Dear Future Math Standards Writers, I’m writing you this letter from the perspective of an educator who has worked as a math teacher and math teacher specialist for a public school district since 2003. I know that one day, maybe years from now, there will be a new set of math standards and I…
Now that you’ve read about the three steps I often follow when trying to raise a math problem’s Depth of Knowledge level, I thought it might be useful to take you through the entire thought process of actually implementing those steps. The experiences I’m describing took place while preparing with some other teachers to teach…
Here’s a question to think about: if you can completely remove a problem’s context and still solve it, can it really be mathematical modeling?
Consider the math problem below from a middle school math textbook. It uses the context of a baseball diamond to discuss rational numbers. It is listed as a “Real-World Link” and demonstrating Math Practice 4 (notice the box in the upper right).
I was watching students work on this page and wondered how important the context was to solving these problems. Then it made me wonder, “What if there was no context? What would change?” This is what the problem might look like it the context was completely removed.
Last week I posted my first attempt to expand upon my previous Depth of Knowledge Matrix that helped make it easier to distinguish between depth of knowledge levels in mathematics. This week I am releasing the secondary mathematics matrix to go with last week’s elementary mathematics matrix.
I’ve decided to expand upon my previous Depth of Knowledge Matrix that helped make it easier to distinguish between depth of knowledge levels in mathematics. While it is still useful, it didn’t cover every grade level and may be too broad in scope. So, I have made two new Depth of Knowledge Matrices: one for elementary mathematics and one for secondary mathematics. This week I am releasing the elementary mathematics matrix and next week will be secondary mathematics.
If you live in a state that uses the Smarter Balanced Assessment Consortium (SBAC)’s assessment for the Common Core State Standards in math, then you want to make sure you avoid letting anyone make the score interpretation mistake I describe in this post. Take a look at the data that comes from a school’s 2016 scores in mathematics.
I recently attended a full day workshop with Jo Boaler where she shared a different way of thinking about convincing someone from Thinking Mathematically by J. Mason, L. Burton, and K. Stacey. In the book, she identified three levels of convincing: Convince yourself Convince a friend Convince a skeptic I immediately realized that this…
In listing the Common Core State Standards’ three shifts, the authors define “Rigor” by stating that: “rigor refers to deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades. To help students meet the standards, educators will need to pursue, with equal intensity, three aspects of rigor in the…
It’s challenging to have a conversation about depth of knowledge (DOK) when everyone has different ideas of what it is. So, I’ve decided to refine how I distinguish between DOK levels and turn it into a tool that can be used to facilitate a conversation. The two-page tool covers topics from 1st grade through high school as well as topics ranging from number sense, fractions, geometry, probability, and functions. The pictures below give you a preview of the tool and you can download it by clicking the button at the bottom of the page.
When teachers begin to implement problem-based learning, several questions consistently come up and I have a slide to discuss them during my presentations. At the 2014 California Math Council (CMC) North conference in Asilomar, Michael Fenton mentioned that these questions would be worth sharing in a blog post. Anyone else think @robertkaplinsky should write a…
I wanted to share a resource from Tina Cheuk out of the Understanding Language department at Stanford University who created a very useful graphic organizer to show that the Common Core State Standards (CCSS) for Mathematics, English Language Arts (ELA), and Next Generation Science Standards (NGSS) have significant overlap and can be collectively implemented for…
I recently shared how I came to realize Webb’s Depth of Knowledge’s (DOK) importance and why I believe that it is critical to integrate these types of problems into our curriculum. I also expanded into how to distinguish between the DOK levels using specific examples that covered fractions on a number line, perimeter and area, and…
The most straightforward method I have found for distinguishing between the first three levels of Webb’s Depth of Knowledge (DOK) is to take a single mathematical concept and provide a problem at each DOK level. Here are three examples that illustrate the differences well using: fractions on a number line perimeter and area surface area and…
When the Common Core State Standards (CCSS) for Mathematics were written, the authors defined three shifts (coherence, focus, and rigor) to articulate “how the standards differ from previous standards—and the necessary shifts they call for.” The shifts are useful in articulating the big picture as to how things have changed. This blog post delves solely into…
How do the Common Core State Standards‘ (CCSS) description for how students are expected to demonstrate their mathematical understanding compare to the Texas Essential Knowledge and Skills‘ (TEKS) description? I wondered about that question as this summer I will be doing my first workshops and presentations in Texas. As I primarily work in California where…
I am no longer using these posters. If you are interested in a tool to help math teachers make sense of the depth of knowledge in mathematics, please check out this post with a reproducible handout for educators.
Today we found this problem on the Smarter Balanced Practice Test (Grade 8 – Question 15): It provided the basis for a worthwhile conversation on the importance of students having conceptual understanding. The problem is based on these 8th grade standards: There are two main ways to approach this problem: conceptually or procedurally. If you…
I’ll be honest with you: I remember first learning about Bloom’s Taxonomy when I was getting my teaching credential but I never really thought it was that big of a deal. I had a decent understanding of what it was and how you could implement it. What I didn’t get was why it mattered. As…
Articulating why the Common Core State Standards are such a big change for mathematics can be challenging, especially if your audience is unfamiliar with them, like parents and other non-educators. After all, isn’t it just changing the standards? Fellow educators also feel the stress, but may have trouble stating exactly why that is. How do…
How do you think 32 eighth grade students would respond to this nonsensical question: “There are 125 sheep and 5 dogs in a flock. How old is the shepherd?”* Take a guess as to what percentage of them would give a numerical answer and then watch the video below: Of the 32 students I…