Impact of Student Learning
Secondary Math Education Example
Day 1 Impact on Student Learning The Pythagorean Theorem Catherine Day Narrative My data evaluates my impact on student learning on the Pythagorean theorem and its application. I administered the pre-­‐test (Artifact 1 in Appendix) after a lesson that addressed squares and square roots of perfect numbers, which was knowledge spiraled during the Pythagorean theorem lesson. Since the Pythagorean theorem was a new skill that all the students had not been exposed to, none of the students knew the theorem nor how to apply, as shown in Primary Artifact A and B (see Appendix). The pre and post test (Artifact 1 in Appendix) allow for students to scaffold their knowledge: first, do I know the sides of the right triangle? Second, what is the formula of the Pythagorean theorem? And third, how can I apply the Pythagorean theorem? I included all of this since these inquiry skills are vital to able to fully understand the Pythagorean theorem. I was aware that since I was teaching a 7th grade class an 8th grade standard, many students would not know the Pythagorean theorem. Despite this fact, the 7th graders have been studying triangles, including right triangles. Therefore, I predicted that students might be able to label the sides of a right triangle, but would know nothing about the Pythagorean theorem. As shown in the data from Primary Artifact A and B, this was the case. About half of students knew how to correctly label the sides of a right triangle, and 0% of students knew the Pythagorean theorem or how to apply it. Using this data when designing my lesson on the Pythagorean theorem, I decided to reinforce the sides of a right triangle, since I could spiral this skill for half the students while introducing the concept to others. As seen in Artifact 2 the Appendix, I used the Promethean Board along with guided notes for an interactive presentation of labeling the sides. I selected a student to drag the names of the sides to the right triangle and then had two examples where students put stars on the hypotenuses of two right triangles. This inquiry method not only accessed student prior knowledge, but also allowed for students to teach other students what they knew about triangles, starting off the “direct” instruction with a skill that was not intimidating. Knowing the sides of a right triangle is integral to being able to apply the Pythagorean theorem. As mentioned, Primary Artifact A and B show that 0% of the students knew the Pythagorean theorem or how to apply it on the pre-­‐test. Therefore, I used labeling the sides of a right triangle as a jumping off point when introducing the Pythagorean theorem since some of the students were familiar with that concept. Mentioning that the Pythagorean theorem allows us to find a length of a side of a triangle when given two, my instruction along with three examples enabled students to develop the concept of how to use the Pythagorean theorem. As can be seen in Artifact 2, specifically in Example 1 through 3, various questions are used to inquire about how students can apply the information given to Impact of Student Learning
Secondary Math Education Example
Day 2 them about the Pythagorean theorem. Finally, my instruction allowed for students to see real life applications of the Pythagorean theorem seen in Example 3, allowing students to develop an understanding that this theorem has real life applications. Following the instructions, students were able to practice applying the Pythagorean theorem in stations including examples of real life examples with buildings and sails. Before I transition the students into station work, I administered a quick check for understanding by giving three problems and having students apply the Pythagorean theorem. This allowed time for me to circulate the room and see how students were doing with the Pythagorean theorem, since 0% originally knew the formula or how to apply it. From the analysis of the post-­‐assessment, it is obvious that students learned about the Pythagorean theorem. In period 6, 92% improved overall from pre-­‐
assessment to post-­‐assessment. Of the 12 students in period 6 that were present for both the pre-­‐assessment and post, 83% knew the formula for the theorem and also how to properly apply it (including all proper arithmetic necessary). In period 7, all of the 13 students present for both assessments improved. This entailed 100% of students being able to properly state and apply the Pythagorean theorem. In both periods, these results imply that students were comprehended what the Pythagorean theorem entailed and how it could be used. This data, specifically for period 7, provides convincing evidence that there was a change of students’ mental functioning and improved critical thinking. Reflection As the data shows, the lesson I taught catalyzed student learning of a skill that will come in handy in their mathematical careers. The few things that I did well were spiraling skills of squaring and square rooting from the warm-­‐up. One specific example used 82+62 which was straight from the warm-­‐up, which can make direct instruction go faster while using student work. Also, my activity post lesson was interactive and included many real world applications of the Pythagorean theorem, which prompts interest in students. I also incorporated the deficiencies that were shown in the pre-­‐assessment, specifically in period 7. I made sure to address labeling the sides, and clearly introducing the Pythagorean theorem and its applications. Despite making strives (overall 92% and 100% improvement for period 6 and 7, respectively), if I taught this lesson again, I would make some changes. One change would be to include more real life examples in my direct instruction. Another would have been to do Example 1 myself (with student input through my inquiry) and then have a student, or a few students, come up to try do to example 2. Also, as it shows from the data, my second lesson was much more effective than my first. Being more consistent and less nervous would have improved my results for period 6. In regards to the post-­‐assessment specifically, I would change a few things to gauge how much students learned. First, I made the mistake of just displaying the post-­‐assessment on the document camera rather than printing out individual ones for each student. This led to less legible answers and some confusion labeling the Impact of Student Learning
Secondary Math Education Example
Day 3 sides of the triangle (although prompted to label each side leg or hypotenuse, many students used labels a, b, and c). Furthermore, I would have designed my post-­‐
assessment to include a real-­‐life application, since my activity was largely based on such examples. Impact of Student Learning
Secondary Math Education Example
Day 4 Appendix Primary Artifact A: Period 6 Data Student
Dayma
Isaiah
Jaida
Kevin
Tatianna H
Danny
Tatiana R
Dominque
Jaleel
Nevaeh
Troy
Nia
Pretest:
Sides
Y
N
Y
Y
N
Y
Y
Y
N
N
Y
N
Pre-test:
Pythagorean
Theorem
N
N
N
N
N
N
N
N
N
N
N
N
Pre-test:
Application
N
N
N
N
N
N
N
N
N
N
N
N
PostTest:
Sides
Y
N
N
N
N
N
N
Y
Y
N
N
N
Post-Test:
Pythagorean
Theorem
Y
Y
N
Y
N
Y
Y
Y
Y
Y
Y
Y
Post-Test:
Application
N
N
N
N
N
Y
N
Y
Y
Y
Y
Y
Summary: Of the 12 students present for the pre and post test: • 92% improved • 0% originally did not know the Pythagorean theorem, 83% of the students knew it on the post-­‐test • 0% originally did not know how to apply the Pythagorean theorem, only 50% of students knew how to apply it on the post-­‐test. • Of the 7 students who did not know the names of the sides of a right triangle on the pre-­‐test, only 3 students showed they knew how to do it on the post-­‐test. Primary Artifact B: Period 7 Data Student
Kasmira
JC
J'da
Linda
Aleema
Thomas
Zahkura
ZaKyra
Dajae
Rykia
Cassell
Natalia
Jerimiah
Pretest:
Sides
Y
Y
N
Y
Y
N
Y
Y
N
N
N
N
N
Pre-test:
Pythagorean
Theorem
N
N
N
N
N
N
N
N
N
N
N
N
N
Pre-test:
Application
N
N
N
N
N
N
N
N
N
N
N
N
N
PostTest:
Sides
Y
Y
Y
N
N
Y
Y
Y
Y
Y
N
N
Y
Post-Test:
Pythagorean
Theorem
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Post-Test:
Application
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Summary: Of the 13 students present for the pre and post test: • 100% improved • 0% originally did not know the Pythagorean theorem or how to apply it, 100% did know on the post-­‐test Impact of Student Learning
Secondary Math Education Example
Day 5 Of the 7 students who did not know the names of the sides of a right triangle on the pre-­‐test, 5 students showed they knew how to do it on the post-­‐test. Non-­‐Primary Artifacts Artifact 1: Pythagorean Theorem – Pre and Post Quiz Label the sides of the right triangle as Find the length of the hypotenuse of the either leg or hypotenuse. following right triangle: •
What is the formula of the Pythagorean Theorem? Artifact 2: Direct Instruction Lesson Plan Direct Instruction/Guided Board/Paper What a
re s
tudents d
oing
Practice (Questions in BOLD) What am I doing/saying? Select student to drag side names onto triangle T reinforces that legs are adjacent to right angle, hypotenuse is opposite to right angle. Use this information to spiral A2+B2=C2 Impact of Student Learning
Secondary Math Education Example
Select student to drag H stars to hypotenuse Check for understanding: vote if you agree Explain Pythagorean theorem only applies to right triangles Step one: label a, b, c Walk students walk through Pythagorean Theorem A2+B2=C2 How can the Pythagorean theorem help us here? What side is missing? Reinforce this is the formula of the Pythagorean theorem What sides should I label a, b, and c? Spiral warm-­‐up 82+62 to make a quick example How can the Pythagorean theorem help us here? What side is missing? What is my first step to finding this missing side? How should I label my sides? Reinforce labeling sides due to data shown on the pre-­‐test Day 6 Example 1: Example 2: Example 3: Real life example Impact of Student Learning
Secondary Math Education Example
Reinforce that there are right triangles in the real world – real life application What is my first step to finding this missing side? How should I label my sides? If needed, show students the square root operation on calculator You’ll see more real life examples in the stations First, let’s check if we understand how to apply the Pythagorean theorem. Circulate room making sure kids are doing the computations correctly Select student to go over 1 and 2 Obtain pulse of room by doing thumbsup/thumbsdown Prompt students to transition to station work Day 7