I am concerned that we are conflating automaticity with fluency. How might we get clear on the difference?

From *Assessing Basic Fact Fluency* by Gina Kling and Jennifer M. Bay-Williams:

Think about how you assess reading fluency. Does your assessment plan involve listening and observing as children read as well as asking reading comprehension questions? Now imagine what you might learn about students’ reading fluency if you used only timed quizzes. How would your confidence in your assessment change?

- Assessing Basic Facts Fluency by Gina Kling and Jennifer M. Bay-Williams – National Council of Teachers of Mathematics
- Fluency without Fear by Jo Boaler – YouCubed Stanford Graduate School of Education
- Fluency: Simply Fast and Accurate? I Think Not! by Linda M. Gojak – National Council of Teachers of Mathematics

From Fluency: Simply Fast and Accurate? I Think Not! by Linda Gojak:

Building fluency should involve more than speed and accuracy. It must reach beyond procedures and computation.

From Fluency without Fear by Jo Boaler:

The best way to develop fluency with numbers is to develop number sense and to work with numbers in different ways, not to blindly memorize without number sense.

Ok, so how do we assess fluency? Do we have common language for mathematical fluency?

From *Principles to Actions: Ensuring Mathematical Success for All: *

Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.

Let’s focus this 3rd grade standard:

#### Multiply and divide within 100.

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Do any of the fluency assessments from the above Google search help us assess fluency?

What if we try a different type of assessment? An assessment that involves listening and observing as children compute, reason, and respond.

What if we confer with learners individually, just like we do with reading assessments, to listen, record, and encourage learners as they think, reason, and compute?

I need, want, and invite your feedback on the following prototype. I hope that I have constructed a viable argument and I seek your constructive critique.

Multiplication Fluency (within 100)

Conferring with Mathematicians

**Section 1** asks students if they know their multiplication facts. We intentionally ask these questions because of John Hattie’s work on student expectations of self – effect size of 1.44.

**Section 2** checks for accuracy and efficiency. The teacher will code the student’s response as recall, uses a strategy, or skip counts. The first 8 facts are common for all students. The next 8 facts can be customized for each student based on their responses to easiest and hardest.

** Section 3** checks for accuracy and flexibility. In the previous section, the teacher gave the multiplication expression and the student responded with the product. Now it is reversed. The teacher gives the answer and student states an expression and are asked if they know another way.

Section 3 also checks for accuracy and flexibility using images from #UnitChat. Students are asked how many they see and how do they see them. If they skip count, their answer is confirmed, and they are asked if they can say or write it again using multiplication.

If you open this Multiplication Fluency (within 100) pdf, you will find each image on its own page so students can touch to count when needed.

Will you take time to offer actionable, growth-oriented feedback using *I like…*,* I wonder…*, and *What if…* to help clarify or improve the assessment?

Thank you in advance.

I have tried this out with third graders and it gives really useful information about how they think and feel about multiplication facts. I especially like the images. Some of my interviewees counted one by one with pictures, so it might be useful for that to be a choice. What if there was space to make note of the specific strategies used by students?

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