Cool Math site

I thought this was applicable for all those people out there like me who said (in a whinny voice)
"Where am I EVER going to use this???"

http://www.youcandomaths.com.au/

The video is ... well... just awesome!

About Rubrics

I found this website good for getting a larger view of "rubrics" and their use in education:
http://learnweb.harvard.edu/ALPS/thinking/docs/rubricar.htm

BC Principles of Learning

- learning requires the active participation of the student
- people learn in a variety of ways and at different rates
- learning is both an individual and a group process

from http://www.bced.gov.bc.ca/resourcedocs/k12educationplan/k12program/k12prog_02.htm

I "heart" Math

I never thought I would say that (and the results of my test may not reflect that - sorry I missed class!) but I took "Math for Elementary Teachers" this summer and had an amazing experience. Finally there was someone who made it make sense - not in getting a particular answer, but in how to approach Math. I had Sarada Herke as an instructor and the "lightbulb moment" for me was in how she got us to see Math as a "language" and not just a bunch of number/digits. She would often "translate" math into english and for someone who used to think "I'm not good at Math" this was something to which I could relate. I may not "get it" right away, but now there was a path to getting there. My math learning in school was very much rote so when trying to help my son in the past it was like I was trying to search the databank back there in my memory rather than understanding how it works/how to translate it. By the end of the class (3 weeks was too short for me!), I wanted to proudly wear an I "heart" Math t-shirt even if I only got a c+ - the enthusiasm for "getting there" was firmly planted and hopefully I'll be able to instill that in my future students!

Math...eeeeeek!

Hello,

Ok...so I'm maybe a little let on getting on here, but better late than never!

Math has always been a subject that I have dreaded ever since day one. I am very much of a visual learner and I guess the approaches taken by my teachers when I went through middle school did not involve much visual learning. Much of the exercises where a set of questions on a page that we had to solve with the right answer (of which there was only one) and get to that answer with the right process (of which there was only one)! As I got older, my grades in Math continued to plumbet, and this is not because I wasn't a good student. I received A's throughout middle school and high school in all subjects, but Math. As I mentionned in class, I was taught that there was only one answer and one way of getting there. All this changed for me when I found out that I was required to take two intro Math classes in university in order to meet the requirements of the PDP program. Well, needless to say: I was terrified! Would you believe me if I told you that I passed both classes with an A+ and and A. I know, I know...it seems a little ridiculous coming from someone that received a mercy pass in her grade 12 Math class in order to graduate, but it's true. I was put in a class with an instructor that took a completely different approach to teaching the subject. All of a sudden there was more than one good answer, more than one way of getting there and when I asked if I was right on something she would ask me things like, "What do you think?" The nerve of this women!! What a difference it made though, I then, for the first time, felt confident in what I was doing and felt good about my abilities in Math. Do I dare say it...I think I might have actually liked Math!!

Been given the opportunity to reflect on my own work and given guidance on other possibilities opened my eyes to the potential that I had in this subject. If it wasn't for this professor I think that I would have probably enter this class with the same attitude I have always entered Math classes with, that being annoyed, frustrated, and bored. I am happy to say today that Math is now one of my favorite subjects and is one that I have indicated that I would like to teach to middle school children with the goal of making them feel like they can acheive too!

I look forward to learning new teaching technics and learning processes that I can utilize and pass on in order to acheive that goal.

Problem Solving

I thoroughly enjoyed reading both Aimee's blog and Kelly's. Both talk about engagement and ultimately problem solving as opposed to rote memorization. Has anyone heard of the term....."Rote Learning" Tell me what that means please, somebody, anybody!!!!!!!!!
This is a good time to mention and talk about the very important BC Principles of Learning......has anyone stumbled across them.....if not, try to stumble and find them.....very important.....often on interview questions by principles....should know them before going into the schools!!!!!!!!!

Love the Book!

I have been reading through Chapter 1 of our textbook and have enjoyed it immensely. My experience with Math has been largely negative, and people who know me well tell me I have a Math phobia. In the early part of the Chapter, the writers state: "If minds are not actively engaged in thought, no effective learning occurs" (Van de Walle, Lovin 2006). This was what I recall a lot of my math experiences consisting of. In grade 3 I remember (with dread), doing "Math Minutes", in which the entire class was timed while we did a sheet full of multiplication questions. There was no time to think or engage, all I was required to do was regurgitate the answers that I was supposed to have memorized. Unfortunately I was not terribly good at memorizing things, so I often cheated off the girl who sat next to me (ahhhh, big confession!). But all this to say, that I never really experienced any math class in which I was "actively engaged" with what I was doing or that allowed me to experiment with "problem based tasks" (2006).

Another thing I noticed about what I was reading is that a lot of what Van de Walle and Lovin advocate as being good ways to teach math can apply to any subject that is taught in the classroom. The idea of a "Mathematical Community of Learners" and the four principals that are needed to help this flourish (see page 6) are applicable to any subject.

Anyways, those are my random thoughts...

I was thinking of procedural and conceptual learning and then turned to my eldests math learning arc. She started in a montessori preschool and went to a montessori school for her primary years. There she learned math concepts almost exclusively by use of manipulatives. where I learned multiplication by rote memorization of times tables, she used what they called 'cube chains'.

She spent HOURS working with those chains, skip counting to huge numbers (9 cubed, 10 cubed) playing with patterns and learning in this beautifully sideways manner.

Then she went to a public school where she was cruelly introduced to math minutes. Now, where in montessori, she might have had hours or days to immerse herself in a task or concept, she was expected to work in 3 minute chunks and complete things as fast as possible, rush in fact.

The result was awful that first year, and in fact the teacher gave me 'remedial' work for my daughter to do over the summer. ugh.

Then something happened, she 'got' something and things started to fall into place after that transition year. She hasn't looked back since.

If i see procedural and conceptual learning on a spectrum, one on the left and one on the right, i had been measuring them as equal and opposite, and unidirectional with the ideal starting at one extreme with the goal being the other.

Now I dont think that's true. at the montessori school, a student was given many concrete tasks, but not always given the tools to extrapolate to the abstract, at the public school the same student was given timed activities. Neither situation was inappropriate, what was missing was the motion, from one type of learning to the other, and that was reflected in her horrible transition.

Yaaaaa,I think I have it.

Ok, I think I am getting the hang of this. Sorry for the double of posts but I am still learning about blogging. Well what a beginning, man I was feeling very overwhelmed until I put all the due dates in my planner. Man it seemed like everything was already due, yesterday. Cheers, Elizabeth.

Conceptual vs. Procedural teaching

I knew there was something missing! My eldest son struggles somewhat with Math, and I believe it is because he has missed the conceptual piece of the puzzle in the areas that he finds problematic. He often misses steps when solving a math problem, or gets things (like place value) backwards and mixed up.
As his mother and tutor, I have tried many times to get him to slow down and back up. We have had cheerios and smarties out many times to create the "groupings" that Dr. Clarke taught us about today.

What is frustrating is that many of the teachers he has had, do not seem to spend enough time teaching and exploring the concepts in Mathematics. They seem to be in a hurry to put pen to paper and move on to the next learning outcome, rather than solidifying the understanding of the concepts by using manipulatives and the other teaching strategies that Dr. Clarke spoke of today.

I am encouraged that the approach to teaching Mathematics has evolved to integrate dialogue, groupwork, drama, as well as other strategies in order to help students better understand Math concepts.

First Day

I am so impressed with your deep and reflective comments about teaching and learning. Did I share this statement that I saw in the gym one day:
If you always did what you always do, you will always get what you always got!!!!!!!! How does that relate to math teaching????

I second many of the comments already made. Working together on problems is like taking something linear and opening it into 3 dimensions. It surprises me how many ramifications this has - for instance, it removes the individualistic competitive instinct that is so deeply ingrained from old-style learning (not just in math).

I love ways that any lesson can involve kinetic experience- using our "name numbers" to have us move around the room and divide into even/odd/prime/composite #s was a breath of fresh air. Furthermore, within each group we helped each other remember what a prime # is. Hurray - brilliant!

I also appreciated Santosh's story about math as a reliable, predictable subject for a child struggling with English as a second language. It's so important that we be aware of individuals' needs for a comfort zone; stretch it without snapping it.

The math competency test we were given - wow! That was scary! I did well in math, yet I felt the stress kick in immediately. Fear of failure, especially if those around me don't fail! (There's a great way to raise people who don't know how to be part of a team!) Collaboration is great. At the same time I have a strong instinct to have students learn, for example, times tables - it's just so deep in me that one "has" to know that. I'm asking myself a lot of questions about my assumptions, and am curious about what changes in learning & thinking are happening with this generation that is growing up online.

New Math

All these things are important -- collaboration, problem-solving, learning where to go for help/answers -- BUT is it not true that children/young people know less (in terms of grammar, algebra, that sort of thing) and do more poorly than, say, college and university students in the past? Maybe I'm guilty of the teacher's worst sin (i.e. it wasn't like this when I was a kid...), and I'm going to be on guard for that as I go along. BUT what I'm saying is that I still think that kids need to learn stuff, to learn, for example, how to do the math, and to actually DO THE MATH. It's just so darn good for the brain... Maybe the old math (and English, etc.) also has some place. So MAYBE if we're learning how to teach kinds to learn (according to their various and individual learning styles), we still need to be rigorous about what they're learning and what we're teaching. I think we need to guard against laziness! In ourselves, I mean. Mental fitness is like physical fitness; you just have to keep doing it to stay in shape. Jill Britten at Camosun has a fabulous website (http://britton.disted.camosun.bc.ca/home.htm), all about how to teach math to elementary and middle school students. She incorporates history, geography, art (M.C. Escher) into her teaching exercises, as well as plenty of computer applets you can use for teaching, and that kids can use and access. Anyway, those are my thoughts. And I'm open to learning!

Wow! Kelly sured sumed the day up. I think I will just read her blog and keep notes.

digging deep

Somewhere deep down there I know I know what 1/4 x 5 is...

It is amazing that you can challenge yourself to recall information you learned 5...10...(shh) 30 years ago, and voila! There it is. It was actually a really empowering feeling to realize my mind still contains information it hasn't used in ... well years.

In some ways though, the ignorance and the difficulty is also encouraging. It puts us in the shoes of our students, who constantly think "I should know this! Everyone else knows this" and start to beat themselves up when they "lack" or "fail." Already, on day one, I have placed myself in the student's chair, and (like all that latent math know-how) know that these realizations will stay with me as a teacher.

My first math class

I learned that math has changed and that we now promote talking to solve problems because working on the process of problem solving is where the learning happens. Telling the answer stops the learning. As teachers, we need to be receptive as to when to provide the answer. We don’t want the wait to be too long nor do we want it to be too quick.
Teaching math is about more than just math. It’s teaching social interaction, listening, how to make eye contact, how to take turns, how to interrelate and so on.
As a teacher it’s always better to say, “This is really hard” than to say “This is really easy.”

First Day

Hi Class,
How was your first day of Math? What did you learn?
Santosh