02 Dec Challenging Math at Schechter Manhattan: Learning Formulas and Much More
Natan jumped up from his seat in the second grade and rushed over to the white board. He carried his fraction flag in his hand. The rectangular piece of paper was divided into four strips and he had colored each of the strips a different color. Now he was looking at a variety of different fraction flags that his teacher had posted around the room, trying to figure out which of those matched the fraction he had represented on his flag, and what the numerical representation of that fraction would be. He counted the different portions of the various flags, and then also noted whether all the sections were colored in the same or different colors, moving around the room until he found a flag that he thought matched his fraction- ¼. He turned with a smile of satisfaction and headed back to his seat.
Watching Natan work, it was clear that he was thinking deeply about fractions. He, and the other students in the second grade, were connecting their visual representations of parts of a whole to numbers and building their understanding of how fractions work. They will bring a strong understanding of what numerators and denominators represent to the more advanced manipulation of fractions that they will approach in the years to come.
At Schechter Manhattan we believe that people learn things best when given the opportunity to engage directly with phenomenon, ideas, text, or problems and figure them out together. So, Schechter Manhattan students are asked and expected to do the hard work, the rigorous study, involved in learning things deeply. This is true in how we approach all disciplines, and this week I focused my observations on what I saw in math classes throughout the school.
Fourth grade students are studying linear measurement as part of a unit that also includes 2-D geometry. They are applying their understanding of multiplication to convert lengths measured in feet and inches to only inches for ease of comparison. In one lesson, I observed various students offering different strategies for converting the phrase “6 foot 2” into inches, each explaining their thinking and math process. Later in the week they were working in teams to measure the length of the hall from Gary’s office to the Ulam, for comparison to the length of the stairwell if all of the steps were unfolded and laid flat. One group found the length of the unfolded staircase in inches and then converted to feet, not daunted by large numbers like 624/12. One student in that group punched the sky and said, “We did it!” as if they had climbed a mountain together. The fourth grade students are practicing the math skills they have built, applying them in new and challenging contexts, and seeing how math connects to the real world. The students had to work hard, and think hard, to figure out how to complete this multi-step math task.
Eighth grade students recently constructed proofs of the Pythagorean Theorem by generalizing procedures they had developed to find the lengths of slanted line segments on dot paper.Their proofs combined geometric and algebraic reasoning. Some derived the Pythagorean Theorem without foreknowledge. As with the second grade students exploration of fractions, and the fourth grade students study of measurement, these students were asked to do some serious thinking and working to come to their own understanding of this mathematical concept. In the end, they all arrived at the standard formula, and because they worked it out themselves, they also understand why the formula works the way it does. In a portfolio reflection about the process, one student wrote, “While I was finding and proving the Pythagorean Theorem, I had a very tough time. In math, I’d never faced a problem that completely stumped me as much as this did. I loved solving it, and having the eureka moment that I had when I understood it.” Another reflected on the need to understand math, and wrote, “For me, just knowing the formula isn’t always enough.” We have set a higher bar than “just knowing the formula”, and this student sees how important that is for his math learning. The eighth grade students are now applying the Pythagorean Theorem to practical problems, such as “How would an Ancient Egyptian land surveyor use a knotted rope to form a right angle?” Practicing use of the formula in real life contexts prepares them to use it with fluency on traditional academic tasks and shows them how they might draw on this knowledge when they approach authentic complex problems, like the engineering challenges in their STEAM study.
This rigorous approach to math instruction at Schechter Manhattan is certainly hard work for students, but it is also highly engaging and rewarding. The students express a sense of accomplishment when they tackle a new math concept and are eager for the next math challenge. In an educational landscape marked by “math phobia” I am proud to have a school full of students who love studying math.
Each week we will feature the written work of our students. We hope that you will stop by every week and see what they are writing and thinking about.
As Kitah Aleph prepared for our family Kabbalat Shabbat we thought about why we love Shabbat and shared the special Shabbat traditions we have in each of our families. We wrote about our ideas and combined them to make a class book about Shabbat.
On Shabat I like to Play with my FaMIly
“On Shabbat I like to play with my family”
Shabbat is SPeshel Pecause I GetMie FaVRRe Food
“Shabbat is special because I get my favorite food”
I love Shabbat because it is A maag!!!!!!!!!!!!
“I Love Shabbat Because it is Amazing!
Click here to see work from Ava, Misha and Ethan T.
In Torah we are finishing our unit on Avraham welcoming the 3 guests. In class, we made inferences about Avraham’s feelings. We then wrote journal entries from Avraham’s perspective.
Click here to read work by Zack, Ariel, Maya, Renata, and Adina.
Kitah Heh is working on five paragraphs essays. Check out their rough drafts.
Click here to read work by Batya, Elana, and Ronin.
After a rewarding experiencing at TEVA, students were asked to write a five paragraph essay arguing whether the future 6th grade class should or should not go to TEVA.
Click here to read work by Maya, Jared and Caleb.
After reading Maus I and II, a graphic novel based on a holocaust survivor’s tale, as narrated by his son, students wrote essays discussing how the main character, Vladek Spiegelman, succeeded, and also failed, in resisting the Nazi’s. Students analyzed the text using multiple lenses: historical, psychological, graphic, or character.
Click here to read work by Alexandra, Itai, and Mia.