Didymath

Closing the Teach For America Blogging Gap
Jul 19 2013

#77: Taking a gander at the new Geometry TEKS

I’m going to take a break from breathing fire for a post and get into my summer plans: digging into the new state standards.

If you teach in Texas, our illustrious legislators approved changes to the Texas Essential Knowledge and Skills (TEKS) standards in 2012. Those changes will go into effect for the 2014-2015 school year. We have one more year officially with the previously adopted TEKS.

Me being the transformational(1) leader that I am, I’ve taken a look at the new and old TEKS and decided that I’m going to get a year head start and use the new ones. I’m finding them much more amenable to the skills-based grading approach I plan to take this year. More on that when I “finish” that project. Here’s what to look out for in the new TEKS:

Process standards. No matter what level of math you teach, elementary to calculus, the state wants you to do this:

(1)  Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

(A)  apply mathematics to problems arising in everyday life, society, and the workplace;

(B)  use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

(C)  select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;

(D)  communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

(E)  create and use representations to organize, record, and communicate mathematical ideas;

(F)  analyze mathematical relationships to connect and communicate mathematical ideas; and

(G)  display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

I am interpreting this to allow for more flexibility to veer outside of your content at your discretion as long as you are engaging in mathematical ideas. Sounds good to me!

Change in strands. The strands are the big ideas and can be considered analogous to units really. Here are the previous TEKS’ strands:

  • Geometric structure [1-4] – includes historical foundation, comparison between Euclidean and non-Euclidean systems, logic stuff, a vague allusion to construction and proofs.
  • Geometric patterns [5] – essentially, how many ways we can teach Algebra, plus some transformation and special right triangles and Pythagorean triples. Kind of a mess.
  • Dimensionality and the geometry of location [6-7] – A combination of three-dimensional topics and coordinate geometry.
  • Congruence and the geometry of size [8-10] – A wide-ranging strand which covers topics pertinent to circles, area of 2D figures, probability, triangle congruence relationships, et al. It’s all over the place.
  • Similarity and the geometry of shape [11] – Mostly scale factor, ratios, trig. Kind of an afterthought tacked on at the end.
Here are the new strands:
  • Coordinate and transformational(2) geometry [2-3]
  • Logical argument and construction [4-5]
  • Proof and congruence [6]
  • Similarity, proof, and trigonometry [7-9]
  • Two-dimensional and three-dimensional figures [10-11] – Application of formulas is a big one. File under “plug-and-chug.”
  • Circles [12] – Finally! A home of their own.
  • Probability [13] – Say, what are you doing here?

Specificity. I’m going to quote new TEKS G.2A and G.2B (2012) first:

…determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint…

…derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines…

Compare to something similar from the previous TEKS, G.7C:

…derive and use formulas involving length, slope, and midpoint.

Not only are there a greater number of TEKS standards, they are a touch more specific in what they are looking for. I think that the breadth of this course as laid out by these standards means certain topics may get the short shrift. I might save that probability unit for the end of the year and have some fun with it.

Contextual vs. non-contextual problems. These two terms appear nowhere in the high school math TEKS except in Geometry. In the introduction to the new Geometry TEKS, it reads, “In the standards, the phrase ‘to solve problems’ includes both contextual and non-contextual problems unless specifically stated.” The phrase “to solve problems” occurs in 16 of the TEKS. Note to self: problem-solving is really important!. I take the phrase “contextual problems” to mean our old friend the world problem. Non-contextual problem is “pure” mathematics, no pithy narratives with all the numeric content you need to plug into a formula (or two or three as is often the case now for STAAR).

I reckon my thoughts on the matter will change wildly when I actually implement the darn things next year. Also, I hope within the next two weeks to be done creating rubrics for my skills-based grading concepts. I will share them with you and throw myself upon your professional mercy at that time.

NOTES

(1) Google Chrome still does not recognize this as a word, by the way.

(2) There’s that word again!

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