During a mini lesson on the carpet, I can generally assess which students understood the concept before I send them off to their tables for independent practice. It isn’t until after I see their finished product whether it is written down on paper or a physical representation using manipulatives in a math lesson that I can tell if the lesson was successful because the students met the learning objective. If the majority of the students did not understand the concept, not only would the lesson be proven ineffective, seeing their work allows me see why they don’t understand the material. It gives me the opportunity to reflect on my teaching instruction and what I could do to improve. The first lesson that will be discussed is a math lesson about joining using connecting cubes and another math lesson on 2D shapes. Both of the lessons that will be discussed came from the PAS math curriculum, Investigations. The framework of how I designed both lessons must be taken into account because each lesson provided different outcomes in terms of student assessment. According to the article Role of the Teacher, the author stated that some of the core issues in lesson designing must have clear expectations and must be explicitly stated in order for students to reach levels of high achievement. Also, committing each lesson where the students are engaged in their own active reasoning and for each lesson to comprise of “accountable talk” to promote learning and encourage rigorous thinking (Hiebert et. al, 1997). A successful lesson will occur if the lesson meets these core issues.
The objective of the ‘Grab and Count Two Handfuls’ joining lesson was an extension from a previous lesson called ‘Grab and Count’. In ‘Grab and Count’ the students had to grab and count one handful of connecting cubes. For ‘Grab and Count Two Handfuls’ I modeled two different objectives in the lesson which resulted as an ineffective lesson. The first being, I asked them to grab and count one handful then grab a second handful by attaching the two sets together into a tower. I suggested making a tower presuming it would be easier for them to find the sum. The second objective was to represent two separate representations of their two handfuls through pictures, numbers and/or words and provide the sum of the two sets on paper. For this latter objective, the majority of the students did not understand the concept of representing two separate sets but rather combined them together into a picture of one whole tower. Some students did not join the two sets together to come up with a sum. My classroom mentor had to bring the students back to the math carpet to reteach the lesson for me.
Below, I selected three students’ work as evidence that they did not understand the lesson. Nat seemed as if he understood the concept of representing the first handful but from his erasures below the ‘7’ he was not sure if he was supposed to represent the second handful. He did not write the sum of the two handfuls. On Shahrin’s page it seemed as if she combined the two handfuls into one tower but did not represent each set separately. Ella represented her two handfuls correctly but her work showed me that she might have been confused as to which handful should go in which box because she switched her drawings. Although correctly represented both sets using pictures and numbers she did not write the sum. From this experience, I realized that this was not a successful lesson because I did not think about the core issues in designing this lesson. I did not communicate clearly what was expected of them by giving them two separate objectives. Also, I did not promote “accountable talk” that demanded rigorous thinking and students to develop good reasoning from it because I suggested putting the towers together.
The objective of the ‘Grab and Count Two Handfuls’ joining lesson was an extension from a previous lesson called ‘Grab and Count’. In ‘Grab and Count’ the students had to grab and count one handful of connecting cubes. For ‘Grab and Count Two Handfuls’ I modeled two different objectives in the lesson which resulted as an ineffective lesson. The first being, I asked them to grab and count one handful then grab a second handful by attaching the two sets together into a tower. I suggested making a tower presuming it would be easier for them to find the sum. The second objective was to represent two separate representations of their two handfuls through pictures, numbers and/or words and provide the sum of the two sets on paper. For this latter objective, the majority of the students did not understand the concept of representing two separate sets but rather combined them together into a picture of one whole tower. Some students did not join the two sets together to come up with a sum. My classroom mentor had to bring the students back to the math carpet to reteach the lesson for me.
Below, I selected three students’ work as evidence that they did not understand the lesson. Nat seemed as if he understood the concept of representing the first handful but from his erasures below the ‘7’ he was not sure if he was supposed to represent the second handful. He did not write the sum of the two handfuls. On Shahrin’s page it seemed as if she combined the two handfuls into one tower but did not represent each set separately. Ella represented her two handfuls correctly but her work showed me that she might have been confused as to which handful should go in which box because she switched her drawings. Although correctly represented both sets using pictures and numbers she did not write the sum. From this experience, I realized that this was not a successful lesson because I did not think about the core issues in designing this lesson. I did not communicate clearly what was expected of them by giving them two separate objectives. Also, I did not promote “accountable talk” that demanded rigorous thinking and students to develop good reasoning from it because I suggested putting the towers together.
During my two-week takeover I did a geometry lesson called ‘Shape Pictures’. [click for Shape LP] The objective of this lesson was to introduce geometry by using real-world objects and comparing them to 2D shapes. They had to chose one shape and draw a picture around the shape by adding details/designs. After that, they had to write about their picture. Frankly, this was one of my best lessons because it showed in every students’ work. Every single learner in my classroom understood what was expected of them in this lesson because they were all engaged, I prepared all of the materials beforehand, I used “accountable talk”, activated their prior knowledge, expectations were explicitly stated and I felt confident during my delivery of the lesson. My Penn Mentor’s feedback indicated that this was a successful lesson as she noted in her comments in the blue box below “You need to reflect on what made this lesson work so well.” In the green box, she even noted one of the student’s excitement as she said, “This sounds like fun!” In the orange box, she wrote down that students were all engaged as they were "diligently working."
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I chose the same three students that I chose earlier from the ‘Grab and Count Two Handfuls’ lesson to illustrate and compare what a successful lesson looks like. There seems to be an axiom that sometimes it is the students fault for not understanding a concept. I realized that these artifacts exhibit, with my careful planning and reflection, the levels of student achievement is dependent on effective teaching strategies. As I began this geometry lesson by activating their prior knowledge, engaging them by implementing real-world objects, creating classroom discourse where I asked them questions to encourage their mathematical thinking, I did not have any classroom management issues. Reflecting on all of these key components from just one lesson, ultimately proved to me that this was a successful lesson.