*What are the 20 most important topics in each math class you teach that you would like for your students to remember for next year?*

*Please put your top 20 (or even top one or two) in the comments section below so we can build a working list!*

Every since I read “What is the point?” in one of Elissa’s posts I cannot stop thinking about how to help our students retain the most important mathematical knowledge that we are teaching them.

As math teachers we spend hours coming up with (hopefully) fun and engaging lessons. We want our students to discover and then understand the many math topics that we present to them. We feel successful when our students have the “ah-ha” moments in class and when we can tell that they really understand the concepts. High scores on end of unit assessments lull us into security that our students have really learned the material. Fast forward two months (or even two weeks in some cases), bring up the topic again, and your students have no idea what you are talking about. As seasoned math teachers, we know this will happen. It is why we “review” topics constantly. It is why we often do an official review of past material before teaching a new unit that is dependent on past knowledge. But it is still so frustrating! It is when we feel the least successful as math teachers. It is when we have the “What is the point?” moments that Elissa described. How could they have learned this material so well, and then forgotten it so completely? What happened?

First of all, you cannot blame the students. They are working hard and they do learn the information. However, think of how much they are learning each and everyday. Also, remember back to your school days and recall the learn and dump method, where you would cram all of the information that you could into your head and then purge your memory right after the test to start preparing for the next test in yet another subject. Honestly, think of all of the stuff that you have forgotten – even in your own subject area.

It is not the teacher’s fault either. We work hard so that our students will learn the material. We make up engaging activities and discovery lessons so they will actually understand what they are doing. And, we make up mnemonics and even songs to help them retain this knowledge past the test day. They are learning. However, we have to realize that they will not remember everything that we teach.

I want to improve this. Since I know that it is difficult for students to remember everything, I want for them to come away from my class understanding and actually *remembering* the most basic and important facts from my math class to carry with them to the next year. These are the facts that are crucial to remember for the next mathematics level. These are facts that are the most important to remember. And, even if they can’t remember all of these facts, I would love to give them a tool to help them remember these facts. I also want them to have easy access to this information so they can go, “Oh yeah, I remember that!” *before* the next teacher has to teach it – again.

The tool that I would like to design could be a “Math’s Greatest Hits” list for the year. I would like to compile the “Math’s Greatest Hits” list slowly over the year, adding to the list each time we come to a crucial concept. Ideally, I would like to keep this under 20 “math facts” so the students can keep it all on one page. I want the students to realize the importance of this list of facts and to have easy and constant access to this list all year long. Ideally, I would like for the students to even carry their list with them to their next math class.

My first thought was to expand upon the index card flip charts that we currently make, but add a twist. For instance, we could use colored index cards instead of white cards just for the “Maths Greatest Hits”. However, some of their earlier flip charts are already lookin pretty ratty. The list needs to be in a page protector to keep it durable and to make it seem more “important”. But then students would have to take the list out of the page protector to flip the index cards. I am afraid that to many students this will not qualify as “easy access”, but will fall in the “too much trouble” category and thus will not be used. So sadly I have realized that the index card method probably isn’t the most effective.

What may be best is one sheet of colored card stock for each student. I can print lines on the paper to divide each side into 8 or 10 sections. This will create room for 18 – 20 “Math Facts”. It would be in a page protector and students could pull it out to add to it, and have it handy for math lessons and homework.

I am not married to this idea, it is just the best one that I could come up with! I would love any and all suggestions. I want to create this list in the next couple of weeks.

** Please comment** to

- Give ideas on how you would design the “Math’s Greatest Hits” list
- Give the top “Math Facts” for your subject.

When I have time (hopefully before summer), I will compile all of these facts by subject and re-post.

It seems like greatest hits could be content (math results) or pedagogy (explorations). Content could be stuff like the three fundamental theorems that offer a chance to talk about what a theorem is, who some of the great mathematicians were, the idea of proof in mathematics, and the idea of structure. I think about my favorite explorations like the geogebra lab where students find the connection between pairs of reflections and rotations, discover the full Pythagorean theorem, or discover the meaning of place value.

I appreciate that you have broached this topic. It is very challenging to reduce an entire curriculum to only 20 ‘greatest hits’. For this reason I am leaning towards process skills that we can look for as students move from Kindergarten to Grade 12. I don’t know how we can assess student mathematical growth consistently, and with clarity, through school if we report on distinct concepts each term across the grades.

Our program of studies here in Alberta is based on the NCTM standards and the 7 process skills that we focus on are:

– communication

– connections

– mental math and estimation

– problem solving

– technology

– visualization

– reasoning

These are the skills that I would love my students to carry with them out of school into the rest of their lives. The more I reflect on these ideas I think that these are the ‘enduring understandings’ and the specific outcomes (standards in the US) are the context for learning.

Yes, those are great things that they learn. I am thinking more along the lines of 20 facts that can fit on one sheet. Some of the things I want to include for Pre-algebra are:

X x = 2x , x • x = x^2

y=mx b, m =slope b = y-intercept

To solve an equation, isolate the variable.

A few exponent rules

Each of these topics would have their own eighth of the page and a short example if there is room. The page wouldn’t even need to be divided evenly. Exponent rules would win more space.

Cathy,

I love that list of skills. The most difficult ones for my students are consistently connections and estimation. I encourage my students to think about what they are doing before trying to just apply an algorithm. I want them to connect the math they are computing to logic and use estimation before coming up with a final answer. So many times, they come up with answers that are not even reasonable.

I do not think it is possible to condense even one math grade into 20 topics. I tried that when I switched to standards based typed grading this year. I can’t even get below 40! Rather, I think of this more as 20 very basic facts, almost like the “baseline” information that all students need to know. It can be their “first point of contact” when they see something that is familiar to them, but they may have forgotten.

Every time a student asks me (again), “Is x + x = x squared?” I pull out the Algebra tiles that I keep on my cart and instantly they remember how we solved that problem originally. I would love for them to be more independent. So instead of relying on me for an answer like this, they first pull out their Sheet and see the Algebra Tiles they have drawn for this exact question.

As all ideas that I have, I just have to give it a spin and see how it works out for us in practice. I won’t know if it is a successful tool until I see that it really does help the students. Now to come up with that list….

Oooh I can’t wait to see your final compilation!

One skill my kids consistently struggle with in Algebra I is the difference between

-x^2 and (-x)^2

Not really understanding the difference in those two seems to come back to haunt them over and over!

Yes! That’s a great one! I got quite a few more from Sam’s #needaredstamp Twitter archives. I’ll get this together in the next few weeks and post the lists and pics of their charts. If you think of any more let me know!

This is coming from my observations of weaknesses that hurt kids in Geometry, Algebra 2, and Trig:

#1-17. operations on fractions

18. the pythagorean theorem (not so much the mechanics but knowing it’s an available tool whenever they see a right triangle.)

19. divisibility shortcuts and finding factors

20. operations on integers

I am really starting to think that the only thing I should teach all year are fractions, decimals, and signed numbers. These concepts seem so tough for so many kids. If I could really get these through to them in 6th, wouldn’t they be so much better off for the rest of their math career?

6th grade wish list:

Quick division (or just division!)

Fraction operations

Operations with decimals

Factors and multiples (GCF LCM)

Divisibility rules

Integer operations

Order of operations

Properties (especially distributive)

Number sense (not specific, I know, however being flexible with number manipulation would support all of the above)

I know you are requesting operations, however reasoning and perseverance would help with all of the above as well!

Also, as you said, students do learn all of the above however, retention is challenging mostly because they start getting everything all mixed up!