Carnegie Learning’s Algebra I Cognitive Tutor–a game changer?

I really want to understand this and I hope you can help me. Matt Townsley’s blog post and a recent direct marketing email from Carnegie Learning have got me thinking.

I’ve had an opportunity to read and share John Hattie’s research on Visible Learning in middle level endorsement classes and I do believe, overall, he’s onto something. There are hundreds of strategies or programs teachers can implement to raise student achievement. Some have greater impact than others.

Hattie’s research has taught me to look for the game changers–any strategy that has an effect size of 0.40 or greater is worth implementing. I’m not a statistician but I’m using that effect size to help me navigate through the maze of educational products being touted.

There’s been a lot of PR of late regarding the results from a study on Carnegie Learning’s Algebra 1 Cognitive Tutor. According to the research students grew from the 50th to the 58th percentile.

This is where I become confused. The research abstract states, “The estimated effect is statistically significant for high schools…” And the conclusions state, “The effect size of approximately 0.20 is educationally meaningful” (page 27).

I’m perplexed. The RAND research says this is statistically significant and educationally meaningful. Hattie’s yard stick would say it has low impact.

What are your thoughts? Can you clarify my befuddlement?


Assessing the 8 mathematical practices

Like Fawn, I’ve been thinking about how to assess the 8 mathematical practices. Eventually I will want to “grade” them, but at the start the students will need opportunities to practice the practices. In addition I can’t just let them practice without giving them feedback. So I’m going to use this ASCD resource to drive my formative assessments, It provides a great framework and walks through the entire process using the Boomerangs lesson, a high school MARS task.

As you can see the feedback is mostly through written questions. When I first read the section on suggested questions I was thinking, “They sound a lot like the 8 mathematical practices.” For example the issue of difficulty in getting started could fall under the math practice of making sense of problems.


These questions and my comments will hopefully provide the necessary feedback for students to improve on the mathematical practices, but I’ll have to do it on a regular basis for the feedback to be effective. Plus I’ll have to provide them with a rubric. Our district created this rubric for students and teachers.

practice tool

In the fall I’m going to focus on only two or three practices to start with, then add other practices. I’m stealing that idea from language arts teachers who use Six Traits of Writing. From what I understand middle school language arts teachers only focus on a few traits at a time.

What I’m also planning on doing is using this recording tool for anecdotal, informal observations. Sometimes I feel like a mad scientist walking around with a clipboard and jotting down my observations but I’ll have to get over it. The tool and rubric were created last month so I have not had a chance to take them for a test drive.

Assessing the math practices will be new to me. If you have experience or see some red flags feel free to chime in.


I’m beginning to get incredible feedback. Your comments deserve attention so I’m placing them within the post. Please continue to share your thoughts.

  • Assessing them is not about “can they” do a specific SMP, but “do they” and can they eventually do so habitually?–Just one of Jessica’s suggestions.
  • Reading their reflections not only gave me great insight into how the students believed they were using the practices but also how they were beginning to think about solving problems in general–Jennifer shared her blogged about journaling.

Would you solve this problem using the distributive property?

From McDougal-Littell, Course 2
From McDougal-Littell, Course 2

Let’s consider revamping this 7th grade problem as a task where the students plan a variety show:


Your group is planning the annual variety show, and you need to make some recommendations about how the time should be spent. The principal insists on 20 acts and the show typically lasts 2 hours.

You must also consider the following:

  • The combined set-up and take down for each act
  • Introducing each act by the host of the show

Provide 3 scenarios that will make the best use of the time. Justify your thinking.


Caveat: It is implied that the students should consider how long each act should be. Should I make it explicit and list it with the considerations?

If I present the problem this way I think the students will begin to recognize the “considerations” as variables. A problem  that has multiple solutions lends itself nicely to variables and the distributive property.

Am I leaving anything out?

Fostering questioning and curiosity

Dan Meyer’s post on The Unengagables prompts this response:

Students are curious. We just have to give ourselves permission to allow them to pose questions and wonder. A couple of years ago I asked my 7th graders to complete the stem “I wonder…”  The initial purpose was to create a Prezi

for fall open house, but I soon realized it would be more powerful to examine these questions throughout the year—and did so. Note: past tense.

Reading his post reminded me that I used to do this and I’m now asking myself why did I stop? 

Summer allows us to recalibrate. I’m going back to basics by reviewing Annenberg Learner videos to remind myself of the power of curiosity and discovery.  I’m also reading Mark Driscoll’s Fostering Algebraic Thinking. By coincidence both used the Eric the Sheep problem. I’m planning on using it and other curious algebraic thinking puzzles throughout the year.  

It’s a hot summer day, and Eric the Sheep is at the end of a line of sheep waiting to be shorn.  There are 50 sheep in front of him.  Being an impatient sort of sheep, though, every time the shearer takes a sheep from the front of the line to be shorn, Eric sneaks up two places in line. How many sheep get shorn before Eric?

I plan to tweak these activities into groupworthy tasks. Hopefully they will foster questioning and curiosity.