At the end of last school year, I wrote down what the last concept I taught and assessed was for each class period. Here are the results:

1 Hr Geometry Concept 28

3 Hr Geometry Concept 28

4 Hr Algebra I Concept 25

5 Hr Trig Concept 28

6 Hr Algebra II Concept 21

7 Hr Algebra I Concept 21

8 Hr Algebra II Concept 20

How is it that in an entire year I only teach 20-28 concepts? That's 5-7 concepts per quarter which translates to about one concept per week or week and a half. That's terrible. And pretty consistent across all content areas.

Maybe it's the kids? Let's look at the current data for the first quarter.

1 Hr Geometry Concept 7

2 Hr Trig Concept 9

3 Hr Algebra I Concept 6

4 Hr Geometry Concept 7

5 Hr Algebra II Concept 6

6 Hr Algebra II Concept 6

8 Hr Algebra III Concept 6

Multiply those by four quarters and that puts me in the range of 24-36.

So it's not the kids.

Let's look at my teaching. Ideally, I introduce a topic through INB pages/lecture and then a handout/activity that pertains to the notes. Ideally, that means 2-3 days per concept. Which means I should be a lot closer to 50-60 concepts per school year.

I have only done INBs since last year. Let's look at some data from pre-INB

13-14

Algebra II Concept 39

Geometry Concept 40

12-13

Algebra I Concept 44

Geometry Concept 45

Algebra II Concept 46

I am getting worse over time.

Let's look at some other curriculums. I was recently introduced to the site http://emathinstruction.com that is aligned to Common Core and PARCC standards. Algebra I has 100 lessons. 100! That doesn't even allow for 2 days per concept. Algebra II is 107.

Engage NY Algebra II has 120 lessons and Algebra I has 105.

I am not even teaching 1/4 of what students need to know. But how are students supposed to master concepts in one day?

I have really been downing myself about this for pretty much my whole teaching career. This is the first year I have been able to back it with data but...I am not preparing my students for their futures.

Here are some possible causes:

- I'm assessing too much. I quiz over every concept and a unit test.
- Interactive Notebooks are slowing me down.
- I'm taking up too much class time with bell ringers.

Now what are the possible solutions?

I don't have a solution (I'm a pretty new teacher), but I can commiserate... I feel like it is taking me so long to get through things, but I still sometimes feel like I'm not giving my students enough time to really get it! I've wondered about my bell ringers... my principal commented in one of my observations that it was almost minutes into the 50 minutes class when we finished doing/discussing our bell ringer. That's definitely too much, but I feel like it's the best way to start the day.

ReplyDeleteI know what you mean. I feel like I am moving as fast as I can without leaving them behind but then when I look at numbers it's like I'm not doing anything.

DeleteHey girly! Possible solution to one of those causes--I quiz every 3 (rarely 2) concepts and I make them short, sweet, and to the point. This has me sitting at about concept 14 for this 9 weeks so maybe that could help?

ReplyDeleteMy quizzes are short too but I guess every concept is too much. But then again, I only had about 8-10 grades in the grade book. Ugh. I don't know.

DeleteMy Alg 2 students are taking quiz 17 tomorrow, and Alg 1 is taking quiz 13. I definitely feel behind, too. I feel like I can start picking up the pace now that students are understanding SBG. I want to try Brooke's idea of quizzing after several concepts instead of after each one. I also am not doing unit tests, so that saves me a few days throughout the year.

ReplyDeleteI'm looking forward to seeing what I can learn from the comments. Thanks for being so transparent about wanting to improve. Your reflections help me reflect on my own teaching.

I don't think you should feel too badly about going twice as fast as me ;)

DeleteHave you done a side-by-side comparison of what you call a "concept" vs what other sources do? Are yours more general than others? What do you consider "mastery"? (It's in our nature, as folks who where good at math to unconsciously expect students to have the same deep understanding of concepts that we do as adults who do this professionally. However, there are definitely elements of the standards that are focused on breadth rather than depth.)

ReplyDeleteI don't teach to mastery so I don't know what I would consider mastery. A concept is pretty specific for me when I feel like others are general and still move much faster than me.

DeleteAt the beginning of the year I created a day-by-day plan for the school year so that I would know how much time I have per concept. Which has been awesome for keeping me on track, but I have found that students are not able to retain a concept when it is taught over one day, and they are not able to retain a difficult concept when it is taught over two. I feel like most concepts need at least two days and the challenging ones need at least three. I want to teach deep understanding but it is difficult to do with the amount of content we are supposed to cover. I do not yet have an answer to the conundrum, but I am thinking about slowing down and picking concepts that are not quite as important that I am okay with skipping. I figure that if I can teach mathematical reasoning in a deep and meaningful way then hopefully they will be able to apply the same reasoning to unfamiliar concepts.

ReplyDeleteI agree completely Ben, I just thought Common Core was an attempt to teach less concepts in a deeper way. Guess I was wrong! I should attempt to do what you suggested, except how to know which version of standards to work with?

DeleteI teach 6th grade math and feel just like you- like we are flying through without any time to master OR in my case work on problem solving!!! But I have started doing a spiral review as our bell ringer at the beginning of class. It's 5-8 problems of skills we have already covered. That way they will hopefully retain them eventually. :)

ReplyDeleteShannon

It's much better to teacher fewer concepts well than to rush through a ton of them. If you've pared your courses down to the essentials that's something to celebrate! We have twelve priority standards this year for algebra 1. Some of those have sub-topics (one variable equations will be quizzed on both multi-step equations and absolute value equations). But the point isn't the number. The question is, are there topics you aren't teaching that are important? If so, share those and think on how to re-prioritize.

ReplyDeleteI wish I could take credit for paring down my course but it's really just me only getting through a 1/3 or 1/4 of my course pacing guide. There are definitely topics I'm not teaching that are important because apparently I am barely teaching anything. Not sure which topics are most important and belong in what course.

DeleteThat's a real question we don't have a good answer to. In an ideal world you'd sit down with K-12 math teachers and divvy up the topics and prioritize certain ones. If you live in the real world you probably have to look at a mandated exam and look at their priorities.

DeleteI think what you're doing is great. My advice would be to say BUMP THE CURRICULUM and keep doing what you're doing.

ReplyDeleteBut that's not very practical. Maybe you should just quiz on major concepts and not EVERY concept and roll in more than one concept on your quizzes.

Maybe take a more general approach to your chunking, but you'll be missing some critical pieces.

There isn't a viable solution other than stretching out the school and/or removing some grade-level standards.

I think what you're doing is great. My advice would be to say BUMP THE CURRICULUM and keep doing what you're doing.

ReplyDeleteBut that's not very practical. Maybe you should just quiz on major concepts and not EVERY concept and roll in more than one concept on your quizzes.

Maybe take a more general approach to your chunking, but you'll be missing some critical pieces.

There isn't a viable solution other than stretching out the school and/or removing some grade-level standards.

I just sent a text to an old colleague asking him how many units he's gotten through and we both exclaimed how we feel like we haven't gotten through anything. I'll be lucky if I cover 4 units in a semester in each of my classes. Not sure how many concepts that is, but I know that my Alg II book, for example, has 14 units. Yeah...not gonna happen.

ReplyDeleteI realized I made one mistake at the beginning of the year and that was teaching the first unit in each book, aka the Review Unit. I'm not going to do that next year. It was just too many random concepts that had nothing to do with each other and was supposed to go quickly but I basically ended up reteaching all the concepts and was just horrible in each class.

And I also am battling the fact that every time I give a reflection to my students, I have many in each class who say the thing I should do to help them learn better is to slow down. How can I afford to slow down?!

There's also just so many amazing resources in the #MTBoS that I just want to try all of them and that ends up having one concept going over 2 or 3 days (I'm on block scheduling so double that for regular periods).

I wish I had an answer for you, but I'm going through the same thing myself. Let me know if there's anything you find that helps!

-Marissa

As a pre-service teacher I find myself very nervous about not preparing my students adequately. The more classroom experience I get I find that I am getting more of a glimpse of the realities of teaching. I know realize it is 100% unrealistic to expect students to be continually engaged and even if they are it is partially out of my control the speed at which each student grasps and masters material. Thank you for being very transparent about your challenges. This sort of informal data collection is a very helpful tool for me to use to monitor my progress as the teacher from year to year.

ReplyDeleteJust don't compare yourself to me- I obviously do not have this figured out!

DeleteJust don't compare yourself to me- I obviously do not have this figured out!

DeleteDo you have co-workers at your school who also teach any of the subjects you teach? It would be great if you could have this conversation with them and decide together what the essential standards are for each course you teach.

ReplyDeleteSince you teach courses that are in sequence, you probably already have a good idea of what prerequisites students should have for each course. Use those ideas to decide the essential skills for previous courses. Also, look into just how deep you need to go with each skill. I've been looking into Algebra I/Algebra II a lot this year and I realized that I actually went deeper into some standards in Algebra I than was expected. I could have used some of that time to devote more to the statistics unit, for example.

I'd be interested in continuing this conversation as my current job has me looking more closely at curriculum than ever before.

I have no co-workers, I'm the only math teacher and I have five preps. I do not have a good idea what prerequisites students should know because I'm not even sure what standards go in which course. I also don't know how deep I am supposed to go or how to even find that out. Every time I think I have covered a standard, I see a question or problem that I would never have thought to pose to my students. So even though I may have taught it, I didn't teach it correctly.

ReplyDeleteI'd be interested in continuing this conversation too since I don't know where to find any answers.

Thank you for having the courage to share your frustration with what we are teaching in math now. I returned to teaching after several years of parenting to discover 7th grade standards now include concepts that used to be high school. Yet students haven't mastered the foundation skills well enough to use rational numbers accurately. I used to wait until the end of the year to teach negative numbers in pre-algebra because I found my students were developmental better able to work abstractly. I am trying to figure out how to meet my students where they are and also show progress on standards that seem out of reach for my typical math students.

ReplyDeleteWe are starting the 19 week of school and in one of the curriculums I am using, I am only on week 7! I teach bell to bell every single day, no free days. How can I be so far behind? Every curriculum that I've tried gives material to be covered in one class period and I have yet to master that- same as my students I suppose.

Delete