Category Archives: Classroom Successes

Math Classroom Success Stories (16-17, T2)

Here’s a glimpse into the world of the Williston math department from the second trimester of 16-17:

Mr. Matthias: The loved the level of engagement my Engineering & Robotics students showed during the last Trimester. Students asked many questions and demonstrated success with the last set of Challenges. I will certainly miss each one of them!

Ms. Baldwin: Three students wanted some extra help before their final assessment for the Winter term. We were not able to meet in person, but planned a time to meet using Skype for Business. We spent about an hour the night before the test going over problems and addressing their questions about all that we have been studying in probability. They were able to share their screens with me and with other members of the group and I did the same with them. Our time together was extremely productive and it was so convenient to meet in this way. We got a lot of good studying done and had a few laughs at the same time. It’s good to have one more way to connect with kids and support their learning.

Mrs. Whipple: One of my students, who works really hard, was discouraged that they were not getting the grades they would have liked on every test. We worked all trimester on their strategy and their confidence when approaching the material and by the final assessment they received a near perfect score!

Ms. Schneider: One of my favorite memories from class this past trimester was when one of my students became the teacher for part of the period. We often begin class by reviewing what we have learned in our previous lessons leading up to that day. This frequently includes discussing the homework assignment. At times the students get into small groups to review; however, on this day one student came to the front and lead the class throughout this activity. She walked the class through each problem, and kept every student engaged. Not only did her classmates gain valuable insight through her explanations and leading questions, but this student, who actually is considering a career in teaching herself, showed excellent leadership skills!

Mrs. Conroy: My Geometry assessment consisted of two parts, a group portion and an individual portion. The group portion of the assessment required students to stretch their problems solving abilities while doing geometry in a collaborative setting. As I described it to the students, “There is little you can do to prepare for this section. It will challenge you. Embrace the challenge.” The first question on the group portion was particularly challenging and involved proving triangles congruent after creating a diagram from specific instructions. Each group had the correct diagram but then the problem became interesting. Not a single group earning full credit on the problem but what I witnessed in the classroom during that question was the best math we had done this year. Students were questioning each other, everyone was participating and incredible thoughts were being debated. I was thrilled to sit back, listen and watch young minds at work. Well done my Geometry students. I am proud of your fighting spirit!

Mrs. Hill: I found a stats textbook that used a real trial from 1964 to illustrate the problems of assuming independence to calculate probabilities. A woman had been mugged in CA, and the prosecutor used the assumed probabilities of a man “driving a yellow car,” and being “over 6 feet tall,” and “having a beard,” etc to calculate that the odds of the defendant NOT committing the crime were less than one in a million. Unfortunately though, as the appeals court later determined, the prosecutor was wrongly assuming independence of events when, in fact, there was no way to be sure of that fact. It was a real life example of issues of conditional probability we had been discussing in class. Moreover, we also got the chance to discuss how, in modern times, DNA evidence is based heavily on probabilities. We were not all in agreement as to the legitimacy of that approach.

Mr. Seamon: The math team has been enjoying a very active and successful year! In additions to competing in the 6 rounds of the New England Math League, returning to the Harvard Math Competition, as well as participating in the AMC8/10/12 competitions, the team has also added in the Middle School NEML competition as well as heading to Yale for their spring HS competition. Not only is the team competing in more competitions than ever, the team is scoring as well as ever currently holding strong at 28th our of 140 teams in NEML, scoring in the top 1/3 of teams at the HMMT, and also qualifying a student for the American Invitational Mathematics Exam!

Mrs. King: I have a student who has been away at ski school during the entire second trimester and will return next Monday. Before she left her family and I had a discussion about what math class she should take, an Algebra 1 class at ski school or work with a tutor to complete our curriculum. Wanting to come back fully prepared for the third trimester she chose to work with a tutor and complete our notes, homework, quizzes and tests. I set up One Note Notebooks for both her and the tutor. After a little bit of a slow start she was off and running. The tutor and I communicated each week about what was due, what was coming up or any questions or concerns that we had. The tutor was wonderful and read all of the notes and assisted Arden after she did her assignments. Arden did a great job! It was great that she was willing to take on extra work so that she would be able to transition back into class next week. I can’t wait to have her back in class.

Ms. Smith: At the end of our unit on transformations of functions, my Pre-calculus students spent a class period designing a mathematical roller coaster. That is, using their knowledge of the parent functions and transformations, they created one continuous, piecewise-defined function that traced the vertical height of the roller coaster with respect to horizontal distance travelled. As students discovered, the trickiest part was ensuring that the functions linked up, that is, there were no unplanned gaps in the track. However, after a period of work there was a wide range of functions (or should I say roller coasters). Highlights included underground tunnels, death drops, and even a loop-the-loop made using logarithmic, exponential and even elliptic functions.

Mrs. McCullagh: We finished the winter trimester with a project in Calculus. The assignment was for each student, or student pair, to decide what they wanted to hang and from where and then find the minimum amount of wire needed to hang their object. They needed to decide how far apart their two attachments should be and how far down they wanted the object suspended. They needed to find, using calculus, the minimum amount of wire needed for their own scenario. It is a challenging calculus problem for students as they are learning how to solve maximizing/minimizing problems. Then they needed to present their findings with all calculations clearly shown and diagrams labeled with the minimum and extremes. They also needed to produce a model made to scale. The projects were outstanding! We had a target hung from a tree, donuts hung for a birthday party, a chair hung is a bedroom, a rubber ducky hung (just because), as well as a number of others. The students all reported that they learned a lot from the project. It is great to have their work on display!

Math Classroom Success Stories (16-17, T1)

At a recent math department meeting each teacher was asked to write about something that went particularly well in the first trimester. Here’s what they wrote!

Ms. Evelti: I had a student who came into my Video Game class reluctantly, unsure if she would be interested in the work. She ended up really excelling in the class both in the technical and creative aspects of the work. She brought humor and visual interest to the stories behind her games while challenging herself to include difficult interactive elements in her projects that extended and deepened her understanding of the topics we covered in class.

Mr. Seamon: As we moved into a different system for graphing (polar coordinates), I worried about the transition. It’s a reorientation of how to look at the basic space we’ve been working in and it’s been a challenge in the past to communicate the new “up” and “down”. This year I tried bringing in a scene from a science fiction classic (Ender’s Game) and it went over quite well, even though most of the students hadn’t read the book! Having a concrete picture of our new space for differentiation and integration has translated into a deeper understanding on the part of the students which has been expressed through impressive board work and high quiz scores.

Ms. Schneider: One of my favorite things to do in class is play a review game. Although I made up the game myself, it is similar to jeopardy where the students pick questions of different difficulty within a topic. The students are split up into teams, and if one group answers a question incorrectly other groups have an opportunity to steal the question. I absolutely love this game because the students work so well together in their groups and are extremely invested in each problem. They have smiles on their faces the entire time as well as they work meticulously to complete the problem within the time frame. The pure exhilaration of getting a question correct or having the opportunity to steal a question brings such a positive energy to the classroom. Every test that we have my students get excited because they know that means we get to play the “review game” the lesson beforehand.

Mrs. Conroy: It has been a treat to return to the Geometry classroom. The biggest change in this class over the past three years has been the use of technology. Now that each student in the class has their own surface loaded with the geometer’s sketchpad software, the variety of classroom activities available to the class are remarkable. Each day feels different. We are discovering geometry through investigations, constructions and traditional class framework notes. My ability to project figures from a variety of sources has led to a much more efficient classroom. Students can see examples in one note as well as on the board and we are able to spend so much more classroom time doing problems. This has not gone unnoticed by my students. They enter class wondering what will we be doing today. Some things never change. Students love to find the missing angles but proofs remain a challenge!

Mrs. Hill: My Topics class can be a bit of a raucous group. The students are all seniors who, for the most part, have not all had great success in mathematics. In this course, however, we are focusing on political and societal applications of mathematics, and the “math” kind of sneaks in under the radar. A young woman in that class has struggled in past math courses at the school, but has had tremendous results in this one due to her intense work ethic and willingness to participate. She talks about how she really understands the relevance of this course and can appreciate how math is used in the “real world.” It is so wonderful to see a person who, before now, has not seen a use for mathematics discovering how it can be relevant to her life.

Mrs. Whipple: During a recent lesson on proving congruent triangles, students in my geometry honors class where given a new type of problem using overlapping triangles. They were put into groups and sent to the white boards to work together to come up with the most efficient ways to prove that certain triangles were congruent. Afterwards, we talked about all the strategies that each group used in tackling the problem and which worked best. After sharing all their ideas and observations, they were given another extremely hard proof to work on together. Not only did they use the strategies that we talked about but the majority of the groups commented on how “this problem was much easier”, when it was actually much more challenging.

Ms. Briedis: In a recent class we were beginning a lesson on composite trig functions. The lesson started with absolute value functions and the students were amazed by how the absolute value of a trig function changed the way the graph looked. We began playing with trig functions such as f(x)=(x^2+1)sin(2pix), and they thought the graph was the incredible. The amazement on their faces was exactly what teachers thrive on. We began playing with different functions on, and each student began creating their own functions and then would share them with the class. We would then work on what the two functions would be that the overall function oscillated between. It was a really fun lesson that the students connected with. They were engaged and excited about the different functions they were creating and seeing from others. It was an overall thrilling time to see them so inspired about graphing.

Mrs. Baldwin: Our class has been investigating random phenomena through use of examples and simulations. The students are doing a great job figuring out what makes a process truly random as opposed to arbitrary or haphazard. We have been noticing that the word “random” is used often in a casual sense in everyday language and have begun to recognize cases where the word is used inappropriately. Students did a great job with a recent project in which they found a probability estimate through a little research and conducted a simulation in which they used a random number generator (or table) to conduct repeated trials. One example involved estimating the number of attempts needed to catch a toy in the claw machine when there is an 8% chance of grabbing the toy on any single attempt. The student discovered, through 20+ repeated trials of this simulation that it took about 12 attempts on average. This corresponded with the estimate published on the website. We will next investigate the theory behind these random phenomena and connect the underlying principles to our observations. It has been great working with these students who bring enthusiasm and a lot of creativity to class.

Mr. Matthias: Each year when the class starts Engineering & Robotics, they aren’t quite sure what they will be facing. There is some concern as we begin with a survey of Engineering and the Engineering process. Then, as we start ROBOTC programming, the class begins to feel more comfortable and confident about the material. We practice our programming with robots in “Engineering Labs” designed to give students practical experience with programming the movement of their robot to achieve certain goals. The Engineering Labs soon become one of the favorite activities of the class and students regularly ask if we are doing one in the day’s class. As a teacher, I am so thrilled that the class looks forward to this engaging hands-on learning activity.

Mrs. McCullagh: Looking back at trimester 1, I am particularly pleased with how the students adjusted to the abstract nature of Calculus. In this course they are asked to use the skills they have built in Algebra, Geometry, and Pre-Calculus. To that we add the concepts of Calculus. While challenging, the students did really well in working with limits and longer problems than they had seen in the past. We spent a block of classes exploring the definition of the derivative. The students have a very good intuitive understanding of what we mean by derivative being the instantaneous rate of change.