Math standards: keeping it (in the) real (world)
Mrs. Hilt’s favorite first grade classes are baking muffins. Mrs. Brier’s class bakes 18 muffins, Mrs. MacAdams’s class bakes 20 muffins, and Mrs. Flannery’s class bakes 17 muffins. How many muffins does first grade bake in all? Is this an even number or an odd number?
It’s one thing to know how to do this: 18 + 20 + 17 = ? It’s another thing to know that’s what this word problem is asking you to do, particularly if you’re in the first grade.
But that’s a good piece of information for students to have, not only because math tests are heavy on word problems, but also because that’s how math works in the real world. Computational skills are of limited use if they can’t be applied in the context of a problem.
You might say the same about math classes: they’ve really not done their job if they can’t help students get behind the plus signs and multiplication tables to an understanding of how math works in the world. For the second summer, LCPS and East Carolina University brought together a group of elementary and middle school math teachers from the district to develop ways to relay that understanding to students. The Lenoir STEM Math Symposium, an eight-day program that ended Thursday, is all about math relevance.
Megan has 19 seashells. How many more seashells does she need to find to have 25 seashells in her collection?
“Word problems are just math applied to the real world, and that’s the ultimate goal, that students can take the math we’re teaching them and use it in real-world situations,” said Katie Schwartz of East Carolina University’s math education department. “We’re trying to look at strategies that help students understand how to use math and apply it instead of just know a procedure to get the answer.”
Schwartz has worked with elementary teachers both years of the symposium and helped write the $482,000 grant from the N.C. Department of Public Instruction that funds the program, scheduled to go a third summer. So far, 60 LCPS math teachers have gone through the professional development.
The elementary teachers focus on getting that message of math relevance across to students and developing what Schwartz describes as “rich tasks that will involve thinking.” The middle-school group learns about real-world math by touring manufacturing plants, Lenoir Memorial Hospital and a local restaurant, gathering information on the math skills their students will need to land jobs in Lenoir County and thinking about how to develop those skills in the classroom.
Leigh Anne Hall is a fifth grade math teacher at Pink Hill Elementary. “We are learning different strategies to teach our children how to become better thinkers when they’re solving problems and how to dig into these word problems and get the meat out of them to know how to solve them,” she said. “In real life they’re going to be presented with situations where there are word problems, not just computational problems. Hopefully this will help make a level playing field for all of them.”
Maggi had 3 packages of cupcakes. There are 4 cupcakes in each package. She ate 5 cupcakes. How many are left?
Math has content the same as words. No one would be considered a good reader if he or she recognized words without comprehending their meaning — that is, how they fit together to form an idea. Too often, however, doing math simply means following the formula and getting the right answer. As part of its mission to prepare students for college and career, LCPS is moving beyond that thinking for teachers and giving teachers the skills they need to take their students with them.
“We’re trying to look at strategies that help students understand how to use math and apply it instead of just knowing a procedure to get the answer,” Schwartz said. “It’s not that the procedures and the ways to get the answer are not important. It’s important to know how to get the answer, but we hope we will see a lot more inventive and creative tasks that let kids get into the application of math as well.”
Led by Ricky Castles of ECU’s engineering department and Ron Preston of ECU’s math education department, the middle-school teachers toured the hospital on Wednesday. In the hospital’s clinical engineering department, which is responsible for keeping thousands of pieces of medical equipment running, they quizzed department chief Dennis Edwards on his background — 37 years at the hospital, an associate degree in electrical engineering and technology from Lenoir Community College — and learned both his coworkers held associate degrees.
In the hospital lab, senior technologist Will Wilkins explained the breadth of knowledge employed in the lab: “Chemistry, physical sciences, some physics, all your maths, trigonometry, geometry — it all plays into knowing how the technologies we have work and how they give you the numbers that we’re actually getting.”
A swimmer is in a 100 meter race. She swims the first half of the race in 32.34 seconds and the last half of the race in 34.83 seconds. How long did it take her to swim the whole race?
This past week, the K-2 teachers focused on number sense and its relation to the basics, like counting, addition and subtraction. The 3-5 teachers worked on fractions, which is typically a stumbling block for students. Those lessons and the information the middle-school teachers brought back from their tours led to the development of “tasks” that will require students to think rather than respond by rote.
These are not easy lessons even for teachers, according to Hall. “It’s helping us understand the frustration level our students reach when they don’t understand the concept behind what they’re doing,” she said. “Instead of us just throwing it out there to them, they have to have that understanding of why it works.”
The 30 or so teachers in each summer session are selected through an application process that also puts a premium of having a range of grade levels and schools represented, “so at least somebody at that school would have that information they could take back and share,” Schwartz said.
For the sake of consistency, the agenda and lessons are similar from summer to summer, according to Schwartz; but there’s another point of similarity. “Both groups,” she said, “have been very committed and very professional and really interested in helping their student learn.”
At the gym, Hillary swims every 6 days, runs every 4 days and cycles every 16 days. If she did all three activities today, in how many days will she do all three activities again on the same day?