Kimberly Samaniego

Algebra for All does not mean access for All Achievement Gaps

Equitable Teaching Practices (student-centered defined by NCTM) Reflection, dialogue, multiple

representations, and regular feedback

Google Your Math designed to provide opportunities to access Algebra at home.

Research Question: How will students use Google online environments in Algebra? How would they dialogue? How would they collaborate? Who will use it? How will it help them in Algebra?

Principles of Knowledge Building (Scardmalia & Bereiter, 1991, 2006) Students take responsibility for their learning by planning,

execution, and evaluation Advancing the current understanding of individuals within

a group, at a level beyond their initial level of knowledge

Sociocultural Learning (Vygotsky, 1978) ZPD and dialogue as a mediation tool

Motivation (Deci, 1995) Using technology for flexibility – allows for student choice

and autonomy Reflective feedback

Communities of Practice (Lave & Wenger, 1991) Central and peripheral participation

Sustain an environment of collaboration and discourse outside of the classroom and increase student practice at home

Improve student performances in algebra

Reduce achievement gaps between student populations

39 students 1oth grade Algebra 1 (2 periods) 20 students credit deficient – classified 9th grade

Gender – 27 boys and 12 girls Ethnicity

12 Latino, 11 African American, 9 Filipino, 7 White Learning Rosters (no crossing over)

10 students with disabilities (IEPs) 8 English language learners (ELLs) 21 regular ed (non-disabled and English

proficient)

Weekly Discussion PromptsPre and Post-implementation

Assessment Mid-implementation student use

survey Semistructured student interviews After implementation student

interest survey

HW prior toGoogle Your Math (18%, n=7)

During GYM56% posted indiscussions (n=22)

5 Reported lurkers

Total 69% claimed participation

Behavior categories

Code IEP ELL REG Total Code percent

Category percent

Contributing HeG 0 0 1 1 1%to the FBG 3 0 1 4 5%Knowledge RI 0 0 0 0 0%of the Group SK 16 8 19 43 54%

Ch 1 1 1 3 4%Ex 1 0 5 6 8% 71%

Seeking Input

HeS 6 0 4 10 13%

FBS 0 1 1 2 3%Ef 0 0 0 0 0% 15%

Reflection/ ME 2 0 0 2 3%Monitoring PC 4 1 0 5 6% 9%Social Interaction SI 3 0 1 4 5% 5%Post Totals 36 11 33 80

45% 14% 41% 100%Participating Students

8 4 10

Average Post 4.5 2.8 3.3Median Post 4 2 2.5Mode 9

outlier 6 10

outlier

Polynomial Pre and Post Assessment Results

With 2 Being the Highest Score Possible Average

ScoreProblem 1

Problem 2

Problem 3

Problem 4

Procedural Pre-Test

1.1 0.5 0.6 0.1

Fluency Post-Test

1.9 (+0.8)

1.1 (+0.6)

1.4 (+0.8)

1.1 (+1.0)

Conceptual Pre-Test

0.9 0.5 0.6 0.2

Understanding

Post-Test

1.8 (+0.9)

1.2 (+0.7)

1.5 (+0.9)

1.4 (+1.2)

Given

Find the product (procedural fluency = 9 correct computations)

23 2 4 5 7x x x

Student Population Pre P 4Related Percent

Post P 4Related Percent

Non-disabled and Language Proficient Students

100% 100%

English Language Learners

33% 83%

Students with Disabilities 25% 68%White 50% 84%Filipino 100% 100%Latino 50% 75%African American 19% 63%

Four highest scoring performances

Four lowest scoring performances

Name Gender Ethnicity Learner Number of 2’s scored on Pre

Number of 2’s scored on Post

Number of posts on Google discussion

Abe Male White IEP Zero 2’s Eight 2’s 9Katie Female Latina Reg One 2 Seven 2’s 3Hudun Female Native

AfricanELL Zero 2’s Six 2’s 3

Sherwin Male African Am Reg Zero 2’s Six 2’s 10

Name Gender Ethnicity Learner Score on post-implementation assessment (overall)

Number of posts on Google discussion

Chris Male African Am IEP 2 0

Lupe Female Latina ELL 4 0

Eduardo Male Latino IEP 5 0

Jamar Male African Am IEP 6 4

Abe(9) – Easy to use “It was organized on the computer. I did not

have to keep track of it.” Katie (3) – Reliable

“I did go on even if I didn’t post. I still looked at what others posted. I didn’t post because I didn’t feel confident.”

Hudun (3) – It was okay “People posts answers. You could see how they

followed steps. It helps your grade go up.” Sherwin (10) – Improvement

“It helps because you can see other people’s answers and compare. The teachers can also explain.”

23 students participated – 16 did not No computer (5) Did not know how (4) No time (2) Forgot (2) Just did not do it (1) Lazy (1) Wasn’t online ( 1)

Alternative Methods 10 – paper 6 – post on Google▪ Resulted in no change in participation

Students thought that Google discussion activities helped them to understand math

Students stated that teacher and peer feedback was helpful in understanding math

Students felt connected to their peers and teacher while using Google

Students enjoyed using Google in math and many believed it would be helpful in other subjects

Google Your Math showed improvement in student performances

Google Your Math showed indication of achievement gaps narrowing

Students liked using Google Precalculus student were more creative,

complex and articulate in their dialogue than Algebra students

Peripheral Participation – lurkers to experts

The Great RaceDiscussion 1 Prompt - AlgebraProject Box it Up

Online chattingDiscussion 3 Prompt – HPCStudent Quote to using Google

Date Posted by Actual PostsApril 79:10am

Jamar LETS JUST SAY I DONT REALLY UNDERSTAND ANY OF THIS IM CONFUSED

April 710:26am

Angelo response from math maniacs......the answer for this problem is 9x^2+12x+4

April 710:30am

Katie response from the variable babes: the answer is not 9x^2 because you can't make a full rectangle or square the correct answer is 9x^2+ 12x+ 4

April 710:33am

Jorge this is for team alpha pie 9x squared + 12x + 4 count each one

April 78:22pm

Sherwin response from slopes: If u lay out the tiles of 9x squared 2+4, it doesnt make into a full rectangle the correct answer is 9x squared 2+ 12x+ 4

April 88:10am

Abe Sherwin thanks for posting that for our groups

April 89:15am

Mazen 9x^2+ 12x+ 4 because 9x^2 its not a rectangle

April 912:07pm

Armando those aswers helped me a lot thanks

April 910:13pm

Mrs. S Math maniacs, Thank you for submitting a solution, but can you explain how you got your solution? (any and all can respond from math maniacs)

Apr 10 5:43am

Mrs. S Armando, can you explain why these answers helped you a lot?  What do you think the solution is and why?  Why is the solution NOT 9x^2 + 4?

Apr 103:35pm

Hudun don't you distributed ? Anybody help!

Apr 105:37pm

Mrs. S Hudun, Yes, distribution is the key to this process.  However, when using distribution, you need to consider both dimensions.  Try using the box method we learned in class on Thursday and Friday to set up the multiplication of (3x + 2)(3x + 2).  How does this answer compare to the one you got originally?

Given:  4x^2+25y^2+16x-150y+141=0 Graph and identify everything you know about this conic section.

(You will need to figure out how to show this on Google!)

Okay let me break this down Chandler’s Way. This is where Doomsday begins.

1) Given: 4x^2+25y^2+16x-150y+141=0  WOW! 2) Put the Xs with the Xs and the Ys with the Ys. SPECTACULAR! Make the 141 equal the equation: 4x^2+16x+25y^2-150=0 3)Take out  4 as the common factor in the Xs and  OUTRAGEOUS! 16 as the common factor in the Ys and complete the square: 4(x^2+4x+4)+25(y^2-6y+9)=-141+(4 x 4)+(25 x 9) 4) Compact the squares and add the multiplied numbers (4 x 4) NOT PLATITUDINOUS! and (25 x 9) to -141: (4(x+2)^2)+(25(y-3)^2) =100 5) Divide everything by 100 NOT PLATITUDINOUS! ((x+2)^2/25)+((y-3)^2/4)=1 Well look at the marvelous masterpiece, it's an Ellipse! As you can see the bigger denominator always being a^2 is under the X^2 making it in the X Axis for the Focal Axis. Well using the equation for any Ellipse, ((x-h)^2/a^2)+((y-k)^2/b^2)+1, we can reflect back at this problems equation as find out: A) a^2=25, so √25=5=a SHAZAM! b^2=4, so √4=2=b c^2=√(a^2-b^2)=√(25-4)= √21=c

B) Major Axis Length: 2a=2(5)=10 DAREDEVIL! Vertices: (3,3) (-7,3)

C) Center: (-2,3) OUT OF MY MIND!

D) Minor Axis Length: 2b= 2(2)=4  LEGIT! CoVertices: (-2,5) (-2,1)

E) Foci: (-2+√21,3) (-2-√21,3)  CAN WE SAY BONUS POINTS?!

F) Eccentricity: e=a/c=√21/5  INDUBITABLY!

G) The graph of the century is one click away. i warn you that it's unique. GASP!

I know, this is some crazy work here. No need to give me a gold medal

My favorite activity on Google was being challenged to solve problems that weren't the ones that we normally see. For example, my group had to solve a problem about the illumination of the moon. Even though there were parts that stressed me out because I was having difficulty solving it, the coming together of people to do the group work was fascinating. Since this group was made up of people that I would never usually talk to it was an unforgettable experience. The thing that makes it so memorable is the fact that I saw that my group was editing the document for over an hour on the night it was going to be due. This demonstrated to me that there were people in my class who were dedicated to finish solving the problem, which essentially made me feel more connected to other people in my class.

Contact information: Kimberly Samaniego

aksamaniego@msn.com