4. Reflections of the First Nine Weeks

Reflections of the First Nine Weeks: Structures and Resources

This We Believe (AMLE, 2010).

* Educators use multiple learning and teaching approaches. Multiple Learning Approaches

The first nine-week grading period ends Tuesday. It is hard to believe that I have been here for nine weeks. On the other hand, I feel like I have been part of this family my whole life. Some of my former university students want to get together. They will be student teaching in January. Prior to meeting with them, I decided to create a list of structures that worked for me this nine weeks.

a) Homework. I believe homework should reinforce what students know. I don't think students should do much on their own until they know enough of the basics to be challenged; if they keep doing things wrong over and over, it may reinforce bad information and bad habits. I give homework on Monday and it is due on Thursday. This allows my athletes time to complete their homework before a Wednesday night game; it teaches students to budget their time; and in my county, students can finish their homework before Wednesday night church. Because homework reinforces concepts, and stretches their knowledge, it is not dependent on what we do in class. I have been surprised at how many students are actually doing their homework. I chose one week each month to calculate the percent of homework completed. The following illustrates the percent of students who completed their homework on time:  August: 88%; September 81%; October: 62% 

Yay for August and September. Hmmmmm. I was at the middle school conference the week of October 7. I wonder if being gone influenced student participation?

b) Quizzes. I give quizzes every Wednesday. Quizzes are between ten and fifteen problems. Students have to show all their work. This allows me time to score the papers and prepare for remediation work on Thursdays, and allowing those who were successful to do enrichment - a modified version of "differentiation". It is called mastery learning and I find it very beneficial to helping those who struggle to get the remediation they need, and those who do not struggle to be able to learn additional content. So, after the first test, if a student failed, on the following Wednesday, the test included new material as well as previous week's content. If students successfully complete the previous week's work, with at least 80% accuracy, I move last week's failing grade up to an eighty. Those who are not successful (I have about eight EC (Exceptional Children) students who really struggle.) The lowest test grade they receive is a sixty.

c) Projects. This nine weeks, I gave two projects (Both are described at the end of this document.) The first project was to find real-life examples of slope (positive, negative, zero, undefined) for the standard students. The following is one of the pictures a student chose to illustrate a slope of zero.

Algebra students had to create a booklet or Power Point on what slope is and how to calculate it. The following is one of the pages from another student.

Slope is the steepness of a line on graph or stuff in real life. You can find steepness or slope by using y₂-y₁ over x₂-X₁.

The second project was called "The Mathematics of Me". There were three parts to this project. First, students had to choose a favorite number, tell why it is their favorite number, and give factors, prime factors, and multiples of the number.

My Favorite Number: Sample 1

            My favorite number is 210. This is because when I was in 3rd grade we had a candy corn guessing contest where you guess how many candy corn are in the jar. I guessed 210 and I was closest (there were actually 225) so I got the jar of candy corn. It sounds cheesy, but it was the first thing, that I remember, winning. Factors of 210 include 1,2,3,5,6,7,10,14,15,21,30,35,42,70,105, and 210, the prime factors are 2,3,5, and 7. Three multiples of 210 are 420, 630, and 2100.

My Farovite Number: Sample 2

My favorite number is definitely 16. This is my favorite number because when I am 16, I will be able to drive, date, and have a job. I will also be in my junior year of high school which means by then I would be in my 5th year of band.  

Next, they had to make a number line with 2000 in the center, mark three decades prior to 2000 and three decades after 2000. Their task was to write down three events that happened before 2000, three events between 2000 and 2015, and three events that will happen in the future - after 2020 (the year they graduate). The following example is from a student who loves to draw.

The last task was to choose three numbers that describe them, and tell why.

            “Three numbers that relate to me are 7, 24, and 2002.  The reason the numbers relate to me is because those numbers are my birthday.  I love these and I have known them for 13 years.  These numbers are also near my sister’s birthday and I will always remember these forever and ever, and I will never forget them!

I learned so much about my students. I learned of tragedies, ‘the year my father died;’ the birth of siblings, ‘bobo was born;’ their successes: “I met my bffs” (best friends forever) and their dreams: “I hope to go to be a teacher,’ “I want to get my license so I can get a job and help my family.”

d) Progress Reports. At the end of four weeks, I printed out their grades. Our state uses a program much like Engrade.com (a web 2.0 tool for recording grades). I gave them the following week to complete missed work. Those who completed their work, received partial credit for their efforts (I grade standard math students on effort; I grade algebra I for accuracy).

Today is the last full week of the first nine weeks. For the last two hours of school, we gave them time to complete any missed work. About twenty students were in my class diligently working away... Those students who had all their work completed, watched a movie about the Biltmore House (We are taking them to tour the Biltmore House in November). Interestingly, I had several students who didn't want to go watch the movie. They stayed in the class and read or worked on other things. In addition, three girls made pink and yellow ribbons for all of the team members for next week’s breast cancer awareness, “Pink Wednesday”.

d) Finals for the nine weeks. I haven’t always given a “final exam.” Usually, I just keep testing on Wednesdays. This year, I separated our final exam into four parts: expressions and equations, the meaning of slope, calculating slope, and for algebra students, Systems of Equations and for standard students, Pythagorean's theorem. Each part totaled 100 points and consisted of between 10 – 15 problems. The total number of points for the final is four hundred. The following is a breakdown of the average for each of the topics follows. As you can see, the average drops when students have to calculate slopes (standard students) and solving systems of equations for the algebra students. These skills will continue to be reinforced.

e) Students reflecting on the first nine weeks. Today I had students describe their comfort level on each of the final exam topics (A copy of the format is at the end of this document). I had them choose work from their folders, including this week’s finals. They had to choose samples of their successes or struggles with the content. I also asked them to evaluate their behavior for the nine weeks. Finally, I asked them to set an academic goal and a behavioral goal for the second nine weeks. Parent Night is November sixth. It is my hope that students will be able to share their knowledge using these resources. In middle schools, this format is called a "student-led conference".

f) Finally, seating charts are your friend. I find that moving students around breaks up the “dendrites”. (: haha;  I heard a session on ‘what connects dendrites’ last week. .. movement, language, art, music…). I find that when students get too comfortable, they begin to socialize more than focus. Moving them around breaks up their comfort level and allows them an opportunity to pay closer attention. On Wednesdays, I always move the desks into test formation (rows); on the other days students are in groups of two, three, or four. Note: I have found that my lowest students need a lot of structure, and so while I move students around, I try to keep these students in the same place.

Resources

Slope Project

You are to create an illustration of four types of slopes: positive, negative, zero, and undefined. In addition, you are to write an equation for the slopes you find using y = mx + b (slope-intercept form). A sample of this was when we drew images of the flag pole, the hallway, the steps, and the path to the soccer field. You may create this in a booklet form, a brochure form, or a powerpoint using images you take photos of.

The Mathematics of Me Project

This week we are looking at real numbers. There are three parts to the project:
1) (Whole/Natural) Choose a number you love "my favorite number" and tell why it is your favorite number (one paragraph). Include factors, prime factors, and three multiples of your favorite number.
2) Create a timeline (integers) to illustrate decades on either side of 2000
-30 - 20 - 10 0 + 10 + 20 + 30
On your timeline include (in words and illustrations) the following:
3 events that took place before 2000
3 events that have taken place between 2000 and 2015
3 events that you hope to take place after 2020
3) Choose 3 numbers that relate to you. Write a paragraph describing how these three numbers relate to you.

Rubric: All three are complete and illustrated (10); Most are complete (9); Some are complete from each section (8)
Turn them in by the 8th.

First Nine Week’s Reflection Tool

Dear __________________ (Put the name of the person who would want to see this.)

During the first nine weeks we studied seven topics. For each topic I have shared how I did. Attached to the document are examples of my work. If I struggled, I have shown how I corrected it. On each document, you will see what I know.

I have added notes to each topic to give you information about how we show our work.

For each topic I have rated my understanding with an

Excellent, Good, Okay, Need Work

Topics:

________________  My Ability on Evaluating Expressions

Expressions – this is where I have to be able to substitute a number for a letter such as x = 7 in the expression  3x means   3 * 7 which is 21.

________________  My Ability on Solving Equations

Equations:  Solving equations are very important in the math world! The equal sign separates variables and numbers. Our job is to combine “like terms”, use opposite operations to get variables on one side of the equal sign and numbers on the other, then to use opposite operations to solve for the variable. Here are four samples:

3n =  24                  2w  +  7  =  21               3(x + 4)  =  32            2x – 4  = 5x  +11

________________  My Ability on Identifying the Slope of Lines

We then studied the slope of a line: Positive, Negative, Zero, Undefined.

(Students will add images.)

________________  My Ability on Calculating Slope

We are able to calculate the slope of a line using right triangles and using an algebraic expression (y₂ – y₁)/(x₂ – x₁).   Look at the following example using the ordered pairs  (4, 2)  and (-3, 5)

(Students will add images.)

________________  My Ability on Calculating the Equation of a Line given points, slopes, y-intercepts

Next we looked at lines and slopes to learn how to calculate the equation of a line. Every straight line as a unique equation  y = mx + b  where m is the slope and b is the y-intercept.  Here is an example:

(Students will add images.)

________________  My Ability to Solve Systems of Equations

We also looked at solving a system of equations. A system is when there are two lines on a graph. The solution is the point (an ordered pair) that makes both equations of the line true. We learned how to do this by:

Graphing

Substitution

Elimination

(One way we did not learn is with Matrices… more to come on that.)

________________  My Ability to use Pythagorean’s Theorem

Finally, we are looking at solving for distance and midpoints of lines using

Pythagorean’s Theorem.

(Students will illustrate this concept.)

The following is how I would rate myself regarding

___ Paying attention in class

___ Participating in class without disrupting others

___ Doing my homework regularly

___ Studying for tests.

My goals for the next nine weeks:

·      Academic Goal:

·      Behavior Goal: