Project Based Learning and its Implications in a Multicultural Mathematics Classroom Curriculum Component

Curriculum

Monday

• Do Now
  • Discussion
    • What are you all most excited about for when you enter high school?
    • How many of you want to go to college? Show of hands
    • Is there anything that you fear about high school?
    • What does it mean to “drop-out”?
    • Project introduction           
      • We will be exploring data from Nation Center for Education Statistics surrounding the graduation rates for public secondary schools for all 50 states and jurisdictions. We’re going to explore what these statistics tell us as well as what they’re not telling us.
      • Each student will receive a “school profile” describing which state the school resides in as well as the total number of students attending the school. According to statistic (use 2009-10), how many students will not be graduating? How many students will be graduating? What information is missing from these statistics? What does it mean to “not-graduate”?
      • Show the students the excel spreadsheet via an overhead projector.
        • What states are you all interested in looking at?
          • Pennsylvania
          • NY
            • I was part of the 2005 freshman class at a secondary public school in NY
            • I did graduate so I am part of this statistic           
  • What trends do you see?
    • What states are improving?
      • What does it mean to improve?
        • Percentage rises. Statistic is number of graduates in the freshman class – success and improvement is measured by MORE students graduating.
          • If we had the drop out rates being shown, success would be measured by the percentage DECREASING
        • Which state has the best graduation rate for the 2009-2010 freshman class?
        • Which state has the worstgraduation rate for the 2009-2010 freshman class?
          • What other variables do we have to take into account?
            • There are more affluent neighborhoods in every state
            • Many schools are included in this statistic. The statistic is the MEAN (average) of the incoming freshman graduation rates from all the secondary public schools in the state.
  • What are some factors that would make it difficult for students to graduate from high school?

Remarks

I’m using the first day of the week as in introductory day to the project. I’m letting the student have a first glance at the statistical data that we will be working with as well as began to interpret as a group what is it that these statistics represent. By opening the class with a discussion about the future and what they’re concerns and feeling are about the near future for them, allows a space for sharing. By focusing more on the statistics than the computation mathematics behind it, I hope to reduce the students’ math anxiety and allow the students to develop an interest in the problem.

By sharing my position as part of one of the statistics, I hope to show the students that being A PART of a statistic is not necessarily a bad thing especially when the statistic is being looked at in a positive light. I feel that the word “statistic” often has a stigma attached to it (i.e. don’t be a part of the statistic”). This statistic is going to be one that the students will strive to be a part of.

By asking the students to think about what it means to improve, I encourage them to start considering what is it exactly that they’re measuring. If you’re trying to see if the graduation rate has improved or worsened, you’re looking for an increasing percentage, while if you were to be looking at if the drop out rate has improved or worsened, you’ll be looking for a decreasing percentage.

Tuesday

Do Now:  There are 20 students in a class. There are 12 girls and 8 boys. How many boys are there compared to how many girls? How many girls are there to boys? How many girls are there compared to students in the class? How many boys are there compared to the students in the class?

• Drawing a diagram (twenty circles: 12 green circles and 8 yellow circles)
  • Boys compared to girls: 8 to 12
  • Girls to boys: 12 to 8
  • Girls to students in class: 12 to 20
  • Boys to students in the class: 8 to 20

Lecture

What is a ratio: A ratio is a comparison of two things of the same type (people, fruit, etc.). Ratios can be written AS fractions, a:b notation and “a to b” notation as well

            “for every ___ of one thing, there is ___ of another thing”

            “for every 12 girls in the class there are 8 boys”

What is a proportion: this is the name that we give when we make two rations equal. We’re able to reduce ratios to make equivalencies.

For every 12 girls there are 8 boys = 3 girls for every 2 boys

What is a percentage: A percentage is a ratio or fraction that is set over a denominator of 100.

For example: 75% of the incoming freshman classes of secondary public schools in the state of Pennsylvania graduated. 75% = 75/100 = 75 to 100

This states that for every 100 freshman that came into a secondary public school, 75 of them graduated.

We’re able to use proportions and ratios in order to convert ratios to percentages and vice versa. We’re also able to use proportions to find out unknowns by cross multiplication:

If the ratio of apples to oranges is 6:5 in the fruit basket and there are 50 oranges in the fruit basket, how many apples are in the fruit basket?

6/5=?/50

6 x 50= 300

300/5 = 60 apples in the fruit basket

Class work

• Students will work in groups to change 10 samples of percentage rated from the charts to fractions and represent them as ratios in the three given forms (ie. 75.5% = 75.5/100 = 755/1000 = 75.5 to 100 = 75.5:100)
• Students are to turn in the class work at the end of the period

Wednesday

Do Now: Discussion: What is a “compliment”?

A compliment consists of all the results that are NOT the desired result. For example: what would be the compliment of graduating? What would be the compliment of winning? What would be the compliment of losing?

Today the students will receive their “school profiles.” An example of a school profile is given below:

School Name: Sunnyside High School for Science and Mathematics

State: Delaware

Size of incoming freshman class: 575

We will do a sample computation in class and then students will be put into groups where they’re going to be working on their individual school profiles, but encouraged to collaborate about the processes with their fellow group members. All students will be receiving a different school profile.

Process:

What is being told to us by the school profile?

• What state the school is residing in
  • The students were told to use the 2009-2010 data for their analysis
  • In Delaware 75.5% of the incoming freshman class of 2009-2010 graduated
  • How can we represent 75.5% as a fraction?
    • 75.5/100
      • for every 100 students, 75.5 of them will graduate
      • there are 575 students in the freshman class.
        • We’re to set the ratios equal to each other.
        • 75.5/100 = ?/575
          • we’re to cross multiply and divide  in order to uncover the unknown
          • 434.125 ~ 434 students in the graduating class
  • how many students in that incoming graduating class will not be graduating? 575-434 = 141
  • how can we represent these non-graduates as a ratio?
    • 141/575 (part over whole)
    • 141 to 575, 141:575, 141/575
      • how do we write this as a percentage?
        • 141/575=?/100
        • 141 x 100 = 14100
        • 14100/575 = 24.52%
          • what do you notice about this percentage in comparison to the percentage of graduates?
            • 24.54%+75.5% ~ 100%

Class work

Students will use the remainder of the class period to work together on their school profiles.

Thursday

Do Now: Discussion: Where do you see percentages in every day life? Where is it that you see fractions and comparisons used in the real world?

Learning Logs:

Students are given time to work on their learning logs. The learning logs are to be collected on the due date of the project (end of the week). Students must demonstrate their processes of how they got to their final conclusions by justifying their computations (ie. I set up this proportion because there are 1100 students in the incoming class and I know that 87.9% of them will graduate, thus 87.9/100 = ?/1100)

By collaborating with their fellow classmates, they’ll be able to work collectively to master mathematical language as well as processes (why is it that you multiplied here? Why did you do this?). By allowing students to work together and share their knowledge and understanding, it puts the students in a position of power and in turn makes them more invested in their learning.

If student does not finish the learning log in class, they must take the learning log home and finish the project on their own.

Friday

Do Now: According to the statistic for the incoming freshman class of 2007 in the state of Pennsylvania, how many students will be graduating from this class?

• Discussion:
  • How many students are present in this class?
  • What does the statistic say? 83%
  • 83/100 = x/20 students
    • 83 x 20 = 1660
    • 1660 / 100 = 16.6 ~ 17 students
      • according to that statistic, it says 17 of your peers will graduate. What does this mean about the other 3 students?
        • They will not graduate

Do you find these statistics to be helpful or harmful?

What is the purpose of these statistics?

Did anyone find anything through their calculations that they found interesting?

What factors go into creating these statistics?

Collection of learning logs

• Learning logs are graded on a mastery rubric (mastery, near mastery, developing and not yet) based on completeness and detail of their description of their processes. Revisions are always welcome for partial credit.