Math musings . . .

[Michelle in MO]

One thing I've been thinking quite a bit about lately, in addition to writing (which still needs some improvement in our household!), is the subject of math, or rather, my teaching math.

All three of my girls have done fine with math until 8th grade, when they started Algebra I. At that time, my oldest was using Lial's Introductory Algebra, which I really like, and seemed to be doing well with it. I had her listen to the lessons with the DVT's and then do the lesson, usually split up over 2-3 days. I checked her work daily, but only mid-year did I find out she was struggling. So, we had to re-do about 4 chapters together.

The next year I had her do Intermediate Algebra, which was a big mistake. I should have recognized the signs that, by mid-year, when all the "review" topics in Chapters 1-4 had been completed, that the material was way over her head. I wish then that I had understood better that the math sequence, at least for our household, should have been Algebra I, Geometry, and then Algebra II.

Now I'm finding out that my middle daughter needs some review with Algebra I, and my oldest is having to re-do the 8th chapter in her Geometry text. So, even though I was good at geometry 30+ years ago, I'm having to jump in "in the middle", so to speak, and help her out.

I think my big mistake in all of this has been the following:

1) They tackle math first thing in the morning, when I'm doing chores. Even though I like to get those out of the way first, I still need to make teaching math my priority, even if the time isn't convenient for me. That is changing here!

2) I don't think I'm going to rely any more on promises from curriculum providers that a certain math program is "self-teaching" or that the child can learn everything they need to learn strictly on the basis of watching the DVT's or DVD's. I think there can be a false security there for the parent; at least there was for me. Both the Chalkdust program and Lial's have a DVD/DVT component, and I'm so glad they do, I'm realizing that my children's success in doing math well relies every bit as much on my being there to help them with their problems. Of course this can vary from child to child. Some children are naturally more adept at math than others and can work their way through very complex problems without his/her parent's help, but many children still need their parent there.

3) I also need to recognize the limits of my knowledge. It may become necessary to hire a tutor, which we did once a week, a year ago, when my oldest was struggling with Intermediate Algebra. If we have to do that this year, I'm going to try to find a good math student to come to our house and help us out!

Well---these are just a few of my thoughts and observations on the math situation in our household. I hope these help someone else!

[8FillTheHeart]

You have reached the same realization I did a few yrs ago. Kids need teaching. Or at the bare minimum, face to face interaction that forces them to verbalize what they are learning. Direct exchange creates ownership of the info. When they are simply listening and doing and never putting it into their own words, even when they are doing it all correctly, does not mean they can explain what they are doing.

It is the basic philosophy behind Bloom's taxonomy. You want them to be able to explain in their own words.....it means they have actually processed and synthesized the info. http://faculty.washington.edu/krumme/guides/bloom1.html

BTW.....I am in total agree about the limits of our knowledge. I do not want my kids to limited to my understanding. There is so much out there to be learned that I know absolutely nothing about. A person passionate about what they know can instill a desire in a topic that might leave me cold. My oldest son loves chemistry (I have always hated it!!) Good thing I found him outside teachers......now he is majoring in chemical engineering. My loves would have lead him to studying theology. :)

[Jane in NC]

I think my big mistake in all of this has been the following:

1) They tackle math first thing in the morning, when I'm doing chores. Even though I like to get those out of the way first, I still need to make teaching math my priority, even if the time isn't convenient for me. That is changing here!

2) I don't think I'm going to rely any more on promises from curriculum providers that a certain math program is "self-teaching" or that the child can learn everything they need to learn strictly on the basis of watching the DVT's or DVD's. I think there can be a false security there for the parent; at least there was for me. Both the Chalkdust program and Lial's have a DVD/DVT component, and I'm so glad they do, I'm realizing that my children's success in doing math well relies every bit as much on my being there to help them with their problems. Of course this can vary from child to child. Some children are naturally more adept at math than others and can work their way through very complex problems without his/her parent's help, but many children still need their parent there.

3) I also need to recognize the limits of my knowledge. It may become necessary to hire a tutor, which we did once a week, a year ago, when my oldest was struggling with Intermediate Algebra. If we have to do that this year, I'm going to try to find a good math student to come to our house and help us out!



Periodic assessments are necessary for me, so I appreciate the time and thought that you put in your list.

I would like to add some comments. First, I follow what I view as the traditional path of Algebra I, (proof oriented) Geometry, Algebra II/Trig, etc. Algebra and Geometry at the high school level are very different beasts and I think that the change is good for many high school students. It distresses me as a math teacher to see some skipping geometry or viewing it only as a course of practical formulae. Students learn not only logic in geometry but are also working on their writing skills. Proofs communicate information in a succinct and flowing fashion. The benefit goes beyond math per se.

Regarding the time of day your girls do math: my son used to do his first thing in the morning as well, but I regularly walk during that time. He has found it easier in general to wait until I return from my walk and am within easy communication distance to do his math. I always told my students in my classes that you need to try things in math, think about things, but don't bang your head on brick walls for too long. It is a waste of time. :banghead:
(I can now illustrate my point.)

My son just completed a chapter on exponential functions and logarithms. Students often have a problem with this material because these guys are a bit different for them. They don't behave like polynomials and there is a notational issue which seems to stump some. So I told my son that I did not want him to do his math until we examined it together first. I took five or ten minutes to walk through each section of the text before he tackled it. He needed help with a couple of proofs, but other than that he flew through it. I sometimes wonder if changing the methodology (more involvement on my part) made the difference or it is more of a developmental issue. His depth of thinking grows and improves weekly.

I recognized the limits of my knowledge with Conceptual Physics last year. I can figure stuff out but I cannot explain Physics well. My husband can wax eloquently on the subject, so I let him step to the plate. (Sorry that I am not closer to give you a hand, Michelle!)

Jane

[Michelle in MO]

is that too often I've made the mistake of relying on the promises of curriculum advisors that they would take over the teaching of math for me! Hurrah! But----that promise may not hold true for every child in every situation.

Let me use an analogy: Jon Krakauer, in his book Into Thin Air, which details the disastrous Mount Everest expedition that he was on with Rob Hall in May of 1996. Scott Fischer's (sp? could be Fisher) team was also involved. To make a long story short, one of the main conclusions Jon Krakauer drew from this experience was that too many "gentlemen adventurers" or "gentlewomen adventurers" were pursuing the dream of climbing Mount Everest. A pride or hubris accompanied these two expeditions and this pride was becoming increasingly part of expeditions to Everest in general. Climbing Everest was now something treated rather cavalierly; it could be purchased by a physically fit individual with a lot of money to hire a guide. Krakauer's advice? No one should be allowed to climb Everest with the use of supplemental oxygen. That alone would narrow down the field of climbers by a huge percentage. He felt that there was a false reliance on oxygen that lent climbers an air of "almost anyone can do it."

Without meaning to, in retrospect I feel like I had the same attitude towards reliance on DVD's and DVT's. (Thank God we weren't climbing Everest, although doing math sometimes seems like it!) I just want to encourage others of you who might be looking at DVD and DVT supplements for your math----please don't expect them to replace you as the teacher!

My analogy was perhaps a bit "over the top", but obviously I'm just using it to make a point. Believe me, I'm preaching to myself, first!

It's kind of like Jesus said to His disciples: "You know these things; blessed are you if you do them."