Breaking the Mold Again

Continued from yesterday...

Unfortunately, the Pippens do not have website. Their e-mail is pippensconsulting@aol.com. One option that is available, is that they will do an audit of your math curriculum. They charge a flat fee of $1200 and require 18 different documents that you mail to them. They then analyze it, write a report, and make a recommendation of things to fix or change. I am curious as to what documents they require because I don't technically have a "curriculum". I have a textbook and whatever I make up to teach.

An interesting point that Sue Pippen made was that economically, the middle class is shrinking. Parents no longer want their children to do better than they did. Because higher levels of math are now required, parents use the argument that they didn't take algebra or geometry in high school and they are doing fine. Fine isn't the goal we're shooting for though. Food on the table every day is important but we want our students to be prepared for the present and future, for emergencies, for retirement, etc. Jobs that parents have now won't exist for their children. They can't expect to get by on the same solution that worked for their parents.

Another interesting discussion we talked about is strategies that teachers have and are not sharing with students. We develop ways in our head to figure out answers before our students can, but then we never teach them those strategies. At the moment, I can't exactly think of strategies I use, but I know the feeling of barely figuring out the answer before they're asking me what it is. Fortunately, the Pippens were prepared with mental math strategies to share! =)

Mental Math Strings. Start with a number such as "number of days in a week". Then add "number of dimes in a dollar" and subtract "number of ounces in a pound" . Now multiply by "number of inches in a yard" and subtract "number of millimeters in a centimeter". Finally, divide by "number of cups in a pint".What is the number?*  The idea is here is that you have all the steps listed on an overhead or Smart Board and only reveal one step at a time. By the end, all steps are shown and students can start over if they lose their place. I like what's going on here because students are mentally converting and then doing the math plus improving ability to hold things in short-term memory. They recommended starting with 4 steps in the process and no more than 7. I also like this because realistically, all students have access to it and it's also recognizing math that we actually use in real life.

Halving and Doubling. I have never noticed this but I love love love it. When you are multiplying, halve one number and double the other, then multiply. This works wonders on decimals! For example, 6 x 3.5. Half of 6 is 3 and double 3.5 to get 7. 3 x 7 = 21 which is a lot easier to figure out than the first problem. Let's do another just because it's fun! 20 x 6.5 = 10 x 13 = 130. They recommend starting this process with practice of just doubling and halving any number and then throwing in the multiplication.

Front-End Multiplication. I've never known the name of this strategy but it is one that I use a lot. It works great when multiplying bigger numbers. For example 524 x 3. First take 500 x 3 = 1500. then 20 x 3 = 60. Then 4 x 3 = 12. It's a lot easier to add 1500 + 60 + 12 in your head than to figure out 1572 with carrying and such.

Rapid-fire Warm Ups. Really like this idea as well. This idea is something you should start on Monday and continue each day throughout the week so that students can feel successful in the fact that they are improving. Say you are in geometry and are naming triangles by their side lengths. In a rapid-fire warm up, you would have students number their papers 1-8. Next, flash 8 different pictures of triangles rapid like, less than a second per picture. Then show the answers. Most students love the challenge of competition and this is a simple concept to implement.

Units. Pay attention to units because they tell you how to solve the problem. I never really noticed it but I think we all assume it. And maybe that's a key point: We can't assume that students assume what we assume. Anyway, we've talked about this in geometry. The formulas for volume and surface area of a sphere are similar and one way to distinguish is that r is squared in the area formula and cubed in the volume formula. And then when it comes to miles per hour or percentages, it becomes even more obvious (to us at least) that we need to divide.

Fractions. Obviously, I don't have much teaching experience so I've never had to teach fractions. I don't even remember how I learned them but they just come easily to me. The Pippens mentioned that in other countries, schools teach students the friendly fractions while our American textbooks are full of 17ths and 13ths and so on. I don't think students conceptualize fractions, they just attempt to follow rules. Oh wait, that's not just with fractions.

And surprisingly, even to me, I still have more to say = yet another blog post! And I haven't even started talking about the classroom activities. You're getting veeerrrrrryyy excited.



  1. I am getting very excited. This is great stuff!

    None of this is completely new to me, and I do share my mental math strategies in the classroom, but it's a great list to have all together like this.

  2. Maybe we can keep adding to the list. Any strategies you'd like to share?

  3. Joe,
    I think students at this age have a hard time generalizing anything, therefore the complexities of teaching Algebra exist. They want concrete, something they can use and understand and see.

    Not sure if I agree with your contention although I do see your point. The steps given are an example of things you could use. I think a better example would be strictly using conversions, or common fractions, or maybe breaking down a process you're currently using in class. The main focus is that students are doing mental math

  4. Dang it!! Joe and Kevin, I accidentally deleted your posts when I was trying to delete my own duplicate. Sorry!