Mathematical Sciences, Secondary Education
WELL-STRUCTURED LESSONS
In order to exemplify this element, I must strive to "develop well-structured and highly engaging lessons with challenging, measurable objectives and appropriate student engagement strategies, pacing, sequence, activities, materials, resources, technologies, and grouping to attend to every student's needs" (DESE CAP). I must also aim to model this element.
FIRST ESSENTIAL ELEMENT
A well-planned, logically structured lesson plan is the foundation of any strong daily lesson. Lessons do not always go according to plan, of course, but I always found it particularly useful to have a good course of action going into a day and a few alternative activities in my back pocket. I noticed that on days when I had an especially strong lesson plan, I always felt more confident entering the classroom and focusing on things other than a last-minute adjustment or printing out extra materials, such as conversing with my students and checking in on their homework completion status, their understanding of yesterday's lesson, or their well-being.
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I found myself having to adjust my lesson plans almost daily, however, so it was rather difficult to plan them far in advance based upon my expected curriculum. The majority of the classes that I taught, by nature, needed more thought and responsiveness than an average classroom, since ELL and Inclusion students tend to pick up on (or need a reiteration of) material in unpredictable ways. This often required me to alter my lesson plans directly in the moment and to nix certain things that I had planned to cover, at the sake of synthesizing the new information properly and not overwhelming my students. Even the nature of Worcester Tech itself required proactive, near-improvised adjustment in terms of retaining student knowledge and focus while still staying true to the curriculum, with class periods lasting for only 40 minutes a day, with students also in shop during the week, and with the district's tendency to cancel or delay school somewhat frequently due to crazy Worcester weather or many students often walking to school or arriving tardy.
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Nevertheless, developing a strong lesson plan involves broad critical thinking and reflection skills, and it is no quick task. In order to develop my lesson plans, I often had to reach back into my own knowledge of the topic and calculate a scope of the subject that could feasibly be attained within a lesson or two. I had to think about my specific students and consider how many days that this would reasonably take for them to process, absorb, and apply to the point where further reiteration (ie., closer to MCAS or during test review) did not require a complete reteach. Once I reached this time balance, I had to break the lesson down into the elements that the kids already may have known as prior knowledge and use them as an introduction to the more novel parts of the subject. I had to chunk these new lesson pieces so that I could describe them in steps or lead into them from the students' perspective. After all, I always valued the power of allowing the students to figure the problem out their own with some light guidance and redirection, as it culturally responds to kids' possible learning gaps and boosts their confidence and problem solving skills. These skills are always an asset to have as a learner and foster a great attitude for students to develop, especially in math class.
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MY LESSON PLANS
Many of my students had already worked with a student teacher by the time that I began my practicum, especially my Inclusion Geometry students, so it was an interesting adjustment to enter the classroom. The students had highly regarded their previous student teacher and had rather high expectations for my impact on their learning, so I had to completely rewire my expected approach to their lesson planning (more of a traditional and lecture-based approach, as I had experienced in my own schooling, with a use of iPad note-taking and Schoology submissions rather than chalkboard lessons or creative activities) and teaching goals in order to cater to their expectations and still respond to their needs. All of my students needed much reinforcement to make it through new topics. As such, a lecture each day or a lack of activities and relevant technology (even though the school is not One-to-One) would not suffice to give students the relevant, holistic instruction that they expected.
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The students seemed to quickly adapt to my teaching style, which involved a somewhat extensive set of daily problems that reviewed and eventually challenged the prior day's lesson and thus led into our new topic rather smoothly. I began to experience an issue with accountability, however, as my students quickly noticed that they could get away with wasting ten minutes of intended review or opener work and converse with their peers instead, as I would eventually cover all of the problems on the board. I tried a few different methods to alleviate this, such as calling arbitrary students to the board to demonstrate a solution, giving a time limit on the problem to provide them with some urgency, or even collecting the problems for participation points before reviewing them on the board. Eventually, I even noticed myself avoiding formal Problems of the Day altogether and simply jumping straight into the lesson or the first problem of the worksheet. Either way, I attempted several different styles of lesson plans throughout my sixteen weeks, sometimes observing a pattern in my "experimental blocks," depending on the nature of the lesson itself and on how much actual review or difficulty that it entailed. Even my ELL
Algebra I students seemed to appreciate this change-up, as it provided students with different experience or confidence levels (eg., some who enjoyed going to the board vs. submitting work on paper or in their notebooks) to trust my instruction and to open up their minds to the content and to different ways in which they could learn it.
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For one of my very first lesson plans, I made sure to address the topic of the distance formula with a large focus on reinforcing vocabulary and keeping in mind the different questions that the students may have brought up, such as an assumed previous encounter with a pythagorean triple while questioning how to use it. I made sure to measure up to standards for each unit of my lesson, and I even brought some of what I had mentioned in this lesson back to the Quiz and the Exam for this unit, as briefly discussed on my Reflective Practice page. I also kept my timing in mind, as this was early in my practicum and I critically needed to section out how I would conduct each activity.
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For another lesson plan, I had to dig deep to figure out how to approach the topic of Proofs for my Inclusion Geometry students. Although I began the Proofs unit with a basic layout of how to write out basic two-column proofs and how to arrange the steps (see guided notes), I had to lead into the unit with some logic-based worksheets so that the students could accustom themselves to this type of reasoning, especially coming straight out of a heavily calculative angles unit. I strived to use relatable, almost silly examples to help build students' confidence and to introduce them to the reasoning that we were about to apply with the reassurance that they already know what they are doing, they just need to apply it slightly differently and strengthen their skills in doing so. I also directly applied the reasoning from this worksheet to my Proofs Quiz later in the unit as scaffolding.
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