DOK, Depth of Knowledge, is the 4 levels of critical thinking. DOK 1 is recall, memorize, follow an algorithm. Honestly, the majority of the math book is simply DOK 1. Here is the rule or formula. Here is an example. Do 30 just like it. That is low critical thinking. It is how I was taught, it is hard to teach differently than you were taught. Wicked hard!
For the daily attendance question, I post DOK ZERO in the description. If I post it in Google Classroom, and I literally post everything in Classroom, I put the DOK level on it. “Copy this down.” That is DOK 0. If they do not have to recall it, it’s just copying so it does not reach the threshold of being DOK 1.
Check Off the Standards
The end of the school year is winding down so I spent time yesterday reading the list of standards for high school Geometry and seeing what I have not covered yet. I realized I had not yet gone over:
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
In an effort to get this checked off the list I created a GeoGebra activity for them to practice constructions.
Create a Live Session
When you create an activity in GeoGebra you have an option in the upper right to “Create class.” This really is a live session. Today I used this to have students follow along with me. (That is not how it is intended to be used.)
I Did ALL The Talking
As I am going through the steps on how to create a line segment in GeoGebra and how to use the compass tool in GeoGebra… I realize it is all ME doing all the talking. I am telling the students “click on this” now “click on this.”
As part of my doing all of the talking I attempt to explain the WHY. I am explaining that the point of intersection of the two circles is the same distance from the endpoints. And that we are trying to create an equilateral triangle which means the lengths are the same side so we use a circle to ensure that the distance is the same.
What my students heard
“Wah wah wah wah wah wah wah wah wah wah put a point here.”
In reading my directions for my assignment above I first notice I had a typo and it isn’t even grammatically correct. I won’t beat myself up about that. But I will beat myself up about thinking my students could explain the constructions on their digital portfolios. How the heck could they explain it when I did all the talking, I did all the thinking?? They just clicked on what I told them to click on.
What did I ask my students to recall? NOTHING.
What did I ask them to figure out? NOTHING.
What did I ask them to apply? NOTHING.
What did my students learn in this lesson? NOTHING. But hey, I checked off the standard.
Covering is not teaching
I know this. If the kids did not learn it, I did not teach it. I’ve said it many times and yet I fell into that trap.
Page 8 of the Standards
I teach high school Geometry in Kansas. Page 8 of the standards provides this guidance for teaching practices:
- Establish mathematics goals to focus learning.
Effective teaching of mathematics establishes clear goals for the mathematics that students are
learning, situates goals within learning progressions, and uses the goals to guide instructional
- Implement tasks that promote reasoning and problem solving.
Effective teaching of mathematics engages students in solving and discussing tasks that promote
mathematical reasoning and problem solving and allow multiple entry points and varied solution
- Use and connect mathematical representations.
Effective teaching of mathematics engages students in making connections among
mathematical representations to deepen understanding of mathematics concepts and
procedures and as tools for problem solving.
- Facilitate meaningful mathematical discourse.
Effective teaching of mathematics facilitates discourse among students to build shared
understanding of mathematical ideas by analyzing and comparing student approaches and
- Pose purposeful questions.
Effective teaching of mathematics uses purposeful questions to assess and advance students’
reasoning and sense making about important mathematical ideas and relationships.
- Build procedural fluency from conceptual understanding.
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.
- Support productive struggle in learning mathematics.
Effective teaching of mathematics consistently provides students, individually and collectively,
with opportunities and supports to engage in productive struggle as they grapple with
mathematical ideas and relationships.
- Elicit and use evidence of student thinking.
Effective teaching of mathematics uses evidence of student thinking to assess progress toward
mathematical understanding and to adjust instruction
8 Mathematical Practices
On every single section of the standards, including for Kindergarten, the list of “Standards for Mathematical Practice” are listed. THESE ARE THE STANDARDS! I can not say, CHECK I did a standard if the students are not doing these practices!
DOK 1 was DOK 0
Since I was trying to “check off the standard” (facepalm, goal should be to teach students) I devised a DOK 1 activity for the students to perform this task. However in reflection, my lesson was actually DOK 0. Teaching is hard. Tomorrow I will try to be better than I was today.
Yesterday I blogged how I created an Open Middle style math problem using Google Jamboard. Open Middle is DOK 2 and DOK 3 level math problems. I set up that task to require multiple attempts. I got that strategy from Robert Kaplinsky who is also the founder of Open Middle. He has templates on http://robertkaplinsky.com for students to show what is their attempts. This lesson went better.
In the image below notice that the student is on attempt #5 before figuring out a solution. Which is extra impressive since it took me over 30 attempts to find a solution.
This lesson starts with the students doing the thinking and engaging in some productive struggle. It tackles MP8: The students “Look for and express regularity in repeated reasoning.” Which goes along with one of my favorite youcubed quotes: “Math is about pattern finding.” Through strategizing the solution the hope is the students pick up on the patterns of how these values work together.
Lack of Confidence
Start a lesson with the students doing the thinking rather than me doing the thinking for them. I know this, so why did I start the other lesson with me doing all the talking and thinking? Frankly, a lack of confidence. My degree is in mathematics with an emphasis in statistics. I’ve mainly taught Algebra since 1999. I’m in a new situation, at a new school, with new standards, and with new tools. I feel that I am surviving every day as I figure out what all the standards are, making sense of them myself, and also trying to learn how to use digital tools like GeoGebra, Desmos, and MinecraftEDU to do it.
I knew this was going to be a challenge this year. I promised to give myself lots of grace and not to beat myself up and not to stress. But to be honest now that we are in the home stretch of the school year…. I am beating myself up and stressed.
I feel proud of myself for trying new things. I have learned SO MUCH! I really had no idea how to use GeoGebra at the beginning of the year (huge shoutout to Tim Brzezinski) and now I feel fairly comfortable with it… 8 months later. The last time I took Geometry was 10th grade (1992) and the math standards have changed since then. It’s a lot to take in for one year.
It helps me to get better when I reflect on each lesson. How can it get better? OF COURSE it can be better, especially this year.