Impact on Student Learning Jacob Choi
Using Period One for this artifact, I compiled data from twenty-three students to further analyze where they needed the most attention to prepare for the High School Assessment (HSA) in midMay. The names and identities of the twenty-three students are protected under the Family Educational Rights and Privacy Act (FERPA) of December 9, 2008.
Pre-Assessment
As a diagnostic battery of questions, the end of two consecutive days’ lesson plans was fitted with a few questions or students to Activote in. Although these usually are buffer questions at the end of a lesson to review materials, the beginning of April marks a crucial time for the students to revise all the learned materials. Day One eased in with only three questions from a topic we had completed about a month beforehand. Exit passes were also prepared for factoring and solving a one line equation. Most of the students were able to complete this in the final minute of class following the Activoting, thus giving a real-time feedback on what the students knew about the Zero Product Property. Although the ZPP was used on both the Activoting questions and Exit Pass, it represented itself in a different form on the Exit Pass where students first had to factor the given equation first before being able to implement the ZPP. Day One Questions Solve (b-5)(2b-6)=0 b=5 or b=3 Solve (2b-1)(2b-4)=0 b=0.5 or b=2 Solve (3b+18)(2b-4)=0 b=-6 or b=2 [Exit Pass] Factor and solve: 9x2-3x=0 x=0 or x=⅓ The first three questions are recorded in the matrix designed to assess and prioritize where our efforts and time needed to be spent as a class for the remainder of the semester. However, the fourth question on the exit pass is NOT recorded on this matrix because it is more an affirmation or confirmation of the above three questions. The only extra step added in for the exit pass is for the students to factor before solving the equation. Most of the students easily recognized that the GCF of the coefficients would be 3, and the GCF of the variables was x, thus the GCF for the left hand side of the equation would be 3x. As shown below, a selected six of the exit passes show the multiple methods that students used to get their answer. While students 1, 3, and 6 have reached the answer, notice that their approaches differed slightly.
Student 2 was tagged for a necessary follow up, and student 5 exhibits a misunderstanding of factoring that leads to only one but not both of the answers. Student 4 is actually a competent student and was only one step away from the answer, but we followed up with him to discover that it was solving 3x-1=0 that stumped him.
1
2
3
4
Brightness and contrast are adjusted for viewing purposes
5
6
Why do we only count correct answers? Absences (white cells) are counted along with incorrect answers because they signify that the student needs a follow up. With a student absent, they are in great need of catching up work that they missed, thus why only correct answers are considered for the tally count. Period One Total 18 questions Total Correct 12 11 16 8 8 5 10 13 16 14 14 17 14 15 7 9 15 11 16 17 11 14
ID 1A 1B 1C 1D 1E 1F 1G 1H 1I 1J 1K 1L 1M 1N 1O 1P 1Q 1R 1S 1T 1U 1V 1W Total 23
15 Class Average: 12.52 out of 18
Day
Day One
Question
Q1 (A)
Q2 (E)
Q3 (D)
Objective
Zero Product Property
Zero Product Property
Zero Product Property
Priority LOW MODERATE LOW HIGH HIGH HIGH MODERATE MODERATE LOW LOW LOW LOW LOW LOW HIGH HIGH LOW MODERATE LOW LOW MODERATE MODERATE
Solve (b-5)(2b-6)=0 A A A B E E
Solve (2b-1)(2b-4)=0 E E E C E E
Solve (3b+18)(2b-4)=0 D
A E
E E
D D
A A A A A
E E E E E
D E D D D
A
E
E
A A A A
E E E E
D D D C
LOW
E
B
C
Correct Answers
14
17
13
Priority
HIGH
MODERATE
HIGH
Rank
4
6
3
D D B D
I had expected question 3 to be a little more difficult for the class because of a negative answer that required division to reach it, but question 1 was perhaps the easiest and I suspect that it suffered from being the jumps-start question—the students were just transitioning in from a statistics lesson. Then again, three of the incorrect students on question one would end up getting less than half of all the three days’ questions correct.
Day Two As with Day One, I put five questions in at the end of the lesson as cool-down questions to analyze how flexible our students were with Unit 5 materials, as opposed to the Unit 6 material from the previous day’s analysis. Fulfilling some parts of Goal 3 in Maryland’s Core Learning Goals for Algebra, these questions focused on two of the newer topics in grade nine mathematics that may not have been seen in middle school: matrices and non-static probabilities. Day Two Q1 (A)
Q2 (C)
Q3 (C)
Q4 (A)
Q5 (B)
Matrix Differences
Read Matrices
Scale Matrix
Probabilty
Probability
A-B A A A B A B A B A A A A A A A A A A A A
What is in A? C C D C A C C C C C C C D C C E C D C C
C(A) where CЄReals C C C A B C C C C C C C C C C A C C C C
Choosing one gift card A A A A A
A A A A A
Choosing many gift cards F B B B B B B B B B B B B B B B B B B B
A
C
A
B
A
C
C
A
B
20
18
19
21
22
LOW
MODERATE
LOW
LOW
LOW
9
7
8
10
11
A A A A A A A A
Clearly, student 1U above is absent for Day Two and I followed up with her to clarify the circumstances and also had an impromptu pre-assessment from Day Three. Although her scores from Day One and Three are satisfactory, if not better than most of the class, I still flagged her as a moderate priority because we needed to have solid evidence that 1U was proficient at matrices and probabilities. We see that Day Two’s questions were a lot easier, and I did expect probability to be a very easy topic for the students to grasp. However, on matrices, a lot of students cannot find the change between matrix [Before] and matrix [After]. I used before and after as dummy matrices to represent a two-time-state, which is a more formal definition of the concept that is present to the students. Most simply, we are given two sets of comparable data: one for, say, Saturday, and the other for Sunday. Students are asked to find the change—ie: the difference of the matrices. But it is the order of differences that boggles those students who got the answer wrong. Instead of performing After-Before as a subtraction, these students will calculate Before-After since that naturally appears to be the order in which the matrices are presented, hence those students answered B on question one for Day Two. We registered a 100% of correct responses on question four, although there were two absentees. Nevertheless, simple probability turned out to be proven easy for the entire class, as proven by these diagnostics. Therefore, for the revision classes, we will not use simple probability questions, but instead work on the “tough stuff” in terms of expected values and other probability problems more complex than simply pulling a number out of a hat. Day Three For the purposes of fitting the data onto these sheets, Day Three’s data is broken up into two parts, although both focus on the Unit 5 material fulfilling Goal 3 of the Maryland Algebra Expectations. Though no matrix operations are involved, students are asked to interpret two matrices. Question three’s solutions are all matrices too, instead of simply asking for a quantity in one cell of a matrix. Perhaps the most difficult questions of the day were questions 4, 6, 9, 10 and 12—none of which had any numerical or quantitative answers. Instead, all of them asked about specific properties of fair and unbiased testing, or characteristics of the mean versus the median. Although this unit of study is fairly easy and simple, compared to other units that involve expanding or distributing monomials, students have to be very careful in answering questions that may have small details that cannot be ignored, such as the words used to describe simulations. As the below charts show, four questions were of particularly high concern to us by the end of the period—a third of all the questions asked on Day Three.
Day Three, Part I Q1 (C)
Q2 (A)
Q3 (A)
Q4 (C)
Q5 (B)
Q6 (D)
Matrices
Probabiltiy
Matrices
Survey Design
What is in A, compared to B? C D C B B
Next draw is? D A A D A
What is in Matrix A? A A A B A
What does "equally likely" mean? B E C C A
Average for next test Find the next test score to reach an average B C B B C
C C C C C C C C
A A A A A A A A
A A A A A A A A
C A C C C C A C
B B B B C B B B
D D D D D D D
C C C C C C F
A A A A A A A
A A A A A A
A C B A C D C
C B C B B B D
D D D D D D D
C
A
A
C
B
D
17
19
19
12
15
18
MODERATE
LOW
LOW
HIGH
MODERATE
MODERATE
6
8
8
2
5
7
Survey Bias Which is not a biased survey? D
D D
Day Three, Part II Q8 (E)
Q9 (C)
Number of Options
Simulations
How many different combinations? B D E C E
Q10 (C)
Q11 (B)
Q12 (A)
Lineplot
Scale of Graphs
Simulate this B D C B A
Box and Whisker Plot What does the box and whisker plot show? A C C A D
Interpret the line plot B B B B A
Compare Graphs A&B A A A D A
B E E E C E D C
B B C C D C C B
B B B C D C B C
B B B A B B B B
A D A A A A A D
E E E E E E E
B B C B B B C
C C C C C C C
B B B B B B
A D A A A A A
E
C
C
B
A
14
8
13
18
17
HIGH
HIGH
HIGH
MODERATE
MODERATE
4
1
3
7
6
Question Average 13.65 out of 23
Period Four’s aggregate performance at the end of the three days is recorded as 13.65/23 questions correct, but that does not gauge much in the end since we examine each child individually according to their own strengths and weaknesses. That measure is kept only to see where students are above, below, or meeting their class on average, but all of them must strive to reach for the 23 out of 23 mark.