# Category: BlogPosts

## Learning multiplication with flashcards

Hey folks…I recently came across this article about learning multiplication facts. Here is my summary of it with some addition thought sat the end… A 2022 study from the Netherlands compared two methods of practicing multiplication facts: reciting equations displayed on a whiteboard and singing songs practicing with flash cards. Teachers used the same scripted […]

## Inserting Productive Failure into your Mathematics Lessons

Check this out! Students were randomly assigned to experience 1 of 2 conditions: Productive Failure (PF), in which students collaboratively solved complex problems without any instructional support or scaffolds; or Direct Instruction (DI), in which the teacher provided strong instructional support, scaffolding, and feedback. Findings showed that although PF students generated pictorial representations and methods for solving […]

## Learning to Count – part 2

In this previous post, I proposed a new way of counting things. If you haven’t already read it, please do so. Otherwise this post won’t make much sense. In that post I ended with the following problem… How many rectangles are in this 3-by-4 figure? I promised you an answer to this problem, so here it […]

## CMF Review of Chapter 9: A case against tracking

As I continue reading through the newly revised California Mathematics Framework, I will occasionally post some of my thoughts. In Chapter 9: Structuring School Experiences for Equity and Engagement, they describe methods of teaching that enable all students to be appropriately challenged while also expanding access to rigorous mathematics for all students. Here  I will […]

## Should we adopt new textbooks yet?

So yesterday I was asked a totally reasonable question: Is it time for districts to start thinking about adopting updated materials…especially since the California Math Framework has been revised. I provided an answer, but I feel like my answer changes weekly. Read on and let me know your thoughts about my response: QUESTION:  “Our district […]

## Learning to Count

Counting is hard. It is far more involved than just saying one, two , three. After all, claiming that saying one, two, three means you are counting…is like claiming you can spell just because you know how to say a, b, c . Sometimes, however, counting does feel as easy as saying one, two, three. Counting […]

## Supporting Equitable Instruction with PD+Coaching

This post builds upon my last posts in which I talk about the importance of high-quality instructional materials (HQIM) and how to design ambitious instruction for your school or district that honors the HQIM.   To make sure that all students are receiving strong, standards-aligned instruction with HQIM aligned to those standards, we need to […]

## Designing Ambitious Instruction

As a math coach who serves schools in multiple districts, I need to be clear on what I am aiming for during my coaching. What am I helping the teacher to do or learn or improve upon? I’ve decided my focus is to support teachers implement AMBITIOUS math instruction for their students. Ambitious instruction deliberately […]

## Getting a new math curriculum is MORE than just an adoption process

Here we are in October, 2023. As you have likely heard, this past July the California Board of Education unanimously approved the new revision of the California Mathematics Framework (this in itself should be a series of blog posts, but I’ll save that for another day.), which means school districts throughout Merced County will soon […]