I’m Placing a Hit on the Pseudo-Context

This robs students of everything mathematics should be…


  • The “real world” connection
  • The step-by-step procedure
  • Circle the numbers you need to solve the problem
  • The pseudo-context word problem.
  • Lesson 19.2 infers that this unit is front-end load with procedures and formulas

What a sham!

I can’t help but ask the question FOR students, “When will they ever use this?

As if that wasn’t enough, the “real world” problem is followed up with mind-numbing practice…

Screen Shot 2016-02-14 at 9.25.28 AM.png

Notice that question #7 has been labelled as “H.O.T.”

Instead of going on a rant, I’ll keep my head down and continue to do my best providing alternative opportunities for students and teachers to engage in math.  The Fish Tank and Got Cubes are two examples that push back on pseudo-context questions and volume.

As for Mike’s DVD box, H.O.T question, and curriculum developers, I’ll offer this new task as a means to undo the limited understanding you promote with every edition you pump out.


Question: How are the sugar cubes packed in the box?

There’s no empty space.


Number of Cubes in the Box

I’ll let students play around with the dimensions for a while. Then I’ll share this video of me putting in the last cube.


Now students have two dimensions and know the total number of cubes.


How the sugar is packed

As a potential extension I might ask if this the most cost efficient way to box the 198 sugar cubes. Sure it dives into middle grade standards but it seems like a natural progression.

I doesn’t seem forced and that’s what I’m after.

About gfletchy

K-8 math consumer trying to listen and learn each day. Stay thirsty my friends!
This entry was posted in 3-5, 3-Act Tasks, 6-8, Against the Norm, Cheese Mover, Intellectual Need, Measurement and Data, Modeling. Bookmark the permalink.

21 Responses to I’m Placing a Hit on the Pseudo-Context

  1. debboden says:

    I hate those problems too, and also get so frustrated talking to others in my district that “love ” this type book “because there are so many real world examples “. We are piloting and just finished with CPM in 7th grade and are now using Big Ideas. One teacher at my school said “my kids just love this book”. I thought “No, YOU love this book .” Luckily the rest of the team loves CPM and doesn’t like Big Ideas. I’ll join your rant. Oh wait, I just did!!


    Perfect, but where are the units? Isn’t m x m = m^2 or ft x ft = ft^2? Don’t we have to know before calculating that a volume needs m^3 or ft^3? So WHY not sugars?

    • gfletchy says:

      Great point Renee. I’m continually talking about being precise but I haven’t done so in this case. Note to self: Attend to precision and identify units moving forward.

  3. Jennifer says:

    I for one, would love for you to expand on the bullets of what you hate. I teach high school and don’t like this either, but I hesitate to assume I know exactly why we agree…and quite honestly, I don’t often see much at this level at all! I’d love to learn more about your views. Your videos are fantastic!

    • Jennifer says:

      Ugh. Typing on my phone has made my previous comment typo-y. Please forgive my fat thumbs!

    • gfletchy says:

      Thanks for the comment Jennifer because you’ve made me realize that I need to flesh out my own criteria and views for what I’m looking for in a curriculum. I’ll start here but probably add more through a future post.

      I think a lot of it has to do with sequence and the way the content is front-end loaded with procedures. I’m a huge advocate of throwing students in a situation where structure and the need for it is limited…at first. Many times students are given formulas and models without ever being given an opportunity to derive the formula themselves or see a need for them (mathematical modeling). I’m interested to know, “How many curriculums start with the procedure?”

      Here’s a tweet with pictures for the next 3 pages after the one shared here in this post. https://twitter.com/gfletchy/status/698909135065214977

      As if giving the students the formulas upfront wasn’t enough, the textbook walks students through the problem step by step.
      And I really have no words for the fact that they have labelled problems as “real world”. For me, it tells students that everything they’ve engaged in up to that point is fake and irrelevant.

  4. Meagan says:

    These books drive me crazy! It is so frustrating to hear my administration say that we need to follow the curriculum with “fidelity” when I know it hurts student understanding. I am putting in frameworks as much as I can, but just keep talking about this! Thanks for the rant, it is good to remember.

  5. I couldn’t agree more! My district is starting a math adoption, and I’ll bet we’ll have some teachers who see this type of book and think it is just what we need. My hope is that your blog can give me some much needed ammunition during our process. Thanks!

  6. stamp36 says:

    You hit the nail on the head again Graham. These math text books are completely backwards. Getting teachers to see that there is no magic bullet resource is difficult. Swaying them to see that quality math tasks and deep content knowledge of the math is more important is a big part of my job and passion for me.. Many teachers I work with as a coach still are looking for a resource to follow step by step. I think it has a lot to do with lack of confidence in their understanding of the math plus possible direction they are getting from admin or boards. These types of textbook examples are like teaching a robot to input numbers when needed in the formula! LOL. Keep these coming Graham you are helping teachers everywhere!

  7. Joshua says:

    Here is another approach to fix the textbook page, using Dan Meyer’s “take away information” method:Polishing a …

    What do you think? Does it work?

  8. gerritam says:

    I love this post! What does H.O.T. mean anyway?

  9. Christy S says:

    My principal told me that I was to review a similar curriculum for a possible math adoption today. I told her I could give her my opinion without opening it, but I’ll gladly turn in that pros and cons list by the end of the week.

  10. @jamiedunc3 says:

    Nice! Or how about, “Hey kids, I have to send my mom as many sugar cubes as possible and I only have this one box! How many can I send her?”

  11. Sara Barring says:

    In these textbooks, are there any proofs of why that is the formula for the volume? Have you been in situations where the students have the opportunity to see a proof of area of a rectangle, or area volume of a rectangular prism? Do you think such proofs would be beneficial to the students?

    • gfletchy says:

      I see very limited examples of why the formula works but I think the most important piece here is for students to derive the formula/proof themselves. In doing so, students become able to reason and explain why and how it works every time. I believe that proofs play a big piece in solidifying student understanding but the proof or formula HAS to be students generated.

      Thanks for the question Sara!

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