Based on the results from the three IPPR pre-tests and post-tests, students improved significantly following the presentation of my lesson and activities. It appeared that the students benefited a great deal from the manipulative tools that I incorporated into my lessons. These tools allowed students to physically see and touch the concepts that they were being taught. My first IPPR involved a lesson on place value for which I used a place mat and Cuisenaire rods as the manipulative tools. Students were granted the ability to use these tools to assist them on their pre-tests. I passed out the short quizzes to each student and informed them that the purpose of the quiz was to show me what they already know. I explained to them that the quizzes would not be graded and that they should do the best they can. The students had utilized similar manipulative tools for a place value unit that took place earlier in the school year. They effectively utilized the tools to help them solve the problems on the quiz. Some of the students demonstrated overconfidence, as they rushed to finish the quiz.
These students made mistakes that could have been avoided if they did not rush. Since students had not seen this topic for a few months, the lesson helped to remind them of key concepts and strategies that would help improve their pretest grades. Following the lesson, I administered the posttest, which was very similar in format to the pretest. Based on the results of the posttests, it was evident that the activities and manipulative tools in my lesson helped to improve students’ grades, as all students met the objective. According to the Problem Solving Evaluation Table, I would rate all of the students that I worked with as “average” or “above average.” All of the students grasped the concept, however, some of them took longer to make generalizations. For future math instruction for the students that I taught, I would not make any changes based on the assessment results. The results showed that all of the students answered almost all of the questions correctly.
My second IPPR was a lesson based on multi-step word problems. For this lesson I used counting blocks and counting bears as the manipulative tools. It was evident that the students had prior knowledge of this topic based on the results from the pretests. Like the first IPPR, students were informed that they could use the manipulative tools to assist them on the pretest. The students were able to effectively use these tools the complete the short quiz, as the majority of them answered all of the questions correctly. A few of the students answered one question incorrectly, which was due to simple math errors not their lack of understanding of the concept. After conducting the lesson, I distributed the posttest, informing students that these quizzes will be graded. For the posttest, students had the options as to whether they wanted to use the manipulative tools to assist them or not. Based on their grades, students’ scores improved from the posttest. Two students answered one questions incorrectly due to simple math mistakes; however, all of the students met the objective. According to the Problem Solving Strategies Evaluation Table, all of the students fell into the ‘above average” category, as they all demonstrated a complete understanding of the lesson material. For future math instruction of this topic, I would not make changes to the pretest and posttest. However, I would likely incorporate activities into my lesson that involve more student interaction with their peers. For my third and final IPPR I taught a geometry lesson on 2D and 3D shapes.
The manipulative tools for this lesson included various objects in the shapes that the lesson focused on. Students had not yet had a lesson on shapes, so the material was somewhat new to them. I distributed the pretest and instructed students that they could use the manipulative tools to assist them. Some of the students were confused, as they were unsure how to effectively utilize the tools, and did not recognize most of the vocabulary on the quiz. The majority of the students used the tools to the best of their ability; however, none of the students answered all of the questions correctly. The highest grade on the pretest was a 4/10. Based on the results from the posttest, students’ scored improved significantly from the pretest.
Three students solved all of the problems correctly, and the lowest score was a 7/10. All of the students met the objective. According to the Problem Solving Strategies Evaluation Table, all of the students fell into the “average”, or “above average” categories. It was evident that the activities and manipulative tools used in the lesson allowed students to develop a firm understanding of the concepts. Based on the assessment results I would likely include a video or book to introduce the topic before distributing the pretest to students. This would allow them to view the lesson material and process it in their own way before engaging in the lesson. In my opinion, providing them with little to know background knowledge is not as productive. Overall, all of the lessons were very successful, as students’ scores improved significantly from the pretests to the posttests. Through implementing my IPPR’s and observing my host teacher and his class I was able to acquire skills and strategies that I will likely incorporate into my own classroom in the future.