needs of students, we can’t be intentional with our instruction.

Our students will get the best math instruction when we can take a step back, look at the big picture, and get out of the “follow the book, page by page” routine. With intentional teaching we can work smarter not harder. We can concentrate on what our students know and what they are ready to learn next, instead of following a generic sequence of lessons designed for “one size fits *nobody*” instruction. When we start backwards-design of our math units, we will get better at intentional teaching in our daily lessons and we will actually be teaching the standards our students are meant to learning.

**Be intentional!**

**Meet the Blogger**

Kathleen Whitney has a B.S. from Central Michigan University, and a Masters degree from U of M in elementary education, concentration in early childhood. During her twenty years at Redford Union School District, Kathleen taught 1st- 6th grade and served for three years as the building interventionist. She is a trained Reading Recovery teacher and Literacy Specialist and has extensive training in early numeracy and elementary math. Kathleen loves the power of the job-embedded coaching model of professional development for teachers and their students.

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