Is there more than just giving tests? Reflections on a math PBL by Shira Teichman.

Anyone who knows of my background in Secondary Math Education and/or my current position as a high school math teacher feels obliged, it seems, to email me links to the myriad of math-related articles that are currently riddled throughout Twitter feeds and newspapers.

Many articles have little to no bearing on my teaching (e.g. the private school that I teach in did not need to reorient their curriculum to fit the Common Core), but one recurring topic did truly tug at my pedagogical conscience: TESTS. How much emphasis should we give to students' performance on tests?  Why are tests so anxiety-provoking, to the point that they often hinder students from showing their knowledge masterfully? What are other forms of assessment that can supplement tests? How truthful is the age-old saying, "either you know it [on the test day], or you don't!"?

In an attempt to answer some of these questions, I brainstormed with a colleague and we decided to assign an Independent Study project to be completed once during each of the four terms of this year in two classes that we co-teach. These projects would serve a dual purpose. They would help diminish the weight of tests in the average calculated each marking period. Moreover, these projects would give students the opportunity to apply some of the skills they were learning to real-world scenarios, thereby reinforcing knowledge in the context of an interesting topic of study. 

My "grade-level" sophomore Algebra 1 class does not cease to amaze me; all of them were receptive to, and most of them were quite enthused by, this idea. The students were allowed to choose from a list of topics of study - ranging from the distance from Earth to the Sun during a year's perihelion, to unit pay rates of entertainers like Leonardo DiCaprio as compared to athletes like Koby Bryant. 

The beauty of this Independent Study was that both the teachers and the students worked independently. Once they chose a topic, the students accessed and printed accompanying worksheets from our class website and answered the questions that followed a graph, article, or excerpt of information. Although they were allowed to confer with teachers and classmates, or look on the web for help, students could complete the assignments entirely on their own. Furthermore, as teachers, we worked very "independently"; these assignments were taken from excellent websites such as yummymath.com, illuminations.nctm.com, and mathalicious.com, which our Math supervisor mentioned briefly in a summer professional development session after she met some of these site-writers at the ISTE Convention.   

We were amazed with the results of these projects. When we eliminated the build-up of pressure and the frantic race against the 40-or-so minute timer that accompanies a test, the students produced work that showed self-motivation, creativity, thoughtfulness,application and retention of skills, and mathematical rigor. We are particularly proud to see our sophomores strengthen their ability to learn and produce mathematical work independently of a structured classroom lesson. Aren't all of these components what we math teachers strive to see students display on a test...?  

Blended Learning: The New Normal for Math at Frisch

The math department at Frisch is using technology in exciting and educationally progressive ways.  From real-time assessments to flipped classrooms, our students are being taught using various modes and the feedback and results have been wonderful.

Digital Storytelling: Math Style

In my and Mrs. Elissa Katz’s 12th grade Precalc classes, students have started creating short videos on various self-selected topics listed on a google spreadsheet  The videos created will eventually become part of a video library future Frisch students who take Precalc can utilize.  The students are graded based on a rubric provided by the teachers beforehand and the grade on the video correlates to a test grade. Here is an excellent video by Frisch student Debra Paul ‘15 on solving for the roots of a quartic equation when given one root. Students appreciate the opportunity for an alternative assessment and are honored to be part of the first of many future video libraries of Frisch math classes.

Feedback in Real-Time

In several of the 11th grade Algebra 2 courses, students were given a review sheet with a QR code for this past week’s test.  After completing the problems on the sheet, students submitted their answers via the QR code and got immediate feedback of their grade on this mock assessment. The students’ scores on the review sheet were also emailed to the teachers who gave a participation grade which will then count towards the students’ average. These juniors, many of whom have started studying for the SAT or ACT, have grown accustomed to practice tests and were happy to see that model reflected in their math course.  The day of the exam, students commented that they felt relaxed walking into the test since they already had received quantitative proof confirming they knew the material.  Other students liked the fact that they had prior knowledge of what to work on before the actual test.  Often students don’t know the material as well as they think they do and the problem specific knowledge gained by the real-time assessment positively guided the rest of their review work

Flipping the Classroom

Additionally in a 10th grade honors algebra 2 course my students are starting to learn about piecewise functions from a “Show Me” video I created. Students were also given a worksheet modeled after the examples in the video to work on at home.  The next class was used for further developing the topic rather than introducing it.

 

Self Check Quizzes

The ninth grade Geometry classes of Mrs. Katz, Mrs. Shira Teichman, Mrs. Debbie Stein and Mrs. Chanie Schlesinger have their own unique blended learning opportunities.  The textbook they use has a rich online component.  The students regularly are assigned online self-check quizzes which correlate exactly to the section and topic they are currently learning.  The immediate feedback gives these students and their teachers are better understanding of what exactly the students understand and what they need further review on. It directly affects the pace and depth of the instruction specific to each class of students.

 

Differentiated Instruction

Through a grant from the Digital Jewish Network, the first blended learning platform used school wide at Frisch is now in its first year. About 200 students are enrolled in some way in a program created by Educaide.  Two senior classes are in a college preparatory program which reviews skills from Geometry to Algebra 2 based on a student’s performance on an initial diagnostic test.  This differentiated coursework helps prepare the students for future math placement tests at their respective colleges and university.  Several 10th grade classes are enrolled in the program as an extra avenue for test review.  The teachers create a custom problem set tailor to the topics on the upcoming test.  The program gives immediate feedback to both the student and the teacher about their performance on the problem sets. Lastly, some of our students with greater challenges in the basics of math are enrolled in skill building courses which review and solidify basic algebra skills concurrently while they learn Geometry.  It is truly differentiated education at its best.

Other 21st Century Tools

While as shown above there are many large scale blended learning initiatives taking place in the department, individual teachers are also branching out from the traditional reliance on just the textbook.  Teachers are using Desmos, Smart Notebook Math Tools, the Ti Emulator among many other apps and programs.

Professional Development

With a strong emphasis on professional development particularly in the area of blended learning, the math department of Frisch bears little resemblance to class just a few years ago and is growing and advancing at a quick pace.  There is still present of course the warmth, support, and humor that has always been a hallmark of the Frisch math department.  Looking forward to future posts about more of the exciting adventures in Frisch math classes!

 -By Mrs. Sabrina Bernath Chair, Math Department

Crossposted from Frisch.org

We are off and running......bring on school year 2014- 2015

School might have been out July and August but the math department kept on learning.  Mrs. Silverman and Mr. Grossman attended intensive week long AP teaching courses in AB calc and BC calc respectively. Mrs. Bernath and Rabbi Pittinsky went to Atlanta for three days to attend the world's largest educational technology conference, ISTE with 15,000 other teachers, students, and educational technology providers.  Additionally numerous math teachers were in attendance during August at Frisch's Seventh Annual Summer Technology Boot Camp learning about the flipped classroom, our new learning management system Haiku, and real time assessment, amongst numerous other software and apps available to them at Frisch.

Without a moment's delay we were up and running, ready to try all that we learned out on our new students.  Below is one example from Mrs. Teichman's 10th grade Algebra 1 class of our progressive and reflective teaching approach.  Never one to simply do the same old lesson, Mrs. Teichman created a wonderful opportunity for collaborative work while developing the students' creative side. Here it is in her own words...

Making Algebra More “Valuable”

I am constantly looking to enrich my sophomore Algebra 1 class, yet I was waiting to introduce any enrichment activity until the students first grew accustomed to our classroom routines and procedures.  Starting on the first day of school, my students proved themselves to be highly motivated, articulate, and cooperative; no math challenge was too difficult for them to try, no student pairing was unsuccessful. Two weeks in, I was ready to try something different.

Problems with Words (aka “Word Problems”)

Our lesson on Cost, Income, and Value Word Problems was, as I expected, a bit more difficult for many of my students. After modeling several such problems and assigning homework,I thought about the main issue: decoding the mathematical language and expressing it algebraically. I thought, "Wouldn't it be beneficial if my students could first see the scenario and then try to formulate descriptive phrases?", and formed the following lesson.

The Plan

Upon arrival to class, my 18 students would be divided randomly into three groups of six and seat themselves as the three desk clusters that I had made.

Each group would be provided with a piece of lined easel paper, a magic marker, and a pocket with their group name and a series of coins underneath it.

During Round 1, the groups were to write a word problem to describe the amount of coins that they had been given. I encouraged students to use phrases such as “3 times the amount of” “twice as many”, and “4 less than.”

During Round 2, the groups would rotate seats and head to the next table, where they saw a word problem and had to decode the language and arrive at a solution.

During Round 3, the groups would rotate to the third cluster of desks where they saw both the Word Problem and algebraic solution on the easel paper; their job was to check for and correct any errors.  

Finally, during Round 4, groups would return to their original clusters and see their classmates’ solutions (and corrections) resulting from their original word problem.

The Outcome

My plan went pretty smoothly, although I had underestimated how much time it would take the groups to accomplish the tasks in rounds 1 and 2. Groups struggled to decide on a word problem whereby one group member came up with a convoluted (and impossible) word problem which his own peers couldn't decipher even with the scenario in front of them. One group arrived at a perfectly solvable word problem, but made careless errors in their solution and therefore could not find an answer.  Yet another group had trouble finding the said error,and simply restarted the solution.

When we regrouped as a class, I posted the posters and led a discussion on "what worked and what didn't" and analyzed each of the group's collaborative works.

Reflections

Before we knew it, class was over, the students filed out, and our busy days rushed onward. Later that evening, I was able to reflect on just how powerful this activity had been for my students.

• Strong Command of Mathematical Language - Students were able to recognize the meaning of tricky statements like “There are 4 fewer quarters than there are dimes” when trying to describe their amount of coins.
• Collaboration - This group of sophomores is particularly cooperative in this regard, but the project helped them realize how important it was to communicate and agree when formulating a piece of work.
• Creating a Word Problem -  Word Problems are often an Algebra student’s worst nightmare. First seeing a solution and cloaking the answers in creative words helped give an entirely different perspective to the task of solving these problems.
• Pride and Ownership - Having others try to solve their unique creation no doubt gave the students a sense of ownership of the material and pride at creating something mathematically sound. Breathing life into a creative work is an act that colors the English, Creative Writing, and Art classrooms but that, unfortunately, our textbook-based curricula strips from the Math classroom.

I am so proud of my students for their effort and I look forward to continuing to show them how math can be the synthesis of creativity, precision, and collaboration.

-Mrs. Shira Teichman 
Math Teacher and Enthusiast The Frisch School

Blending Math Class with Student Buy-in

 Here is a link to a reflection I wrote on the JDigitial blog about blended learning in math classrooms.  It is exciting to share with others the knowledge and success we have had at Frisch. Ithttp://bit.ly/1uEwG42

The Frisch Math Department Grows Exponentially: Our Year in Review

It has been a productive and successful year for the Frisch math department. Below is a “Year in Review” of all the math department’s activities from flipped classrooms, blended learning, real time assessment, continued standardized test preparation, and an integration day of Torah and math. Additionally the math department took part in more professional development than ever before. We are proud of all our ventures into these progressive venues of education and are happy to share brief descriptions of each and knowledge gained from them during this past year.

Flipped Classroom Videos:
Mrs. Rhona Flaumenhaft paved the way creating various videos she posted on her own YouTube channel. Students and parents were able to easily access her videos created with Explain Everything. The videos, created for both instruction and test review purposes, have been particularly helpful for various students. For instance, those who find the typical speed of classroom instruction possibly too fast for various reasons can now could stop, review, and play again. This is especially helpful for those students who are auditory learners.

Additionally, Mrs. Shira Teichman and Mrs. Chanie Schlessinger have also started to explore Flipped Classrooms in the spirit of “virtual snow days”. “Virtual Snow Days” became a hot topic in the press and media this past year as schools attempted to continue student learning even when the building was closed. The math teachers at Frisch feel likewise that every day is a chance to learn. So, by the fourth frustrating snow day, Shira and Chanie each created a video in place of their usual frontal classroom instruction. Then when students returned to the classroom, they worked on problems corresponding to the topics in the videos. Since there was less time spent on introducing the topic, students appreciated having more classroom time to work on the algebraic skills whether as a group and individually.

A third benefit of flipping the classroom is that by outsourcing the basics to the video, students can spend additional class time conquering harder, higher-order thinking math problems in class while the teacher is present to guide and assist the students. Both teachers were grateful to not lose yet another day of teaching. There are plans to create additional videos on the topic of direct and indirect variation this summer in preparation for what could be another harsh winter.

Blended Learning:
The Frisch math department received a generous grant through the Digital Jewish Learning Network to start a blended learning component for several of the math tracks at Frisch. The overall goal of the program is to have students gain more mastery and then better retention through differentiated review and assessment. Through customized problem sets students will be working on prior fundamental skills or current classroom topic dependent on their math track. Though the program will not be fully launched until September 2014, Mrs. Sabrina Bernath and Mrs. Elissa Katz were able to pilot the program this year with 40 students. Using a free three month trial of Catchup Math, Sabrina and Elissa, implemented a blended learning component into their 10th grade Algebra 1. Using Catchup Math, students were either assigned homework from the program rather than the textbook or did test review work in custom made problem sets. Besides greater student accountability, there was more more time spent on instruction and less time spent on administrative tasks like collecting and returning homework since all of the classes work was all accounted for on the program’s teacher dashboard. Catchup Math also gave students instant feedback on whether their answers were correct rather than waiting to check-in the back of the book or until the teacher looked over the work.

The benefits of this new initiative were evident within the first few weeks of our pilot. Quiet students were given a chance to shine. For example, one girl in particular was always very quiet in class simply shaking her head when called on by the teacher, but through Catchup Math the teacher was easily able to see her effort by getting readouts of her time spent on task and the number of problems she completed successfully. Not only did she do the assigned problem sets but she did all 9 of them entirely in one night. While her work was not perfect, it showed the teacher she had not only a strong grasp on the material but also that she put forth tremendous effort to succeed.

Other students felt the break from learning from a textbook was refreshing and made the homework actually more fun. Although the initial pilot has only provided us with anecdotal evidence thus far, the test scores on the material supplemented with Catchup Math appeared to be higher than the grades of students from past years on the same material. Additionally, student errors on the exam were more careless than conceptual in nature which seems to show a greater understanding of the concepts than past students have demonstrated.

Real-time assessment: 

This year several of the Algebra 1 and Algebra 2 courses benefited regularly from real time assessment provided by a program called Problem-Attic. Whether as “ Do Nows”, exit slips, or structured group work, students used their phones or iPads to enter their answers to various multiple choice or fill in the blank questions on a worksheet after scanning in the paper’s QR code. Once the code was scanned and answers were submitted, both the teachers and students were emailed the students’ scores. Additionally on the teacher dashboard which could be displayed on the Smartboard, the teachers and students were able to see breakdowns of what percentage of the class understood each individual question and what were the percentages of students who chose A, B or C for the multiple choice questions. When 80% of the class picked the same wrong answer for a simple question, the teacher got immediate feedback what skills had to be add to the day’s lesson.

The speed and level of detail of this real-time assessment was invaluable. For instance when teaching a lesson on percentages, Mrs. Bernath was quickly able to decipher which topics the majority of the class already showed mastery of and more importantly which ones the students did not seem to know. Rather than starting her lesson with more percentage word problems which the class was not yet ready for, she was able to step back and review the idea of solving simple percent problems such as 80% of 30 is what number. This type of lesson quickly became an exciting and popular choice with the students. They were able to articulate that they felt in more control of the lesson both in terms of its pace and content.

Standardized Test Preparation:
Tenth graders in our Algebra 1 class help pilot an SAT/ACT prep initiative. After each exam, students were given 4 to 5 SAT questions which corresponded to the material they were just assessed on. This supplemental program is being expanded for all tenth grade math classes next year with the goal of including more classes in the coming years. The worksheets are also being put into a Google Doc where students can access the questions remotely.

Integration Days:
Rabbi Gedaliah Jaffe, a teacher in the Frisch Talmud and Chumash Department gave the honors 9th grade Geometry classes a wonderful talk about the mathematics involved in determining an eruv. Students got to see the direct application of math topics such as area of a circle and right triangle trigonometry as the Gemera discussed the concept of Tchum Shabbos. To see the direct use of mathematics in halachic discussion was fascinating and particularly relevant as the students had just finished studying those very topics. Here are some student reflections on this Torah and Geometry integration.

Professional Development:
As lifelong learners whether it is in the areas of math or teaching, the Frisch math department looked for and enjoyed various professional development venues. Teq came for a full day seminar and showed us first hand the educational value of project based learning utilizing iPads to video student created “catapults” and analyze the dataset. In April, five math teachers went to Rutgers University’s 28th Annual Precalculus Conference. They took various classes on teaching methods, technology, AP calc, and Core Curriculum standards. The highlight of the day was an entertaining and stimulating talk by mathematician, professor and author , Dr. William Dunham, Professor of Mathematics at Princeton University on the various ways to prove Heron’s theorem for the area of a triangle. All the math teachers agreed that they thoroughly enjoyed being the students for a day. You can read more about this conference here.

Additionally we have taken advantage of several professional development opportunities through the Digital Jewish Learning Network, an off-shoot of Jewish Education Project. Our department chair, Mrs. Sabrina Bernath attended a panel discussion on blended learning called “ Moving Beyond the Pilot” which was informative and especially timely as we move ahead on our blended learning initiative funded by DJN described earlier in this posting. You can read her reflections here.

Additionally, just a few weeks ago, two of our Math teachers, Mrs. Chanie Shlesinger and Mrs. Rhona Flaumenhaft attended a conference sponsored by the Lookstein Center on Flipping the Jewish Classroom together with four Judaic Studies teachers and administrators from Frisch. Although the focus was on the Flipping the Classroom in Judaic Studies, both Chanie and Rhona felt they gained much valuable information and had many thoughtful discussions that they can apply to their Flipped Classroom model in math. You can read Rhona’s reflections on this valuable just in time professional development day here.

Finally, this post is being written while Mrs. Bernath and Rabbi Tzvi Pittinsky, Director of Educational Technology, are on a flight to the ISTE conference in Atlanta , Georgia. ISTE is the largest educational technology conference in the world with some 15,000 attendees. Stay tuned for further posts about this conference and how the cutting edge technologies featured at it will be utilized to further improve student engagement and learning in math classrooms at Frisch.

It is an exciting time to be learning and exploring math for both the teachers and students at Frisch. We are grateful for the summer break to have the time to reflect on this past year and to start planning for what will sure to be an exciting new school year in the 2014- 2015 school year.

How to Flip a Classroom; Let Me Count the Ways

On June 10th, thanks to the urging and assistance of our beloved Director of Educational Technology, Rabbi Tzvi Pittinsky, with support from Rabbi Eli Ciner, Mrs. Chanie Schlesinger and I, stalwart members of The Frisch School Math Department, headed to Ramaz to attend the “unConference on Flipped Learning in Jewish Studies”. Many of the session leaders had trained in the year long course, The Flipped Jewish Studies Classroom, sponsored by The Lookstein Center with a grant from the UJA Federation of NY. They were eager to share their excitement and the expertise garnered over this past year.

What we learned is that there are many different ways to “flip a classroom”. Not all of them require intensive use of technology, but they require a re-evaluation of how we teach. What all Flipped Classroom models share is a recognition that we, as teachers, need to engage our students in new ways to promote meaningful learning that will prepare them for the world in which they will live and work. The world has changed dramatically. Julie Schell from Harvard University, the keynote speaker, made the point when she contrasted the differences between an operating room in the 1800’s with the operating room of today. They were shockingly different; technology had transformed the OR. When these OR photographs were contrasted with a comparison of the classroom of today and of yesteryear, the differences seemed shockingly non-existent. Sir Ken Robinson, in a video clip during one presentation, spoke about this lag in the development of new ways to teach, and warned that it was something we needed to address.

The emphasis is now on creativity, for both teachers and students. The availability of real time feedback to make sure all the students are set up for success, allows the teacher to rethink how he or she will teach her lesson. By empowering our students to take ownership of their studies, and encouraging and supporting their natural desire to collaborate and work together, the expectation is that our students will be able to learn better, deeper, and with an increased ability to apply what they have learned. The hope is that we can replace rote learning and memorization with analysis and critical thinking. What was very exciting was the idea that there isn't one method, one app, one style that is “the way”. Each teacher can adjust and adapt the process to mesh with his or her own strengths and talents. The key is to be willing to change and embrace new methods.

We were warmly welcomed by everyone; no one seemed to mind that there were Math teachers in the room! Many of the sessions were led by educators who were using some very powerful and exciting apps in their classrooms. They provided information and support. The keynote speaker also shared examples of ways to adjust our thinking to a Flipped Classroom Model that is not totally reliant on extensive use of technology.

There is no question, however, that technology gives us tools to interact with more students, often almost instantaneously in “real time”, so that we can have a better understanding of what they know and what they don’t yet know. Google Presentation, Google Forms, Socrative, eduCanon, were some of the apps we learned about. We learned about Club Academia which showcases student-made videos, allowing students to teach students. Both Mrs. Schlesinger and I hope to perfect our own video-making skills, in the coming year.

Both of us returned home eager to implement these programs in our Math classrooms. We look forward to sharing these ideas with our colleagues during the weekly meetings, organized by our Math Department Chair, Mrs. Sabrina Bernath, that are an important tool in our search to improve and keep abreast of new developments in Math education. We both agreed that Math at Frisch was going to be even more exciting in the coming year.

More important than any single app or program is the way this conference made us both feel. It inspired us to increase our efforts to find new ways to make our teaching more effective. We saw these changes as incredible opportunities for our students that we wanted to foster. As Mrs. Schlesinger put it, “I’m so excited that I can’t wait to get started. But I don’t think the summer will be long enough to do everything I want to do.” This is why we feel fortunate we have Rabbi Pittinsky and his famed summer Boot Camp to provide all the help we need. Bring on summer!

The Timing could not have been more perfect-- “ Moving Beyond the Pilot”

                

                The math department at Frisch  is at an exciting and pivotal point in its 41 years of existence.  This past winter we were the recipients of a grant from the Jewish Education Project (JEP) which is enabling us to supply up to 200 students , about a third of our student body, with an online component to their math class.

Through the generosity of JEP we have had a wonderful time this past semester experimenting with different ways to integrate our chosen blended learning program called "Catch-Up Math".  As the school year is drawing to a close, I , as department chair, am left though with the daunting question “ now what?”  After running a three month pilot with around 40 students of various math ability, I now have even more questions than when I started exploring this option for my school back in June of 2013. 

I needed a workable plan come September and I needed it soon. Luckily for me I was invited this past Tuesday night to “Moving beyond the Pilot” , a panel discussion about blended learning at the Jewish Education Project headquarters in NYC. The ideas and messages expressed by the distinguished panelists could not have come at a better time.

 The honest, realistic and insightful observations from four blended learning experts on what works and what does not gave me knowledge I would have needed months to learn on my own. 

It was an incredibly worthwhile evening and I am excited to begin this new phase of math education at Frisch.  While I know it may take time to figure out the best way to make this program successful for our students at Frisch, I am optimistic for this coming September and grateful for the resources and people at JEP and JDigitial Network.

The DigitalJLearning Network is an initiative of The Jewish Education Project supported by funding from the AVI CHAI Foundation.

The Joy of Being a Student Again...Rutgers University PreCalc Conference

This past Friday five members of the Frisch math department drove down to Piccataway bright and early to attend the Rutgers University 28th Annual Precalculus Conference.  It was a fabulous professional development opportunity for Mr. Herb Grossman, Mrs. Shira Teichman, Mrs. Elissa Katz, Mrs. Chanie Schlessinger, and Mrs. Sabrina Bernath, department chair.  The teachers specifically went to different sessions ranging from ways to teach probability, introduction to the latest iPad apps, to a discussion on the diagonals of Pascal's triangle with the goal of sharing what each individual teacher learned in our coming weekly meetings.

Frisch Math Teachers at the Rutgers Univeristy Precalc Conference

All agreed the high point of the day was the plenary session given by the brilliant and extremely entertaining professor and author Dr. William Dunham, Professor of Mathematics at Princeton University.  It was pure joy for the teachers to once again be students themselves.  It was an honor to be taught and entertained by a living mathematical legend on the proofs of Hero's Formula of the area of a triangle.  By Sunday a few of the teachers had already been in contact for ideas and resources with people they met at the conference.  Some of what they learned will benefit Frisch students as early as this coming week.

How is Geometry applicable to a Jew's Life?

“Many of you have asked us, and probably more of you simply wonder to yourselves, “How is Geometry applicable to ‘real-life’?” While we cannot necessarily answer how it will be useful in YOUR life, we can show you how Geometry was extremely relevant to people hundreds of years ago.”

The Geometry behind Eruvin.

With these words, Mrs. Elissa Katz, a second-year math teacher at and graduate of The Frisch School, introduced “The Circle of Life”, an Integration Presentation of Gemarah and Geometry last week. The idea originated as Mrs. Katz was teaching her 9th grade Geometry students a unit exploring how trigonometric functions (remember “SOH-CAH-TOA”?) related to area of circles and squares. She recalled studying a Talmudic text that discussed a scenario in which sailors had to calculate their ship’s distance from shore to determine whether or not they could continue in their journey, as the Sabbath was fast approaching and it is forbidden by Torah law to travel outside certain parameters of a civilized city on the Sabbath. With the help of Rabbi Gedaliah Jaffe, a Talmud teacher at Frisch, and Mrs. Shira Teichman, another second-year teacher who teaches the parallel Geometry class, the three teachers created a lesson surrounding the said text as well as several other texts that incorporate Geometry into discussions surrounding rabbinical explications to derive practical laws.

Rabbi Jaffe explaining the mathematics behind determining an Eruv.

Last week, around fifty Geometry students assembled in an assembly hall at Frisch and were provided with a packet of the Talmudic texts and a Guided Worksheet that asked mathematical questions relating to the ideas of the lesson. The students were intrigued by the natural synthesis of mathematical ideas and Torah law and were excited to apply their knowledge to everyday encounters. Read some of their reflections below!

*                                              *                                             *

“Today … I was able to use the tools I have learned in math class and relate it to real-life situations. It changed my perspective about the amazing world around us. It taught me how to [connect knowledge] that wouldn't necessarily seem to have any significant connection. It was a wonderful experience."
- Sara Knoll

“The program finally answered the question so many students ask themselves: ‘When am I ever going to use Geometry after high school?’ Rabbi Jaffe shared cases in the Gemara regarding T’chum Shabbos where many of the skills we have learned this year are used in the process of putting up an eiruv, and to show how far one may travel outside an eiruv on Shabbos. The program was not only educational, but very interesting as well, and I hope to have many more like this during my upcoming years here at Frisch.”

- Adam Auerbach

"Geometry is useless!!" Those are the typical words of any high school student who is learning Geometry in math class. This week …we had the opportunity to take [our] understanding of Geometry and bring it to a whole new level …with Rabbi Jaffe, a Gemara teacher who integrated Geometry and Gemara into one lesson. As a group we learnt many different cases that that require us to use Geometry. As a freshman class, we can certainly say "We learned something out of the ordinary today!"

- Aliza Pavel

ShowMe the Math

I was absent from school today, chaperoning students on the Yeshiva University National Model UN, and, as such, could not check or review my math students' completed homework. I therefore emailed the students a small assignment: they were to produce and send me the solution for one of the two hardest problems from our most recent homework as a narrated, step-by-step solution using the ShowMe app on their iPads. I listed a few guidelines (duration of the video, that it was due in my inbox at 10PM, that they needed to show the "check", etc.) and then watched as the videos trickled in. The results were rather amazing.

• Preparation for Video: It was very evident how little or how much time a student spent prior to the final recording. A number of students erred slightly as they solved the problem, and immediately corrected and erased the error, but others had a perfect run-through. In response to the email in which I gave comments and the score (100%) for her video, a student wrote to me "I really liked this, although I had to record it many times!" [Still others prepared well, but struggled with the technical aspect (their iPad wasn't at home, they didn't check their email to see the assignment, the sound did not record, etc.) and how students dealt with these issues was eye-opening, as well.]

• Student Voice: Students who normally tend to shy away from voluntarily producing their solutions on the board or even asking clarifying questions had a voice that exemplified a confident, poised mathematical thinker. When the clock wasn't ticking a 40-minute countdown, when the pressure of peer approval/disapproval was not a factor, when they had practiced and checked the problem and were simply reciting what they knew was correct, these students had a voice that was clear and strong.

• Mathematical Language: The purpose of me asking them to produce a ShowMe rather than send me a picture of their worked-out solution was so that I could hear them narrate through the process. "Math is not a spectator sport", yet it is a subject that is taught best by example. This exercise had the student do the showing, and I was able to see not only their mastery of the concept (all solved the problem correctly) but also their command of the mathematical language. Some said they were "doing this" while others specified that they were "multiplying the binomials". Some students said that they will "bring it down to the next step" while others said they were "simplifying". Descriptions like "substituting" instead of "plugging in" showed that students had caught on to the language with which I converse with them, and were able to speak with it, too.

I find that Algebra I is a fast-paced curriculum. That, combined with time constraints, class size, and other factors, can sometimes rob teachers of the opportunity to pause and listen to their students. Analyzing their errors that they have made on the test is helpful only to a certain extent, especially for score-minded students who know that test grades do not change even if they can detect their errors ex post facto. Asking my students to produce a ShowMe was a way of telling them, "I trust you; I want to listen to you; and I care to know how you are doing what you're doing." To hand the talking stick to a student, give her your undivided attention for just 2.5 minutes, and analyze her proficiency in a concept while she is trying to master it is empowering and eye-opening. I anticipate that this act of narrating a problem and emphasizing the "check" will further encourage my students to find their true "math voice", even when I don't ask that they ShowMe.

By Mrs. Shira Teichman, Math Teacher

Round Two of the Ulpaniada

This was an important morning for four of Frisch's brightest female math students. Abigail Katcoff '14, Jamie Lebovics '14,  Ronit Langer '15 and Rivka Zimm '17 took the second test in the three part Ulpaniada Math Contest run by Jerusalem College.  This round's exam consisted of two parts: twelve multiple choice questions and two open ended questions that required detailed proofs. Today's questions lived up to the exam's reputation of being extremely challenging and having little in common with any high school math test these students have taken before.  With these unique questions requiring creativity and the ability to abstract on a whole new level, it was an intense three hours as the pictures below show. These young women were up to the challenge and stayed incredibly focused for the entire duration of the test.

Rivka Zimm '17

Ronit Langer '15

We are hopeful that at least one of these bright math super stars will make it to the final round in Jerusalem. Regardless of the outcome of this morning test though, Frisch is proud of these four young woman. Even qualifying for the second round in such a rigorous and demanding competition is a huge accomplishment in and of itself. Go Cougars!

The snow is gone and the results are finally in!!!!

 The snow is gone and the results are finally in!!!!!

In the first round of the Ulpaniada math competition run by Jerusalem College, about 140 educational institutions participated from Israel and abroad. Literally thousands of students rose to the challenge and competed and the math department at Frisch could not be prouder to announce that  Rivka Zimm, Ronit Langer, Abigail Katcoff, and Jamie Lebovics have all advanced to the next round. 

The second round will be held at Frisch shortly after winter vacation.  We look forward to sharing more good news as hopefully one or more of these bright young woman advance to the third and final round.

Mazel Tov You Calculating Cougars!!!!!!