I can’t be alone in thinking that this stretch of the academic year could be better used. We have been practicing for state tests, administering state tests, and administering district assessments since March. Here we are 2 months later getting ready for the next round of state assessment and end-of-year assessments.
If you are ready to say “uncle”, raise your hand.
Recently I heard suggestion made that we should “double up” on our mathematics instruction so the students would have more math exposure ahead of the MCAS. Think about that for a moment.
Exploring erosion with a stream table.
I enjoy math and I actually enjoy TEACHING math. But I don’t think force-feeding math standards down kid’s throats in anticipation of state math assessments is good for anyone. Remember college and cramming for a final? Well, this is just as effective, except the people cramming are 10 years old.
What makes my students happy and excited these days is science. So far I’ve been able to resist the suggestion to bag science instruction and cram for a math test. I’ll continue to do this even in the face of state testing and suggestions that my class is “behind” the district schedule. Why? Because for some of my students, it is the highlight of their day.
Standardizing stream table variables.
Why does school need to be so full of drudgery and test preparation and sticking to artificial schedules that do not reflect developmental learning? Ten year olds need to be filled with the excitement of discovering something new, of making sense of something; they need to learn to love learning. And if that something is science (or math, or reading or writing), then that’s where we will be going.
Learning should be happiness.
My fourth graders had a burning question all year long: How old are you?
I’m not so much embarrassed by my age, as I am shocked at how quickly I got to this ripe spot in my timeline. However, having said that, I do not directly answer that question.
Instead, I always give the students an equation on the last day of school. It usually involves a cube root. “But you didn’t teach us that!” they complain. And my reply is, “When you learn what that means, you’ll have earned the answer to your question.”
This year one of my fourth graders told me she didn’t need to know a cube root to figure out my age. Curiosity engaged, I asked her how she proposed to find the answer to her question.
“Easy. You told us you were in sixth grade when John F. Kennedy died, so I can figure it out without a cube root.” And off she went to find a JFK biography in our class library.
Which reminds me of two things. One, be careful what personal facts you reveal. And two, being flexible thinkers in math is just as important as working through an equation.
I don’t remember when I first came across this game — I suspect it was during a Math Solutions Summer workshop week. For certain, it is included in several of the multiplication resources Math Solutions publishes, including the Third Grade Month-by-Month resource.
It is empowering to find a game that children can just pick up and play. Circle and Star uses only a dice and a piece of scrap paper. Sometimes I get creative/fancy and use some wooden cubes that I have numbered from 5 to 10 so when the children play the game they’ll have some larger numbers to work with.
So here’s what we do:
1. Roll the die once. The number that comes up is the number of circles you need to draw on your scrap paper.
2. Roll the die a second time (or alternatively, roll the 5-10 die). The number that comes up is the number of stars to be drawn in each circle.
3. Write the resulting multiplication fact as number of circles times number of stars in each circle. Compute the product.
When we begin playing this game, I have students write the resulting multiplication fact 3 different ways:
NOTE: C = number of circles, S = number of stars
C groups of S equals Product
C S’s = product (use the number words)
C x S = Product
The students always are looking for this game on our Daily Five Math board. We both like it – the kids because it’s fun, and I like it as a way to keep students practicing those important multiplication facts.
This year I’ve made an attempt to follow the “Sisters” in implementing the Daily Five and the Literacy Cafe. So far, I’m happy with what is starting to take shape. Conferencing is more focused. Tracking those kids who need more than a once a month reading conference, keeping kids accountable through the Literacy Cafe Menu, all are clearly going to be helpful when presenting a case at an RTI meeting.
Now if the Daily Five can help me with getting to those students who need some extra one-to-one support, maybe it can help with meeting the needs of students in mathematics. The Sisters are way ahead of me on this one — the Math Daily Five provides a way to organize “guided mathematics”. In my classroom, the five categories that I’m playing with are: Math Fact Drills, Landmark Math Games, Exploring Data, Problem Solving, and Featured Activity. The math fact activities are games – electronic and otherwise – that provide fluency practice in addition, subtraction, multiplication and division. Landmark Games are the “go to” games we teach throughout our third grade Investigations in Number, Data, and Space units and include games like “Close to 100/1000”, “Capture on a 300 Chart” and “Fraction Cookies”. Exploring Data is a new category — our school has identified interpreting, representing, and constructing data as a focus for this year. Activities in these categories will provide students with activities for practice. I want my students to solve problems in context and I have been providing a problem for students to solve and later share solutions in this category. Finally, in the Featured Activity category, we will work on explorations that accompany the launches for the daily Investigations lesson.
I want to keep the launches down to about 15 minutes – whether it’s a model launch or a discussion. This isn’t easy for me. But by limiting my talk, and getting kids actively involved in activities while I meet with smaller needs-based groups, we should be able to make some progress toward students meeting Grade 3 Math Standards.
Will it be noisy? I’m sure it will be. Just like the Daily Five and Literacy Cafe, I’ll need to build students’ stamina for staying on task. But in the end it should be worth the time it will take – hopefully we can work smarter not longer.
Some part of the ARRA money allocated to the Lowell Schools is being used to give teachers time to look at assessments and collect data about how our students best learn. Grade level teams and cross-grade level data teams have formed since late summer all with the purpose of methodically looking at our assessment data and making decision about what to do next. We use the ORID protocols to analyze our data while the mechanism for assessment of our own teaching is the process of Learning Walks.
My grade level, Grade 3, has been contemplating a mathematics inquiry that will help us improve our instruction and, ultimately our students’ learnings. The development of the question has taken us in a circuitous route through methods for comprehending a particular operational skill (multiplication) to the question we’ve agreed upon this morning: What does best practice look like when we are teaching our students to generate or identify a correctly constructed equation matching a word problem situation.
We’ve noticed that our students, particularly our ELLs, meet the standards for whole number computation. However, many students, regardless of whether or not they are ELLs or native speakers, cannot for the life of them select a reasonable equation to match the word or story problem. This is critical mass for our kids — the bulk of the MCAS testing that will take place in the Spring requires students to decipher story problems in just this way.
Those of us who have a strong background in Constructivism dislike the very idea of teaching students “key” phrases: for example, in all means to use an addition equation. Personally I feel that there are other ways to get kids to comprehend the problem and generate equations from their understandings. I want my students to visualize the events in a story and be able to logically create an equation that will get them to an answer.
But what about of kids who have so many language issues that visualizing is not a strength? Is there another, better way? The data analysis tells us there has to be – at least with the students we are currently working with. As my colleagues and I work through this cycle of inquiry, we will be peeling away our preconceptions; this can be pretty scary.
Our next meeting will begin the process of researching what might work with our students, and maybe, we’ll invent something new. Now that would be something!
WNYC – Radiolab: Numbers (October 09, 2009).
This broadcast from PRI’s Radio Lab on number is pretty interesting if you can stay with it. If the interviewees are to be believed, I should have taken that Calculus course I failed in high school sometime around age 2. That’s right. The researchers interviewed assert that babies are logarithmic and they cite several sources and experiments to try with 2-year olds. (Sorry, I don’t have a toddler so I can’t prove or disprove the theory with the pennies.)
How does this impact teaching? I have no idea; I’m still trying to wrap my mind around the South American people who have no counting system or number above 5!
Thanks to Adrien and our discussions about mathematics — yeah, we definitely are America’s fun couple — for the heads up.