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.
The pictures below give you a preview of what each page of the matrix covers. There are eight topics: one kindergarten, two first grade, one second grade, two third grade, one fourth grade, and one fifth grade problem. You can download and share a high resolution printable version by clicking the “Download PDF” button at the bottom of the page.
It is highly unlikely that there are no issues with this matrix, so please let me know if you have any questions, concerns, or comments by leaving me a message below. Also, if you’re wondering about where Depth of Knowledge level 4 is, those are usually represented by performance tasks or problem based lessons like the ones I have here. They don’t fit neatly into a matrix like this, so I haven’t included them.
Note that these problems focus on the depth of knowledge for the math content, not the conversation. None of these problems ask students to explain themselves, but all of them require increasing depth of math content knowledge to solve. You could easily incorporate some “Why?” and “How?” questions to make a more rigorous conversation.
If you like these problems and want to find more DOK 2 and DOK 3 problems, check out openmiddle.com. Open Middle is a collaborative website where all problems are free and new submissions are welcome. The more problems people submit, the more problems we all have access to. It was co-founded by Nanette Johnson and I with help from Bryan Anderson, Daniel Luevanos, and Zack Miller.
Hi Robert,
Your DOK chart looks great and I would like to explore it further. Over the past three days, I have followed the download procedure five times, recorded the required info, clicked on download and have not received an email with the attached chart. Any suggestions????
Kind regards,
[email protected]
Hi Debbie. I can see how that would be frustrating. Have you tried using a different email address that is not for your school? The most likely reason is that your school district has an aggressive SPAM filter and is blocking the emails. I’d try that and I’ll be it works. Let me know if you still have a problem.
Hi Robert,
These are great and I like how you’ve expanded the ideas. However, I am having the same issue as Debbie Schwantz is despite giving a work and a personal email. Any ideas?
Thanks,
Jana
Ooops! I see they were emailed to me.
Thanks!
Jana
Thank you so much for adding the second comment. Technology can be wonky at times, so I am glad it got figured out eventually.
You rock. Have been interacting in edchats on twitter once in a while, but don’t believe I have ever perused your blog before. I am always blown away by the amazing blogs teachers find/make the time to write. Thanks for sharing. I just downloaded and emailed both this post and the post about increasing the DOK of math items. I am a team leader for 11 public Montessori teachers of 3-6 year olds. We have received lots of resources, training and support on increasing rigor for ELA but none, really, for math or any other subject. People tend to assume that it should be easy for teachers to do this kind of rigorous questioning/practice in math, science and social studies. However my experience as a teacher trainer has been that many elementary teachers feel like they are not great at math and therefore struggle with new CCSS strategies as well as increasing rigor. Have provided PD & shared other resources (particularly love the books Good Questions to Differentiate: Open Questions & Parallel Tasks, Good Questions for Math Teaching K-5, 5 Practices for Math Discussions, and The Core Six) but often find that teachers just use the textbook & TE unless provided lots of guidance and structure.
Perhaps you could write a textbook?
Thanks for the kind words Teresa. I am glad that this was useful for you. I have actually contributed to the current HMH high school math textbooks on their module level performance tasks and contributed a problem to a Pearson textbook. Hopefully there will be additional opportunities in the future.
Hi Robert,
This is an amazing resource. I have been looking for great examples for K-2 especially. Do you know where I can find something like this for reading/English Language Arts in elementary (K-5)? Teachers need to see true examples so it is concrete. Thanks again for the invaluable resource.
Sheryl
Thanks for the kind words. Unfortunately, I don’t know of anything like this in other subject areas.
Hi Robert,
I was wondering where could I find information about your next presentation or conference. I would love to attend, and a team of teachers from my school. Also if I can contact your office to see a possibility for you to come to our school in Shanghai. It is the Shanghai American School.
Thanks Ana. I’ll email you about this.
This has been very helpful for me when teaching math to my first graders. I struggle with my current curriculum to get kids thinking critically about math and this has been a wonderful tool. Do you have any direction on where I could look that would give me practice sheets for my grade level? Time is of the essence in a teacher’s life and I could spend days making up my own examples for my students. Thanks for any help!
Carrah
Hi Carrah. Thanks for the feedback. I am not sure what you mean by “practice sheets for my grade level.” If you mean additional problems, check out what Open Middle has for first grade here: http://www.openmiddle.com/category/grade-1/. There are currently 12 problems for 1st grade.
If you mean the Open Middle worksheet, you can download it here: http://robertkaplinsky.com/resources/
If it is neither of those, let me know what I am missing.
This example seems to be a misunderstanding/misapplication of DOK. It seems to be using DOK as a linear model in order to assess individual student growth.
Thoughts?
To be DOK 1-student got one of the 2 problems wrong on the half sheet or student got both problems correct on the Baseline half sheet, but missed #1 OR #3 on the DOK 2 and 3 paper.
To be DOK 2- student must have #1 and #3 or #5 correct
To be DOK 3-Student must have gotten #1,3, and #5 correct, plus #2 OR #4
To be considered for DOK 4-Problems #1-5 on the DOK 2 and 3 sheet all need to be correct.
To be DOK 4- They must have all problems correct
Hey Bret. Is there an image or something you are referring to that is missing?
Sorry, the example is in the statements below:
To be DOK 1-student got one of the 2 problems wrong on the half sheet or student got both problems correct on the Baseline half sheet, but missed #1 OR #3 on the DOK 2 and 3 paper.
To be DOK 2- student must have #1 and #3 or #5 correct
To be DOK 3-Student must have gotten #1,3, and #5 correct, plus #2 OR #4
To be considered for DOK 4-Problems #1-5 on the DOK 2 and 3 sheet all need to be correct.
To be DOK 4- They must have all problems correct
Sorry, the example is in the statements below:
To be DOK 1…
Example is below “Thoughts?”
Based on the limited information I have, it doesn’t seem like that is what was intended by Webb’s Depth of Knowledge.
Hi Robert!
I’m working on a blog post about making data and statistics more meaningful to K-6 students. I’m using the DOK matrix above (page 1) and referencing the third column.
I’m wondering about the value of deleting the numbers on the y-axis for DOK2. And about removing the numbers and the categories from the graph in DOK3. I think this adds more choice to students and also requires them to read each others graphs more deeply and talk about the different choices they made. It’s this type of structure that makes Numberless Word Problems so much fun.
Just a thought of something I’m noticing and wondering. Thanks for all the amazing resources.
Hmm. Those are interesting variations. I haven’t used that problem with students yet so I’m not sure how it would affect the problem. If you get a chance to try it out, please let me know what you uncover. Thanks!
I sure will! I just wrote a blog post about it here using your matrix: http://undercovercalculus.com/making-data-matter-more-1/
On there (near the bottom) are links to Numberless Graph problems I’ve created using the ideas coming out of the work of Brian Bushart (and others).
Thanks Chase. I like where you’re going with that. I appreciate you letting me know.
I, too, have been unsuccessful at downloading the DOK document. Any advice?
Thanks!
Try using a non-work email address.
Hi Robert Thank you for the great resource. This coming week is the new semester of Math for Elementary Educators. They are college juniors. Students seem to expect very parsed topics but I prefer to go broader as your DOK for Elem does. Do you have suggestions on how best to incorporate this? (cutting into strips for grade level?) thx
I like to just give the entire worksheet to people and let them choose at least two columns to work through, starting at the DOK 1 (so they have perspective) and then to the DOK 2 and 3. I have found that to work well for giving teachers choice. Thoughts?
I have a problem my 2nd grade kiddos are going to do tomorrow for a brief walk around with other teachers. It’s a VERY simple problem (the next one in our lesson) but I need to ask a question that shows depth of knowledge. How could I make this a level 3? 2 at best.
Mr. Wally’s class collects 36 cans for the recycling program.
Then, Azniv brings in 8 more cans.
How many cans does the class have now?
I was thinking of asking them to share with their partners: make a plan with your partner,, what operation will we need to use to solve this problem and what is the evidence to prove that it is the operation we need to use.