Envision: Math Online in the Lower School

Having realized that online resources for teaching math have come a long way since a CD was taped to the back of a text in the early 2000's, GA's First grade team piloted a fully online math curriculum called EnVision, based off the Scott-Foresman text currently being used by students. The success of the Envision Pilot in engaging students was impressive. The Lower School's Math Think Tank then recommended the EnVision program to be adapted by the Lower School in 2013-14.

 When asked about how Envision has impacted his teaching, Dan Stahl reports "I have found that through the online resources and text, I am able to better differentiate my teaching to reach all the needs of my students. I can decide, based on the lesson results, what kind of independent practice each individual student should work on!  The resources are easy and plentiful, and really help to enrich our math curriculum in First grade. I also really like how visually stimulating the lessons are and how they introduce topics using stories about everyday occurrences. It really helps the students concretely understand more abstract math concepts. Students in older grades will be able to access their text and workbooks from any computer; all they need is internet access."  He continues saying, "EnVision enables the students to interact with digital technology everyday. They no longer have to “lug” heavy textbooks or workbooks to their tables. Most importantly, should students need a challenge on a particular concept, I have the resources to quickly and easily meet their needs."

What We are Watching

This is why the folks at TED thinks you should be listening too (and watching) this talk by their own Lisa Bu.

"At TED's annual staff retreat, everyone has to get up and talk about something -- either about work, or about something interesting from their own lives. In fall 2012, our own Lisa Bu prepared a talk about her love of reading. And our quiet, funny and efficient Content Distribution Manager simply brought down the house, with a story that's too good not to share. We are thrilled and proud that Lisa is the first TED staffer ever to be invited to speak on the mainstage at the TED Conference.

Born and raised in Hunan, China, Lisa Bu has been with TED since 2011. Before that, she spent seven years as a talk show producer and a digital media content director at Wisconsin Public Radio. She's also a computer programmer, with a PhD in journalism and an MBA in information systems from the University of Wisconsin-Madison, as well as a BA in Chinese from Nanjing University in China."

Counterfeit Coins and Hiking in the Desert? Welcome to the MS Problem Solving Project

Math teacher Matt Notary, along with his department colleagues, has devised and implemented The Problem Solving Project for all students in the middle school. Designed to help students become more persistent in their solving abilities as well as shifting focus from getting the right answer to the process of doing mathematics, students have been gleaning the benefits of this innovative approach to teaching since it was introduced into the curriculum last year.  Assigned once each semester, all students in a particular grade level choose one of three problems to work on for two weeks.  Then they submitted their process answer packets to their teachers that included not only their work on the problem but a summary and reflection about their process.

To quote Notary, "Mathematicians often work hours, days, or even years on a single problem. The purpose of this project is to give students an opportunity to investigate a problem at length. The goal is not to solve the problem quickly; it is not even necessary to successfully solve the problem." He instructs students to "try to come up with a different strategy for working on the problem." Urging them not to use resources such as books or websites, but to work with their teachers on the process when they get stuck. Patience, resilience, persistence, and self advocacy are developed in students and they delve into the project, so is a new understanding of what constitutes mathematics.

Sample questions from the 8th grade project 2012-13

Counterfeit Coin

You have a pile of 24 coins. Twenty-three of the coins have exactly the same weight, but one, which is counterfeit, is heavier than the others (though it looks exactly the same). Your task is to determine which coin is heavier, and therefore counterfeit. You are given a balance scale, which will compare the weights of any two coins or sets of coins. What is the minimum number of weighings that you will need to do to find the counterfeit coin?  Extension: a) What if there are 64 coins and one is counterfeit? b) What if you don't know if the counterfeit coin is lighter or heavier? Does it change the solution?

Mathville Middle School

Mathville’s roads are designed as a grid of horizontal and vertical lines.  The horizontal streets are numbered with consecutive integers from 1 to 10, while the vertical avenues are labeled with consecutive letters of the alphabet from A to J.  A student, who lives at the corner of 1st street and Avenue A, attends Mathville Middle School, located at the corner of 5th street and Avenue E.  If the student always walks toward the school, but never diagonally, how many different routes are there from home to school?  Extension:  Try changing the location of the school and finding the number of different routes again.  Do you notice any pattern in your answers?

Hiking in the Desert

Three hikers head from home camp to an oasis.  They can carry only 10 days supply of food and water in each of their packs.  Since the oasis is more than 10 days away, they agree to try to get only hiker #1 to the oasis.  After walking together for a spell, hiker #3 refills the packs of hiker #1 and hiker #2 and returns home.  Hiker #1 and hiker #2 continue, and later hiker #2 refills the pack of hiker #1 and returns home.  Find the maximum distance from home to oasis such that hiker #1 can get there with hiker #2 and hiker #3 both safely home.  Extension:  If the oasis is 18 days from home and two hikers are expected to reach the oasis while the others return one at a time after refilling the packs of the others, find the least number of hikers needed.

Design Thinking Simulation for Upper School Faculty

In preparation for Challenge GA, an Upper School initiative that gives all students and faculty an opportunity to learn how to apply Design Thinking methods to a unique problem at the school, the US faculty engaged in a simulation where they were charged with designing a wallet for their partner. Employing empathic interviewing followed by the development of a needs statement, each pair sketched ideas, and prototyped solutions for each other.  They will continue this work in advisories and house meetings throughout the year. Earlier in August a small group of lower school faculty engaged in the simulation as well to begin introducing Design Thinking to the lower school. Their handiwork is seen below, donning a table in the McVeigh Community Room.

Richard Culatta at TEDx Beacon Street

Richard Culatta is the Director of the Office of Educational Technology at the Department of Education. His recent TED Talk on Re-imagining Learning distills his thoughts on a changing learning landscape culled from his work in k-12, higher ed, and work environments. His work focuses on leveraging technology to create personalized learning and using social media to create efffective large-scale distributed learning.