Posts Tagged ‘Algebra’

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Linear Wars – “Destroy the Death Star!”

March 26, 2011

A cool game idea S and I just developed for either 1 or 2 players:

Each team is given a 4-quadrant grid with several enemy ships positioned at different locations around the origin (the Death Star). Before the student can shoot the Death Star, he and his partner must take out all of the opposing fighters. Each student takes turns rolling two different-colored dice. These are their two coordinates. The student then spins a spinner to find out which quadrant their point is in. The student then selects a fighter to shoot and determines the equation of the line from his point to that fighter. The students take turns blowing up the fighters. If a student’s coordinate lands on a fighter, he loses his turn. When all of the fighters have been eliminated, the students can roll one more time to blow up the Death Star.

Linear Wars

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Commutative Property Fail

August 14, 2010

WordPress won’t let me embed the post here, but I think I’d like to use this as an illustration of the commutative property.

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Algebra I EOC Success PD

August 13, 2010

For the last two days, S and I have attended the Region XI training on the new Texas Algebra I EOC test. On the one hand, it was good to get some training on this test, since we will be going live with it next year. On the other hand, the state board has still not finalized the test yet, so we really have no resource materials for the test.

Things I Liked

Organization of the lessons
The sample lessons we worked through were well-thought-out and even practical. They were all organized around the 5E Instructional Model: “Engage, Explore, Explain, Extend, Evaluate”.
Each sample lesson included a copy of the lesson plan, which again, was well-organized.
The activities were not lame. In fact, several of them were quite clever.
Differentiation
This was the word of the day(s). For each lesson, the presenters offered ways of assessing, and then differentiating the lesson for ELL or slower students.
Problem-Solving Boards
This laid out the problem in terms of the “See-Plan-Do-Reflect” model. There were actually three levels of differentiation on this: one board could be completely blank, one could be partially filled in, and one could be partially filled in and given a word bank. Very cool.
Slopes
For this activity, we could print out a transparency of arrows that slower students could use to see how the slope changed.
Domain/Range poster idea

Things I Didn’t Like

Teachers are some of the worst students.
I sometimes had trouble hearing the presenters because my fellow teachers were talking so much.
The presenters were not always courteous either.
It’s one thing to fuss at those teachers who were just making general conversation; it’s another thing to cut off productive conversation. This happened several times until one teacher finally spoke up this morning. One presenter was very snarky about waiting for us to get quiet, which, while understandable, was not helpful.
Line dancing
Repetitive format
While I generally liked the lesson format, it did get somewhat repetitive doing four lessons over the course of two days. I know it was helpful to analyze the previous TAKS questions, but we were saying the same things over and over.
What was the purpose of the Day 1 data analysis?
At the very beginning, the first presenter had us analyzing TAKS data. We looked to see how many objectives had 85% passing (tier 1) and what how the passing percentages broke down more generally (80%, as I recall). This was interesting (if somewhat depressing), but I’m not sure how it was supposed to tie into what we did later on.

As I said, in general, this was a good experience (especially since I will get paid for it). I’m glad I went.

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My SBG Pitch

August 5, 2010

S and I will be meeting with B, the assistant principal regarding our proposed SBG schemes for Algebra I and Geometry. We had talked about just going ahead and doing it (better to ask forgiveness than beg permission), but since we don’t operate in a vacuum, I didn’t want to take the risk of having B find out after the fact and being blindsided. In addition, we have a good rep with the special ed. department because all of our scores went up last year. So …

I. What is wrong with the current system?

  • In the regular curriculum, there are homework, quizzes, and tests, which all count towards the student’s grade. There are several problems with this scenario:
    • Even when we only give completion grades for homework, we are still grading practice. It’s as if my old band director had graded me on whether I practiced my flute last night. Practice shouldn’t be graded.
    • Sometimes a student doesn’t understand something on the homework, and so he fails the quiz. Our current “solution” has been to replace quiz grades with test grades, but that practice doesn’t tell us whether the student ever mastered that particular concept. Nor does that give the student much of an incentive to learn the material.
    • Suppose we have two students who both made a 100 on the chapter test. Student 1 got all of the homework and aced all of the quizzes. Student 2 didn’t do most of the homework and bombed a couple of the quizzes. Because he came by for help, he caught on by the time the test was given. Why should Student 2 have a lower grade than Student 1?
    • Because math is always building on earlier concepts, a concept that a student may have bombed earlier is now easier for him. Too bad — the test has been given.
    • When a student makes a 75 on a test, what does that mean? Does it mean:
      • He missed 1/4 of the problems.
      • He got all of the problems right except for this one concept in which he missed all of the problems.
      • He understood all of the concepts, but he made some careless mistakes.
      • He really failed the test, but because he got the bonus problems correct, he made a passing grade.
      • The whole class bombed the test, so the teacher square-root curved the grades. He really made a 56.

II. What is different about SBG?

  • SBG stands for “Standards-Based Grading”, and while there are several different definitions for it, at its core it represents a change in the way students are assessed. In SBG, the important goal is how well the student masters a concept or skill, not when (or if) the skill is mastered.
  • The curriculum is broken down into a group of standards (or concepts, or objectives, etc.). These concepts are then taught and assessed. It is a much more itemized list than just “Chapter 3 – Parallel Lines”.
  • One of the key tenets of SBG is a more focused assessment policy. Instead of a “Chapter 3 Test”, there are assessments for each of the standards in chapter 3. Thus, we (and the student) can see that he really understands Angles Formed by Transversals, but he is weak on Parallel and Perpendicular Slopes.
  • Because SBG is more about mastering the concept than when it is mastered, students are allowed to reassess any concept they haven’t mastered. There are some practical limitations on this idea (end of the grading period, etc.), but it’s certainly more than they can do now.
  • As educators, we like to talk about teaching kids to be “life-long learners”. SBG actually provides a framework to help this goal. Because the concepts are so delineated, students can see where their weaknesses are. And because SBG allows for multiple assessments, students are encouraged to continue trying to build mastery.

III. What will our implementation of SBG look like?

  • We will generally be following the same sequence as everyone else (the same schedule we followed last year). Also, our focus on hands-on notetaking (foldables) won’t change.
  • The big change will be in the assessments. About every three objectives, we will give an quiz over those objectives and the three previous ones (every objective is quizzed twice, once at a basic level, once at a more advanced level). The sequence would be teach 1,2,3, quiz 1,2,3, teach 4,5,6, quiz 1,2,3,4,5,6, teach 7,8,9, quiz 4,5,6,7,8,9, etc.
  • Students will receive a grade for each objective on the quiz (six objectives -> six grades). Grades will be on a 0-4 scale.
  • 4 Demonstrates thorough understanding
    3.5 High level of understanding, but with small errors (computation, etc.)
    3 Demonstrates understanding, but with significant gaps
    2 Shows some understanding, but insufficient for a passing grade
    1 Attempts the problem
    0 No attempt
  • If a student makes the same or higher on the second assessment, that becomes their grade; otherwise, their grade is the average of the two assessments. Any student who has not made a 4 on the second assessment can re-take a quiz for that objective until he makes a 4.
    • Re-takes must be done either before or after school or during lunch.
    • Students may not re-take more than one quiz per day.
    • Students can either come by for tutoring or re-takes, not both on the same day.
    • If a student has a 1 or lower, he may not re-take the quiz without coming in first for tutoring.
    • The deadline for re-takes is the last Thursday of the six-weeks.
  • Our grading scheme is thus going to be:
  • Algebra 1 Geometry
    Quizzes 50% 60%
    Tests (6Wks and CA) 30% 30%
    Notebook Check 10% 10%
    Class Participation 10%
  • We don’t want to take a grade on the homework, but we want to give them some sort of incentive to do it. Therefore, we’ll give them a tenth of the percentage of the homework that they do as a bonus grade (if they do all the homework on time, that would add 10 points to their grade).
  • Because we’re eliminating the chapter tests, that gives us at least 12 additional instructional days for the year (the test review days are eliminated as well).
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Draft Grading Breakdown

July 21, 2010

For my three classes:

Algebra 3

Type Percentage
Class Participation 10%
Quizzes and Presentation Problems 50%
Problem Sets 15%
6 Weeks Test 25%

Homework: Not graded, except for “Presentation Problems” which random students are responsible for presenting to the class.

Geometry and Algebra I

Type Percentage
Quizzes 60%
Tests 30%
Notebook/Spiral 10%

Homework: Not graded, however, students who do their homework on time earn points that will be added to their six-weeks average.

After talking with S, I’m pretty well settled on my homework scheme (and, if nothing else, reconciles me to making 10% of their grade be their spiral organization).

The Algebra I percentages may change after I talk with S, since this is really more her class than mine.

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Distributive Property

July 11, 2010

I just read a really cool idea on teaching the distributive property that I will suggest to S: Combo meals!

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Contemplations on Homework

June 29, 2010

I have never been fond of taking a grade on homework, which is why I’ve always done completion grades, and why I’ve eliminated the grade for it in A3. I’ve continued taking a grade because that’s what we’re “supposed” to do to stay in sync with everyone else. It’s occurring to me, however, that since we’re going off the reservation so completely with SBG that we might as well go whole hog and stop taking a grade on the homework.

Based on what I was seeing at the end of school, I think this would be a good thing, as I was able to nudge kids into passing grades just by knocking out some homework zeroes. Unfortunately, the kids who need the homework the most are the ones who are the least likely to do the homework unless it is incentivized by a grade. Grr.

Here’s what I’m thinking to blend these two ideas together. Count how many homework and warm-up opportunities there are during a six-weeks. Double the homework number — that’s our “Homework Hero” number? — and add it to the warm-up number. During the six-weeks, students get 2 points for homework done on time, 1 point for homework turned in a day late, and 1 point for doing the warm-up. At the end of the six-weeks, total up the points, divide by the total possible, and add 1/10th of that percentage to their final grade. There’s no penalty for not doing the work, but it can definitely help their grade (someone like Maria would be able to pass with a 60).