Mathematical Sciences, Secondary Education
HIGH EXPECTATIONS
In order to exemplify this element, I must strive to "effectively model and reinforce ways that students can consistently master challenging material through effective effort; successfully challenge students' misconceptions about innate ability"
(DESE CAP). I must also aim to model this element.
FIFTH ESSENTIAL ELEMENT
Not to necessarily call myself a tough teacher, but I definitely kept my students working and adopted a slightly different outlook on homework and on work ethic than my mentor teacher had previously established when I was just observing. Although I stuck to his tendency to assign worksheets and to keep binders in check as often as possible, as it increased equitable access for students who would otherwise have to bring textbooks home or who generally have issues with taking proper notes and with organization, I was not one to easily allow extra time for quizzes and tests that easily could have been completed in class with slightly more focus (unless there was a special circumstance) or to give answers out when asked. I also readily gave weekend homework, much to my students' dismay who had had my mentor teacher during another year.
​
Setting high expectations in a classroom involves getting students focused and taking ownership of all of their learning aspects. Each day leads into the next, and if students can relate the information that they have previously learned to what is coming next and even make predictions for how it will challenge them, then they can easily reach their benchmarks and tackle new questions in their every day lives. Of course, in an academic career, problem solving involves reading the question and isolating necessary details as well as the question itself, and relating to prior knowledge (much like a chemistry or a physics question, where it is often helpful to copy the necessary formulas next to the question and to underline pertinent information while reading). Thus, I made sure to always ask my students, "What do we know? Why do we need to know this? What are we trying to find?" with the hope that they could apply these skills and this reasoning when taking assessments or when facing a novel concept or a new twist on an old one.
​
I also believe that keeping students accountable for their own information and learning involves withholding the answer to an inquiry to the extent that a student can get it themselves with the proper encouragement and by asking good questions. I often led my practice by answering questions with another question, as frustrating as this is often portrayed. This proved quite effective for getting students to think about what they were specifically confused on and about how they could progress from that point. For example, if a student would ask about how to solve a specific triangle problem with variables and an angle given (and flat-out ask, as in "How do I do this? I have no idea how to do this"), I would initiate a guided a series of questions and answers, such as, "What are you trying to find?" "Okay, are you sure you're trying to find x?" "Right, you want the measure of the angle itself. So what do you need to know to find that?" "Alright, so write that down in the margin. Now, what information do you already know? Write it down." "Nice, so what formula did we learn that needs all of these pieces? Think back to the other day...." "Great, now plug it in! Remember that you're not just solving for x!" I often reinforce the same reasoning of what we have, what we need, and how we are going to get there in guiding my problems, and I encourage that students write everything down. Once I have discussed these ideas at length during a lesson and through practice, I always expect these results and this reasoning to shine through on my students' worksheets and assessments, as they now know what I am looking for.
MY EXPECTATIONS
In order to build off of the concept of reasoning and of connecting previous ideas with new challenges (a higher order thinking skill when utilized critically), I often created ten-minute sets of Problems of the Day for the beginning of class so that students could work under a timed environment directly when they entered the classroom (although I admittedly left some time for chatter before the bell rang so that students could get their energy out and distract themselves briefly between classes, as they only had four-minute passing periods in a rather large school and were often groggy or in other classes and mindsets all day before coming to mine). These problems began with a review question that came from the homework or from the classwork of the previous day's lesson or which reviewed a pertinent concept to the new lecture. The next problem or two challenged that concept and led into the daily lesson. I always made sure that these latter problems were indeed solvable (to an extent) with the knowledge that the students had already gained, but that they also involved a new concept that was worth a lesson to cover! Even though I often spent a large portion of the class period on my daily problems (to the chagrin of observers and which had to be modified if I had a longer activity in mind), this seemed to be the best method to gauge if I could truly move on from the previous topic and still get information across or if it was imperative that we focus more class instruction on a topic that we had already covered. My students appreciated this approach and tended to ask many more questions the second time around if we decided to halt the further lesson and to step back for a reteach / review.
​
I wanted to increase autonomous work and reasoning in my classes, which I accomplished in a few ways. During my Proofs Project, specifically (discussed more on the Final Reflection page), I made sure to check in with my students often to see how their group work was going, especially since I was not able to give them as much in-class time to work with their groups as I would have liked to. However, I kept them accountable for their own contribution to the project with their strengths charts and with their rubrics, as well as expected them to apply group work and public speaking skills that they had previously established when presenting and producing the project (although I did not judge them on these when it came to the rubric as much as I looked at effort). Students also had to find the steps for the proofs on their own, autonomously researching which theorems were needed (although they were all given in their notes) and reaching a compromise on how to get the steps done and how to communicate resources, et cetera.
I also often established high expectations in class by assigning online work that could both be completed in class with proper concentration and which could also be accessed at home if needed (with any special exceptions to this worked out privately and equitably, such as the always available option to use Chromebooks for work during lunch or after school, or the resources in the school library). It was up to the students to get their work done outside of class if they could not complete it during school, as I gave them many opportunities to access online work if they were not able to do so at home, but if they were, then I also did not assign much other homework, if any, on nights that I had assigned online work, as well as gave two days to complete this work in general. At one point, I utilized a website that I found called Feromax, which utilizes an online proofs platform to give my Inclusion Geometry students access to the steps that they needed for various types of two-column proofs, at different levels, while letting them know if their solutions were valid. I also dedicated some time in class to demonstrate how to use this software. I assigned a few proofs to my students, with the final one as extra credit, and I asked that they completed the proofs online and copied the results / original proof and diagram(s) onto a separate sheet of paper, both proving that they completed the proofs and reinforcing the process of doing so via physical handwriting.