My math-teacher-friends get mad at me when I say things like, “I’m just not a math person.” I certainly understand their reactions because I get mad at myself — and my fixed math mindset! Although I had a number of really memorable math teachers from elementary school all the way to Calculus at UVA, I still remember the days of four digit subtraction problems (with borrowing) that sent me to doctor with a case of hives that took a couple of days to go away.

@kplomgren is good friend, a former classmate, a cheerleading and gymnastics coach, and a JuniorHighMathTeacherExtraordinaire at The Westminster Schools. Formerly an accountant with a Big Five (at the time) Accounting Firm, @kplomgren’s is a natural in the classroom. Her approach to learning (first), teaching kids (second), and teaching junior high students math (third), is truly remarkable. Although I’ve never taken the opportunity to sit in her class, I am so impressed with her approach to math instruction and realize that I need to overcome my fear of hives and multi-digit subtraction and pay @kplomgren a visit. The reason? She’s aware of what’s happening in the world of math instruction (think: Khan Academy) and is breaking away from traditional instruction to meet the needs of her students in an authentic, thoughtful way.

I asked her to share her reflection below…

*I initially started recording myself going through various concepts for a student-athlete in my class who misses quite a bit of instructional time due to training. Although no video can replace live classroom instruction, my videos would at least allow this student to keep up with the notes being taken in class, and in turn, complete the homework. Particularly with second semester, the material we are covering is no longer simply a review of what my students previously learned in elementary school. When I covered converting repeating decimals to fractions, I knew I would have to re-teach the lesson to this student in Office Hours when she returned. Since I teach 62 students, my Office Hours is often packed. Students come for help on homework, for me to clarify concepts, and for any other general questions. I am not afforded the luxury of spending 10 solid, uninterrupted minutes with a single student to re-teach a concept. In fact, if you divide my Office Hours time equally amongst my students, each one would receive approximately 45 seconds of my time per day.*

*So, when I had a few minutes of free time during the day, I would put on a set of headphones and record myself going through the notes. This is not repeating the entire 55 minute class period; however, it is me going through some of the main examples I did in class. *

And I realized, if I am doing this for a particular student to keep up when she misses class for training, why don’t I post this on my website (Moodle) as well? Couldn’t other students benefit from hearing me go through the examples again?

*So often, I realize that I teach things too quickly. I think I am constantly trying to manage a balance in my 6 ^{th} grade math class. Since we don’t differentiate our 6^{th} graders in terms of classes (Honors Pre-Algebra vs. Pre-Algebra) until the 7^{th} grade, I have a diverse group of learners in my classroom. I have some kids who wish I would move faster and give them harder, more advanced problems; however, I also have the other end of the spectrum, students who think I speak so rapidly that they have a hard time following what I am saying and doing. For those latter students, having the benefit of recorded notes, that they can listen to, stop, and replay at their leisure is invaluable.*

*I will say, recording notes isn’t always the easiest thing. Today, I made a 14 minute recording walking through commission and profit. I was really proud of my work. I thought I explained it clearly and articulately; however, at the very end of the recording, I made a simple mistake. Yes, even math teachers make simple arithmetic mistakes! When calculating the final costs in a profit problem, I said that $7,500 less $1,500 was $5,000. That was the last step of the problem, I hit “STOP” on my smartboard recorder, and the file was complete. OOPS!! It was supposed to be $6,000. I don’t have the technology wherewithal to know how to edit the video; how could I change the last part, yet save the other 13:45 of “good” video? Despite my perfectionist tendencies, I just left the video. I will explain to my students in class my mistake (maybe they can learn from it?!), and if I can find another 15 minutes in the next few days, I might consider re-recording the lesson. So that is a frustrating aspect. In an article I read this weekend called “Shifting from Writing to Videography,” I relate to what the author said, “If I say three bone-headed statements in a single video, I cancel those and start again.” *

Also, as a personal challenge, I have become more self-aware of my math “vocabulary” that I use.

*I didn’t go to school necessarily to be a math teacher, and sometimes I am self-conscious that I don’t always use the appropriate math terminology. However, learning and growing with my colleagues in the PLC has taught me a tremendous amount about this. For example, I made a short video on how to find a fraction in between two fractions (think: name a fraction between 5/7 and 6/7). One option is to multiply both the numerator and denominator by 10 (so you end up with 50/70 and 60/70). When I initially recorded it, I said, “just move the decimal one place,” when in fact, what I really meant to say was to multiply the numerator and denominator both by 10. A small tweak, but a pretty big difference in terms of number sense and terminology.*

*Despite my reservations, I do believe that posting recordings has been invaluable. *

My principal recently reported that a student spent her free time watching math videos instead of having story time with her parents. I was out for two days chaperoning my 8^{th}grade girls on a retreat; instead of depending on a sub to cover what I hoped they were capable of covering, I made a quick video of myself and had her play it in my absence.

*I can now spend 10 or 15 minutes recording certain lessons and when a student, who missed class, comes to Office Hours, I can refer them to Moodle. In fact, today, I had two students miss my first period class. Because I knew I would have to explain the concepts to both of them (and the chances I could knock it out at the same time was wishful thinking!), I recorded myself quickly going through the notes and posted it on Moodle. Then, when one came to Office Hours at 2:50, I could refer her to Moodle; and when the other one showed up at 3:15, I could also refer her to Moodle, all the meanwhile, continuing to help other students on homework and later supplement their understanding. *

As far as I see it, it is my responsibility to help these students know and understand the material, regardless if they are in class or not.

*Having the concepts recorded on video helps to reinforce the concepts for students who are in class, yet get those students who miss class up to speed. It is really a win-win for all, including myself.*

Here are a few examples of @kplomgren’s videos…

Megan,

This is very interesting, but I am somewhat weary of Kahn Academy and the movement to “flip” instruction.

I also wonder if your innate feeling of not “being a math person” is more because of how it was taught in traditional instruction. There’s a right answer, and you get it by following the right algorithm that is taught to you. “borrowing” and “carrying” are key examples of these algorithms that have been shown to have deleterious effects on student’s understanding of mathematics in elementary school.

Here are three posts about Kahn and Math teaching that do a great job of summarizing my thinking.

Kahn Academy and the Mythical Math Cure

Kahn Academy algorithms and autonomy

Kahn academy is an indictment of education

Finally, there’s some research, at least in science, that having students watch videos of explanations/problem solving doesn’t help their understanding. The way to help students learn from videos in science seems to be having a character in the film present the wrong explanation, and then working through to the right one. Surprisingly, although students report these “mistake” videos as much more confusing and difficult to follow than the “right” explanation ones, the “mistake videos lead to quantifiably more understanding. You can find a great explanation of this phenomenon here:

Kahn academy and the effectiveness of science videos

My big takeaway from all this isn’t whether video instruction is/is not effective, but that we really need to think about what it means to learn math and science in the first place, and once we’ve decided that, decide how best to teach it.

John,

Thanks for your comments (and for the links to the very interesting posts about videos, math/science, Khan Academy). A few thoughts…

As I think back to my “math days of yore,” I especially remember feeling behind in terms of skill understanding. I loved the application of the math (I even enjoyed word problems) but it took me a bit longer to understand certain pieces — ones that (in my opinion) would ultimately make math puzzles whole. I spent a fair amount of time in various teachers’ office hours, at the Math Set, and also working with father, the accountant, at the kitchen table. I was waiting to be taught because I wasn’t quite sure how to learn (interestingly, this was really only the case in math not in science). The “one size fits all” pedagogy that I experienced didn’t take into account that students learned in different ways and at different paces. If I had a few more options, I may have been able to make sense of some of the things I was learning. Part of my appreciation for the work that @klplomgren, Khan, and all of the others who are flipping their classrooms is rooted in their willingness to think differently about instruction, students, and a subject that so many kids love to hate.

I certainly don’t think what they are doing is the “cure,” but I do think it’s an interesting step that only enhances students’ learning and teachers’ thoughtfulness about what’s happening both in and outside of the classroom. You’re exactly right when you say that “we really need to think about what it means to learn math and science in the first place, and once we’ve decided that, decide how best to teach it,” but my argument is that schools (especially middle schools situated between traditional elementary instruction and high stakes high school math/science courses) aren’t in a place to throw the baby out with the bathwater. They are, however, in a place to think about how best to use instruction time in order to combat the issues that Meyer raises in his TEDxNYED talk from last March:

1. lack of initiative

2. lack of perseverance

3. lack of retention

4. aversion to word problems

5. eagerness for formula

(link: http://www.youtube.com/watch?v=BlvKWEvKSi8)

Specifically, with @klplomgren’s work, I see that she is doing her best to combat Meyer’s #1-#5, and I suspect that these videos are only stepping stones…not only for the teacher but also for the students. It’s certainly not the radically divergent path in terms of math curriculum/instruction, but on the well-worn path of one-size-fits-all, it seems like a pretty good step in the right direction.

I’m just so proud to call two such fine educators and human beings my dear friends!! And seeing that I failed math in 6th grade at the same school where Katie teaches, I have nothing of substance to contribute to the discussion 🙂

Maybe if I had a teacher like Katie through out my schooling I would have felt differently about math. Kudos to the realization that some students may need to hear things in a different way to truly gain meaning. Also, taking your valuable time to record your notes and put them on the moodle shows such dedication to not only your students but the profession as well.

Here’s the latest post in the series by Sylvia Martinez , president of Generation yes, and the author of the the posts critiquing Kahn academy and the view of math instruction it presents.

“Don’t we need balance?” and other questions about Khan Academy

I think Kara is right that we need to recognize that students need to hear things a different way. I’d go even further and say students need to

do things in a different wayto really understand what math is about. While I don’t want to criticize anyone for making videos that students find helpful, I wonder these videos are helping students to see that math is a creative endeavor where students can develop their own approaches to solving a problem in the very same way that they can write their own thesis statements about Romeo and Juliet.For more on this, I would also suggest reading math teacher Paul Lockhart’s wonderful, wonderful essay titled A Mathematician’s Lament. This is a passionate critique of math education today, that has implications for all of education.

A few thoughts on the posts regarding Khan, “flipping,” and the like.

Seems to me that nothing will replace a good teacher in a “classroom setting.” The thing is the classroom doesn’t have to be four walls, with desks, computers, and SMART boards. If our view of the classroom is extended beyond what we have experienced, then videotaping a lesson, recording a lesson, Skyping a lesson with students far away, etc. are merely tools in the toolbox to engage students and help them learn.

If Khan Academy works for some students to learn math in ways they couldn’t in their typical classroom, then so be it. I would rather my child learn math from a teacher in real time, but if she needs help with a concept and gets good feedback from Khan or Katie’s instructional videos, that’s OK with me.

For me it is more about having a diverse set of tools in the toolbox to engage students. A good teacher is able to construct a lesson using lots of different tools that draw students in. Always trying to be aware of the student who is not being engaged. What to do?

I do worry about the idea John raises about teaching through presenting a problem with mistakes and letting students come up with the right path or process. Good idea and probably works well in the hands of a very good and well-trained teacher. I would worry about using that technique without some training.

All of these ideas are worthy of a workshop on instructional strategies. Maybe the CFT could run such a workshop in the summer. Anyone game?

Bob Ryshke

Center for Teaching