Download Collaborative knowledge of student work

Collaborative Knowledge of Student Work
This collaborative analysis was going to be done after the unit 3 in geometry. This unit is
looking at the relationships of lines, specifically parallel and perpendicular lines. The unit
starts out with angle relationships that are created from parallel lines. Then the unit looks
at triangle sum and exterior angle measurements because the proof of triangle sum is
based on parallel lines. Then students relate algebra with parallel and perpendicular lines.
Students also finish off the unit with proving parallel and perpendicular lines.
A week before we gave the test during one of our meetings the geometry team sat down to
decide how the test was going to be graded. This helped us when we were analyzing the
tests we could use the same percentages to identify our high, medium, and low students.
One teacher did not pass this information on to his student teacher, so she had different
scores. This made it difficult to quickly identify high, medium, and low students. This was a
little frustrating because if we are trying to do things collaboratively we all have to be on
board.
1-5
6-9
10-11
12
13
14-15
16
17
18
19
20-21
22-23
24
Grading Criteria on Test
(1 point given for identify each correctly)
(1 point for identifying all pairs of each type of angles)
(1 point for each variable found)
(2 points, 1 for correct parallel lines, 1 for justification)
(1 point for each correctly labeled variable)
(2 points for correctly setting up equation and identify x and angle)
(1 point for missing angle)
(1 point for correctly graphing)
(1 point for finding slope)
(2 point for graphing correctly, slope & y-intercept)
(3 points Finding slope, finding equation, graphing correctly)
(2 points for identify correct slope and writing equation)
(4 points for writing out the proof)
After each teacher had graded his/her tests we came together to identify our groups and
which concepts needed to be retaught and to determine what the students understood
about the four standards. We noticed that in our low group there were other concepts that
students also needed help with that were not an assessed math standard for this particular
test. For our team, this was the first time we had ever collaborated on analyzing student
work. At first, it was challenging to get a productive conversation started because it was
intimidating to analyze our individual students tests. However, after we identified some
successful standards and areas of growth for our high students, the process of analyzing
the data became easier for the medium and low students. The three of us that went through
the process are newer teachers, so it was a great experience. We were able to really see the
breakdown of how our students performed. It was not just looking at what problem they
were correct on and wrong on, but the actually skills they understand and don’t
understand, yet. The below information helped us develop a plan to help our students
understand and learn the concepts for future lessons that uses this same skill set.
Students knowledge/ Need for Reteaching on Test (High  Low)
G.C.O.1: Know Precise definitions of…… parallel lines (Q; 1-5)
Know
 Identify planes, parallel
 Identify parallel planes
lines and planes, and skew
and parallel lines (pg 11
lines. (pg 2)
& 15)
Need
 Order Correctly (pg 6)
 Order Correctly
 Lines parallel to planes
and skew lines (pg 15)

Label planes (pg 20
Order Correctly
Label skew lines,
parallel lines and
planes. (pg 24)
G. C.O.9: Prove theorems about lines and angles when a transversal crosses parallel lines (Q: 6-12, 24)
Know
 Identify angle
 Identify angle
 Identify angle
relationships
relationships. (pg 11 &
relationships, except
(Corresponding, Alt. Int.,
15)
corresponding angles.
Alt. Ext., & Same-side
(pg 20 & 24)
 Apply angle relationships
interior angles) (pg 2 & 6)
for parallel lines to set-up
 Apply angle relationships
equations. (pg 11)
for parallel lines to set-up
equations. (pg. 2 & 6)
Need
 Prove parallel lines when
 Prove parallel lines when
 Apply angle
given two congruent
given two congruent
relationships for
angles. (pg 3 & 7)
angles. (pg 12 & 16)
parallel lines to set-up
equations. (pg 20 &
 Prove perpendicular lines
 Prove perpendicular
24)
given parallel lines
lines given parallel lines
 Prove parallel lines
perpendicular to a line.
perpendicular to a line.
(pg 5 & 9)
(pg 15 & 18)
when given two
congruent angles.
(pg 21 & 25
 Prove perpendicular
lines given parallel
lines perpendicular to
a line. (pg 23 & 27)
G.C.O.13 Prove theorems about Triangle measures of interior angles sum 180° and exterior angle (Q:13-16)
Know
 Solve and apply algebra to
 Solve and apply algebra
 Finding missing
triangle sum and exterior
to triangle sum (pg 14 &
angles when given
angle. (pg 3 & 7)
16)
angle measurements
in triangles. (pg 21 &
 Find exterior angles, no
25)
algebra. (pg 14 & 16)
Need
 Solve and apply exterior
 Setting up and solving
angles. (pg 14 & 16)
algebra equations for
triangle sum and
exterior angle. (pg 25)
G.G.P.E.5 Prove the slope criteria for parallel and perpendicular lines (Q: 17-23)
Know
 Finding Slope (pg 4 & 8)
 Finding Slope (pg 15)
 Finding Slope (just a






Need

Writing equations given
two points. (pg 4 & 8)
Graphing equations in
point-slope and slopeintercept. (pg 4 & 8)
Solving point-slope into
slope-intercept. (pg 4 & 8)
Identifying parallel and
perpendicular slopes, then
writing the equation.(pg 5)
Graph horizontal and
vertical lines. (pg. 7)






Graphing equations in
point-slope and slopeintercept. (pg15 & 17)
Solving point-slope into
slope-intercept. (pg 15)
Identifying parallel
(pg 17
Graph horizontal and
vertical lines.
(pg 13 & 16)
Writing equations given
two points. (pg 17)
Identifying perpendicular
slopes (p15 & 17)
few mixing the rise
and run) (pg 22 &26)

Graph horizontal and
vertical lines. (pg 21)
 Writing equations
given two points.
(pg 26)
 Graphing equations in
point-slope and slopeintercept. (pg 22 &
26)
 Solving point-slope
into slope-intercept.
(pg 26)
 Identifying parallel
and perpendicular
slopes, then writing
the equation. (pg 23 &
27)
Extra Items that are needed:
 Reading with Clarity
(pg 24)
 Solving Algebraic
equations
 Attempting all the
problems (pg 21, 23 &
27)
PDF File: High, Medium, Low students
The reason I chose these students tests is because it showed each component of the above
knowledge and need for relearning. You will notice that some standards are shown in both
tests, but others are only shown in one and not the other. If I only had one test for each
standard I was not able to show that some students in a group may get it, but the majority
does not. Therefore, the standard would appear in the needs to learn category since over
half does not understand the concept.
Plan for re-assessment and differentiated instruction:
During the discussion with my team we came up with a re-assessment of the test by
standard. Now for students that failed more than one section they would be encouraged to
retake the whole test. When we were discussing this concept it stemmed from the fact that
the low students seemed to miss a standard or two, not random items throughout the
whole test making them have a low score. The re-assessment would be broken up into the
standards above and students would retest all the questions from that standard, not just
the ones they missed. Due to the timing of our test, starting a new unit, and winter break
the other teachers were not thrilled about any differentiated instruction for reteaching.
Now, I agree with this statement, but these concepts need to be learned for future use in
geometry and advanced algebra. These teaching sessions would just need to occur after
school. So for students that want to retake their test they will have the opportunity to come
in after school for a study session and each day will be a different standard offered for two
weeks. They will also need to make corrections to their whole test before they can retake
one section of the test they did not meet standard in or the whole test. Lastly students will
be asked to reflect on two items: the first is their learning process from beginning of the
unit, taking the test, to reteaching and the second is are they able to teach someone else the
material and if not what do they still need to know. Katie DeFazio posted the idea of
students thinking about whether or not they are ready to teach someone else in her week
3-discussion post. I want students to feel confident enough in their abilities that before they
take an assessment they are able to teach others around them.
For the study sessions, I will be using stations for the students to move through. The
stations idea comes from the 75-minute math workshop article, “Teacher-initiated
Differentiation: two classrooms become models for their large, urban district”. The teacher
has the students group by ability level when she is teaching them, but in different levels
when at the stations around the room. She is then able to give direct instruction to students
that are of the same learning level and then rotates them out to go work at another station
while another groups come into the lesson. I would use this idea by having different
stations around the room while rotating students in to relearn the identified above
standards for that level.
As the class moves forward I will be taking these skills and identifying where they are going
to reappear. During those lessons I will have the low learners spotted so that I can be
monitoring their progress during that instruction and reteaching if needed for those
students. One standard that will come up through out the year is solving algebraic
equations. So during winter break students will have the opportunity to get some extra
credit through working through some algebraic equations both written and in application
problems. This will hopefully help these students with this pre-geometry standard.
At the beginning of this process I was a little weary as to how it was supposed to all come
together in the end. Now, there are still pieces that need to be changed for next time as a
first time it went pretty well. The next time I do this I would like to of had some prior
documented formative assessments that I could have used to give more data comparison
for the end of unit exam. It could have also saved a lot of the confusion that was happening
during the test. When working with my team next time I think I need to layout the process
more clearly for all to understand each component. I believe they understood the main
ideas of the process, but missed things like the differentiated instruction piece, the
importance of grading consistency, and building more discussion around really how to help
students learn these pieces even though we have to move on to the next unit. I would really
like for our department to begin to use this process on different formative and summative
assessments. The trick will getting them to see that value in the process so that their time is
not being wasted.
References:
Ensign, Jacque. Teacher-initiated differentiation: two classrooms become models for their large,
urban district.(2012). Teaching Children Mathematics, 19 (3), 158-163. www.nctm.org
DeFazio, Katie. Week 3 discussion post.