The mathematics content coaching cycle was a bit different than the previous content coaching cycles. For this cycle, the mathematics coach will focus on three or four residents each week. I designed and implemented my lesson plan for mathematics in the first week. The mathematics coach wants to make sure that she gives everyone ample time to perform a pre-conference, observation, and post-conference so it was decided that each resident would receive specific coaching for one week. I will continue to work with my collaborating teacher to co-plan and co-teach mathematics during the semester but at this point in time, I will not participate in the content coaching observation cycle for the remainder of the semester.
Before my mathematics lesson, I met with the mathematics content coach to discuss my five page lesson plan and how I would pose purposeful questions. We talked through some of the elements of the five page lesson plan such as the goals, possible misconceptions, and prior knowledge but the main focus was on question types. It is important for me to not only use and create higher order thinking (HOT) questions but to pose questions of various types to elicit student thinking. There are four types of questions that we analyzed: gathering information, probing thinking, making mathematics visible, and encouraging reflection and justification. I believe that it is important to focus on these questions so that I do not only ask questions on the lower levels of Bloom’s taxonomy. By working with the mathematics coach on my questioning, I met FEAP 3F – “Employ higher-order questioning techniques.” We worked together to create questions for each framework and I determined how I would use them in my lesson.
After our discussion, I revised my lesson plan to change some of the questions, add new questions, and charge the order of some questions in my lesson. The majority of my lesson plan was the same. I aligned my lesson with the standards MAFS.1.OA.1.1 –
“Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem” and MAFS.1.OA.3.6 – “Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten,; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums by creating the known equation.” This allowed me to meet FEAP 1A – “Aligns instruction with state-adopted standards at the appropriate level of rigor.”
For this lesson, I designed my own groups based on previous data that I collected through anecdotal notes and observations. This allowed me to meet FEAP 3H – “Differentiate instruction based on an assessment of student learning needs and recognition of individual differences in students.” There were a few students that I believed would need additional support for the lesson. I collected data through observations and used this to inform my instruction by pulling a small group as the other students worked in pairs. I designed the assessments based on the abilities of my students to match their learning needs. This allowed me to meet FEAP 4B – Designs and aligns formative and summative assessments that match learning objectives and lead to mastery as well as FEAP 4D – “Modifies assessments and testing conditions to accommodate learning styles and varying levels of knowledge.”
When I implemented the lesson, I modified it in order to meet the needs of my students and address their misconceptions, which allowed me to meet FEAP 3D – “Modify instruction to respond to preconceptions or misconceptions.” I asked the students to show me two ways to make ten. We listed these methods on the board and I asked them if there were other ways to make ten. After we had about five methods (all addition) on the board, I asked how many ways we can make ten. Not surprisingly, my students counted the methods on the board. I decided to take the time to show my students there are many ways to make ten using addition of two and three addends as well as subtraction. I tried to grant the students the opportunity to list ways to make ten without explicitly mentioning using three addends or subtraction. After some gentle pushes, the students grasped the concept and realized that there are a lot of ways to make ten.
I wanted to highlight this point because I want my students to become familiar with the various basic facts within twenty. My students have been working on balancing equations on each sides of the number line and finding equations that are equal. This lesson connected to these previous lessons by showing students there are multiple number sentences that equal ten or any other number. By doing this, I met FEAP 1B – “Sequences lessons and concepts to ensure coherence and required prior knowledge.”
After my lesson, I watched the recording and took notes about my questioning strategies and the types of questions that I asked. One important aspect of my teaching that I noticed is that the majority of my questions were unplanned. This is important to know so I can focus on planning more questions ahead of time. This could also show how I respond to my students. I noticed that I repeated some questions a lot such as “are there more ways to make ten?” I did this because I wanted to probe my students’ thinking without explicitly telling them to use subtraction or three addends to find a number. In the end, they needed some guidance to understand this concept but I assumed this would occur. My students typically have more success with addition as compared to subtraction. I assumed that my students would easily see the addition facts and need some help finding subtraction facts, which is what occurred. This shows me that my collaborating teacher and I should provide extra support in the area of subtraction and provide our students with many opportunities to practice subtraction. This allows me to meet FEAP 4A – “Analyzes and applies data from multiple assessments and measures to diagnose students’ learning needs, informs instruction based on those needs, and drives the learning process.”
As always, I am excited to continue taking the lead on planning and teaching various subjects in the classroom. I hope to continue co-teaching mathematics with my collaborating teacher and taking the lead on lessons to increase my comfort level with mathematics and gain more experience. I am excited to continue focusing on mathematics in the upcoming weeks even if I do not participate in formal observations and conferences.