Geometry and Measurement in the TEKS
TEKS Treatment Transcript
ROZEAN: So one of the task of this assignment was to sift through the paragraphs of the Texas Essential Knowledge and Skills, specifically relating to Geometry and Measurement. So that is what will follow so if you are looking for a thesis of this video that follows. It is that, from the very time a kid begins Kindergarten, what we are doing is building up these mathematical concepts that deal with Geometry and Measurement. They actually, when you follow through, you begin to see that they actually are supporting the Pre-Calculus course, which is the senior level class and eventual graduation. So that is what I am going for here. The goal of our education system should be high school graduation. If it is not that then I really don’t know what it is. The goal is not graduation from Kindergarten, to graduate from elementary School, to graduate from middle school. The goal is to graduate from high school because those are the skills that we want our citizens to have. So if you look through these Texas Essential Knowledge and skills, which we are about to do, as tedious as it is, it becomes clear that we are supporting high school graduation from the very time students enter Kindergarten. So, the analysis is as follows.
ROZEAN:
So what we are looking at is Chapter 111 from the Texas Essential Knowledge and Skills for mathematics, subchapter A, Elementary. We are looking at Kindergarten skills right now. We are just sifting through to see what we got. We are looking for instances of Geometry and Measurement. Here we go, “2-dimensional shapes, circles, triangles, rectangles, spheres cubes in the real word,” “two and three dimensional. “We are identifying attributes. And we are classifying. We are sorting. Using two dimensional materials to make these shapes. We have length, we have capacity, and we got weight. So these are attributes. Then we got another comparing two objects, then looking at more or less.
ROZEAN:
Now let’s look at the next grade, looking at grade one – symbols, diagrams, graphs, organize. Communicate mathematical ideas, communicating mathematical ideas is something recurring all the way to Pre-Calculus. This is something that is clear all the way through the TEKS. Then we have comparing objects again. Now we’re just going to look through here just a little bit more. Now we going to go. So at the bottom of the screen you going to begin to see the New Zealand curriculum This is just to remind us that these TEKS are pretty common and universal throughout the world’s curriculums. They do coincide with the New Zealand curriculum as well. Make connections and relationships. These are the things of Geometry and Measurement. These are the things that help us to quantify our world. There we see attributes – Geometric language, shapes, so what we have done is expand those special quadrilaterals, well we don’t use that word yet, but that’s what we are going for. We throw Rhombus and Hexagons in there.
ROZEAN
Ok, we are going to speed up a little bit, but in the fourth grade, the big thing here is that we are using formulas to calculate perimeter and area. So let’s move on to the fifth grade. So as we go through these grades what we are doing in progressive with the fractions and decimals and getting more and more precise and stuff. And if you’re looking at fifth grade we are up to a thousandths place. So that is very significant. Our attributes of those things that we are describe through characteristics are becoming more and more precise. IN addition, a very interesting thing is that there is something that was never covered while I was in elementary school is the hinting to the linear equation. That was something that I never learned until high school. But as I said before, we are starting to use equations to describe Geometric concepts, so what where are getting is support for Algebra and things in Algebra and of that nature. So let’s just kind of skip ahead here, and go on to the sixth grade.
ROZEAN:
So we’ve made a pretty big jump here what were talking about here is the transition from elementary to middle school – fifth grade to sixth grade. So what we are going to see is more equations. But lets just sift through the paragraphs for just a minute here. So I had said earlier that, in the introduction, that elementary and middle school grades are all supporting the ultimate goal of graduation. And If I were to overlay these middle schools within the curriculum of the high school I would have to say that 6th and 7th grade are something like Algebra mainly. And we will start to see that some of these grades are actually more focused on Geometry as well. Sixth grade is very related to functions. And if I were able to overlay it, these are some very basic introduction of concepts that support the function concept in high school. Let me just say that the function concept in high school contains graphs, tables and mapping and one-to-one relationships and proportionality. And yes, it goes back to Geometry. And we have to remember what we originally said was that the basic Western math concepts of abstract math comes from Euclid’s Elements and the idea. So it is really hard to separate Geometry from Algebra. So it is really hard to say, “oh I like Algebra” or “Oh I like Geometry,” because they are really just one in the same they are just different ways of looking at the same thing, that’s my opinion anyway.
ROZEAN:
Were going to go and skip ahead here to seventh grade, and let me say that that grad is more of the same of sixth. And what we are dealing with is a buildup to the concept of a function. A lot of linear stuff going on there. A lot of mapping a lot of tables. A lot of things of that nature. So that I say that 7th is supporting the concept of a function, which is building to Algebra 1, 2 and eventually Pre-Calculus. Another interesting comparison is that when I was in middle school, this function concept was only covered in more advanced high school course, so we have come a long way. What we are starting to get to is the slope of a linear equation – rate of change, which is a proportion, which goes to distance and time, and back in the elementary years where the students were first learning about time. Showing a relationship of attributes. So what where are getting to here in the 7th grade and the middle school years is that we are starting to relate those two measurement and Geometry concepts which is another way we attribute and assign characteristics of the world.
ROZEAN:
And now skip on to the eighth grade. And I am going to have to pretty much say that the 8th grade is the Geometry course in middle school. It goes very much into proportions. It goes very much into these definitions – vertices, sides, shapes, perimeter. . .It also goes into that old concept of the x and y, which was kind of touched on in earlier classes, the x-y coordinate, the plane, that thing that students have trouble understanding as compared to a piece of paper that goes on forever in all directions. So we are getting into the slope of a line, and we are getting into the y=mx+b stuff. These are all Geometry concepts, that’s Algebra that coordinate Geometry. So that’s where we are heading on that one. So all these things consideration, you just can’t forget about Geometry. That is what I’ve been trying to say through this video. That Geometry is the basic building blocks of all these math concepts. The linear equation is about rates of change. What is a rate, it is distance divided by time, those are two measurements that go back to Kindergarten and that is very related to Geometry.
ROZEAN:
So lets just look at Algebra 1. And I am going to have to say that even though is has the title is Algebra there is still a lot of Geometry in there. Because there is a log of these equations that the students are dealing with are actually the formulas for volume, area, perimeter, circumference where you are solving for variables. The big thing in Algebra 1 is coordinate Geometry. So now we are at the sophomore year which is high school Geometry. The big thing in Geometry, I suppose, is the coordinate Geometry because the Texas curriculum has a lot of focus on linear equations. A big thing is finding the slope and equation of parallel and perpendicular lines. But in Geometry there are things that area specific to Geometry such as the transversals, angles and special right triangles. You get into the special right triangle in 8th grade, but is really important because you what you built upon in 8th grade is critical because in high school sophomore Geometry because you start to work with more complicated numbers such as irrational numbers. These things make it a little more complicated, as a little higher level. And you going to have to use all your concepts to piece things together bit by bit. You solve this part of the equation and that leads you to the next part. It’s not just solving the Pythagorean Theorem solving for a, b, or c. You actually going to have to identify the right triangle then work forward part by part. You are using everything and the problems are much more complicated so that 7th and 8th grade concepts are critical for success in the Texas curriculum.
ROZEAN:
So now where are at Algebra 2 which is a junior level class, so the question might be, how does Algebra 2 have anything to do with Geometry? Look right here, problem solving model – models – and we also have communicating mathematical models, also have communicate through symbols, diagrams, graphs and language. All these things are Geometry and Geometry provides those mechanisms for communicating mathematically. And of course measurement. We see communicate mathematical ideas, communicate mathematical ideas, through written and oral communications. Measurement leads to Geometry and Geometry leads to mathematical concepts. So in isolation, Algebra 2 seems very un-Geometry-like, but if you take all the pre-requisite skills that we built up through the previous grades, through the previous TEKS years; it is very Geometry-like and it becomes clear that our goal is high school graduation and making it through these high school courses.
ROZEAN: So were going to end up in Math Models, which is my favorite class to teach because it applies all those things that we have learned in school and applies it to the real world. Again, we have models, and the concept of modeling things and using the tools of math and we are applying these things to a real world situation. Proportionality, population growth and decay, and you know that is what came up in the New Zealand curriculum. Science and Engineering. Geometric Transformation. Right triangle relationship is something that you cannot get away from, especially if you’re going to go to college. And as I said, this course is all about applying mathematical concepts to …that’s what love about this course…and then there you have music…what does Geometry have to do with math. And this course goes back to what I’ve been saying all along Geometry and Measurement as it provides the basis for these things. And then we look at scale factors, that’s a very Geometric concept of proportionality. And what you have here is what we were talking about with measurement, and in those middle school years were saw how measurement is actually related to statistics. And statistics is best explained in the “shape” of Geometric concepts – scatter plots, dot plots, stem and leaf graphs. All those things….very Geometry stuff. Then we have regression models, so we are going back to that linear function stuff. That slope, that rate of change, those are the reasons that I really love this course, Mathematical modeling, because it really tells you what is going on with the real world, and I wish the course was more wide spread use. It is sort of presented as an alternative to Pre-Calculus, and there is a certain situation. I feel that this course can be used as a sort of tool to help students figure out what they want to do. So this will help us transition to the senior level course Pre-Calculus.
ROZEAN:
So now we are going into the dreaded Pre-Calculus course. This course may seem so far away from what we have been discussing about Geometry and Measurement. Remember the line? The line that goes on forever in both directions. I think that we should use and emphasize the infinitely symbol earlier and more often. Because from that symbol, we are showing that a line can do that. Maybe that might help to understand this concept of a line . Then you can transition that concept over to the definition of a plane. This symbol is a mechanism that shows us this weird concept of infinity. It communicates that to us. Notice that paragraph 4 says “Number and Measure.” I thought we were finished with measurement. We are still measuring things in Pre-Calculus. We are measuring angles, locations, circles, distance, all those things…Relationships, proportions, etc. Those are those things that we originally learned in the previous years going back to those early years in grade school. So now let’s try to conclude this thing.
ROZEAN:
So there is not really much to conclude. There is no need to communicate further. I think we have pretty much demonstrated that the TEKS from those kindergarten years all the way through elementary, middle school and high school, all those prerequisites are there to support graduation from high school. And that about it. Graduation from high school is the goal Texas public education system. If it is not that then, I don’t really know what it is. That’s what I believe it is and I think we have demonstrated that as well.
