Mathematical Sciences, Secondary Education
MEETING DIVERSE NEEDS
In order to exemplify this element, I must strive to "use a varied repertoire of practices to create structured opportunities for each student to meet or exceed state standards / local curriculum and behavioral expectations" (DESE CAP). I must also aim to model this element.
THIRD ESSENTIAL ELEMENT
Throughout my practicum, I made sure to attempt to respond to the needs of as many of my students as I could, as often as I could. Many students at Worcester Tech often come from family situations where they spend much of their time outside of school providing for their families and working many jobs, thus they do not always have much time for homework and for projects that take a significant amount of time outside of school. I often had to utilize class time to introduce new online programs and activities, as well as to work on larger assignments or on problems that were out of textbooks. I provided my students with worksheets, packets, and printed textbook assignments as often as I could, both for in-class notes and for homework / practice work. I attempted to culturally respond to students who walked to and from school, who had lower access to resources outside of the classroom (only requiring a pencil, a notebook, and perhaps a binder to succeed in the class), and who had limited "homework" time on their hands and could only afford to spend 20-40 minutes on their homework on most nights. I tried to avoid weekend homework and to work on projects in class, both for individual instruction and to ensure that students stayed on track and could all keep at the same pace (see my Culturally Responsive Teaching Proofs Project analysis on the Final Reflection page).
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I also provided my students with ample attempts (or at least as many as I could) to apply their shop or external subject knowledge to their classroom studies. I used these as opportunities to scaffold my instruction in ways in which the students could apply their previous knowledge to the topic and still lead themselves to the answer (as rather became a trademark of my teaching style). Part of this was inspired by my Sheltered English Immersion (SEI) class from A-Term, where we discussed the consideration of students' possible learning gaps and family or lingual backgrounds in our instruction. Many students came from situations outside of my classroom that I did not fully understand, even with their various shops (Worcester Tech has about 23 vocational options, after all), and as I wished to aid my kids' learning in any way that I possibly could to cause them to synthesize the information effectively, it was a goal of mine to openly provided them with opportunities to demonstrate what they could do. I engaged students by including their names in my Problems of the Day, and I kept the shops in mind with my extra credit problems and with my self-made worksheets, as well as provided different opportunities for students to express their capabilities and to demonstrate their knowledge, as in the examples discussed below. Scaffolding was the most useful technique that I could put into place to assess and to adjust based upon students' capabilities.
MY DIVERSE RESPONSES
Each day is a new learning experience, and sometimes it takes a new approach for information to truly sink in. Depending on students' situations and on how they need information reinforced, they may or may not synthesize prior knowledge or absorb new information the first few times around. I took full advantage of the concept of scaffolding to reach each of my students as thoroughly as I could. For one, I decided to do a "Multi-Step Proofs" activity with my geometry students so that they could internalize the concept behind finding their own steps for a problem. I took a packet that my mentor teacher had previously used a few weeks earlier with our Algebra I students (and thus which all of our Geometry students had also familiarized themselves with in their prior year's studies) and I tweaked it so that the columns that had previously asked for a description of each arithmetic step to solve a basic algebra problem now requested the Property of Equality that specifically led to their reasoning. I gave the class some modified slips of paper that they could work with their groups to organize into the proper steps rather than generating these themselves, aiding them in breaking down the exact process that they needed in order to fully expand upon a rudimentary algebra topic that they are overly familiar with. I feel as if this activity was critical to solidifying their understanding of proofs after we had briefly introduced them and had discussed logic-based approaches, and I made sure to further quiz my students on problems like this in a two-column format so that they felt confident in generating their own proofs and in applying the skills that they had mastered in previous years to a new concept. Students also had the opportunity during this activity to copy down the steps simply of their own accord or to work with their groups to organize and to lead its progress, as each group member needed to be on the same page before the group could trade its slips in for a new set with a new question.
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Similarly, on the final day of my practicum, I wanted to ensure that my Algebra I students could continue their school year strong after I left. I noticed on their recent exam that they had been particularly struggling with the concepts behind linear inequalities and how they behaved when the x- and y-axes related to tangible object relationships, such as food or clothing correlation. As it was my last day with these students, I decided to bring in treats, and I felt inspired to base my activity on the cookies and snacks that I had purchased, showing my dilemma over how well to treat my kids as a real-world application of the problem-solving methods behind dual-element inequalities and graph shading! I made sure to scaffold each section of the problem thoroughly, using alternative yet practical vocabulary for various aspects of the problem throughout the worksheet. To my surprise, most kids completed this entire worksheet in exactly the class time allotted, and they all seemed very engaged when I asked them to pair up and to eat their sugar while solving a real issue for me. They also seemed very eager to receive their tests back and to re-attempt the related problem that they had near-unanimously missed the day before!
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As an established goal of Worcester Tech's math department for the school year is to utilize technology near-daily in the classroom, I made sure to introduce various online platforms and calculative programming tools to my students. In our class, we often used EdCite, which offers benefits for each grade level. It is a great resource for creating online assessments and for tracking grades, difficulties, and mistakes in one place. I created many problems and compilations here, which I often assigned to multiple classes depending on their level of review need. Students learned how to use this program during their freshman orientations, and we completed many exams, review assignments, and MCAS mock questions on the platform in class such that the students had ample opportunity and access, both in and out of class, to our current material. I also utilized DeltaMath, another online hub for assigning problems and for specifying exactly what the students should be focusing on. This program conveniently recorded the number, the details, and the duration of the attempts at each assignment for each of my students, which gave me great insight into how they were viewing the questions' premises (which was especially helpful for my ELLs) as well as how they responded to various challenges that were not necessary analogous in format to those which I had presented in class. I devoted part of a day in class to creating accounts through this program and to instruction on how to use it, increasing inclusivity and giving students a chance to ask questions. In addition to its plethora of useful features, this program conveniently contains a graphing calculator function as well, which I often projected on the board for students to attempt their graphs for the class and to view my input. This paired nicely with our frequent in-class review of calculator usage, where we often passed out graphing calculators in lecture and demonstrated how to perform our current calculations during exams with ease.