DreamBox Learning®» Teaching Math

Tuesday Teacher Tips: Small Gems

Lisa W — Tue, 06 Sep 2011 15:00:13 +0000

Welcome to the Tuesday Teacher Tips series! Each week we’ll highlight teaching and learning resources, ideas to use in the classroom, as well as things to ponder as you go about your teaching day. One of the best things about going to workshops is the unexpected “aha” moments that aren’t on the agenda. They are the little gems that prove to most valuable, because I “found” them accidently. Sometimes the presenter will use a management tool to get our attention and I’ll incorporate that into my own classroom. Maybe the presenter will off-handedly refer to a resource book that ends up being one of my go-to books for the rest of the year. This summer I was at the training “Introduction to Singapore Math Model Drawing” with Susan Midlarsky. She showed me an important step in the problem solving process. She told us that when she’s working on word problems with her students she always requires them to write a sentence that contains the answer before they begin solving the problem. This easy technique focuses students on what needs to be solved in the problem before they dig into it. It gets them thinking, “What do I have to find out in this problem?” This is not a radically new idea, but it's one that's easily skipped. Requiring students to actually write the answer sentence before working the math teaches them to stop and carefully evaluate the problem to decode what the question is asking of them. The sentence provides direction, as well as a concrete tool to use while solving it. For example, The ratio of average attendance at River Bats baseball games to attendance at the Dukes games was 4:1. If 4,000 people attended the River Bats game on average, how many attended the Dukes game? On average, _________ people attended the Dukes game. What is the little “aha” gem you’ve gleamed from a workshop this summer? Email and let us know. We’ll share them in a future blog.

Tuesday Teacher Tips: Model Drawing

Lisa W — Tue, 30 Aug 2011 15:00:29 +0000

Welcome to the Tuesday Teacher Tips series! Each week we’ll highlight teaching and learning resources, ideas to use in the classroom, as well as things to ponder as you go about your teaching day. This summer I attended the workshop, “Introduction to Singapore Math Model Drawing,” presented by Susan Midlarsky. Model drawing is a problem solving technique in which students draw bars to represent problems pictorially. This method easily moves students to solving problems algebraically, because they can visualize where the missing variable is and how it relates to the problem. My district does not use Singapore Math, but our new math curriculum does use a form of model drawing and contains a heavy emphasis on problem solving. This year, I found that using bar models proved to be an excellent strategy to use with most students. It allowed them to clearly visualize the problem, especially when we learned more abstract concepts like ratios and fractions. However, for those students who easily solve word problems drawing models was a challenge. These are the students who when you ask for an explanation of how they solved a problem tell you, “I just knew it.” Being able to translate and explain their thinking is difficult for these students, but bar models can help them process their thinking and grasp how they arrived at the answer. So in the future, when they are presented with more difficult problems that they don’t automatically “know,” they have tools to aid in solving them. Do you use model drawing in your math program? What benefits and challenges have you experienced in implementing it in your classroom? Email and let us know. We’d love to hear from you.

Math Soft Spots in Child's Understanding

Sherry B — Mon, 20 Sep 2010 16:21:02 +0000

The DreamBox curriculum is focused on Number and Operations, as well as Number Sense. This content is so core to elementary mathematics that it takes up about 80% of classroom math instruction. With a new school year upon us, assessing what student's understand about numbers is a priority for teachers. I thought I'd share some soft spots I look for as I begin assessing young children's understanding of mathematics in the fall:

Counting items more than once or two at once

Counting one past the actual number of items

Being misled by perceptual clues

Confusing cardinal and ordinal numbers when counting

Reading a written number doesn't ensure an understanding of the number as a quantity

Thinking of a number as a group of symbols side by side rather than as an entity

What soft spots would you add to this list? As Director of Education Programs at DreamBox, I'll post regularly about teaching young children mathematics. We can share ideas, questions, and challenges through our blog postings. I look forward to hearing from you!

Great Article for Teachers to Share With Parents!

Mickelle — Wed, 15 Sep 2010 17:58:17 +0000

A colleague forwarded the following article to me that I think is fabulous for teachers and parents. (Thank you to our fabulous developer Aja!) As a teacher, I would have loved forwarding this article when setting the stage for math as it’s taught today. Maybe it will be useful to some of you: BBC News Magazine’s Why Parents Can’t do Maths Today. Please let me know how you use it, and I’ll continue to look for other articles to bring to your attention.

How Can I Possibly Differentiate In Math?

Neal M — Wed, 25 Aug 2010 16:11:13 +0000

Anyone involved in education these days has surely heard the term Differentiated Instruction. Used in many ways, differentiated instruction is a proactive teaching method that centers around each student as a unique learner. Simply put, every child arriving in my classroom shows up with differing skills and interests. It is paramount to use varying strategies and materials to meet these varying needs. However, as any teacher knows, it is a Herculean task to develop a unique curriculum for each student. We are left with finding ways to adjust our existing lessons to appeal to our kinesthetic students who learn by building, or our musical students who will thrive if we can set our material to a beat, or a tune. In mathematics, differentiating instruction is especially difficult. How do we teach multiplication when seven students mastered it last year and five students still need work in basic addition? We ask ourselves, how can we, as teachers, possibly differentiate math and reach all our students? It is here that DreamBox Learning fills a glaring need in today's classroom. DreamBox accurately places students in a fluid curriculum right at one's instructional level. When students use DreamBox, a student can work on a 1st grade counting lesson while sitting next to a classmate working on 3rd grade place value. If a first grade teacher has a group of students ahead of their classmates, DreamBox will accurately place them in more challenging and engaging material. It is this placement on a unique learning path for each student that makes DreamBox such an outstanding addition in today's classroom. So, as summer break winds down and we head back to set up classrooms and welcome a new group of students, take comfort in knowing DreamBox Learning can and will differentiate math instruction and provide your students with a truly individualized learning experience.

Home for the Holidays? Count Those Coins!

Mickelle — Thu, 31 Dec 2009 00:12:59 +0000

Every year my husband rolls his annual collection of coins and donates the money to charity. Last night he had our 4-year old daughter, Elle, helping him for the first time. He knows (because he’s learned from me!) that rolling coins offers many learning opportunities for children of all ages. With schools closed for winter break, now is a great time to deal with all that spare change. Here’s how your children can help:

Preschool: When sorting coins, start with pennies and dimes. Quarters and nickels can be confusing because they look alike. But when your children a're ready, comparing quarters and nickels will help them learn to distinguish between 5 and 25 cents. Preschoolers can help make piles of ten if you give them a mat with a place for each coin. I prefer a mat with two rows of 5 each.
Kindergarten: Sort coins and count piles of ten. Later combine the piles of ten to make groups of 40 (nickels and quarters) and groups of 50 (pennies and dimes).
1st grade and older: Sort coins, count piles of 40 and 50. Watch to see if your child uses a strategy such as stacking one pile of ten and making other stacks have the same height. Another of my favorite strategies is laying the coins in rows of ten and making additional rows.

This takes longer than Coinstar, but the time spent engaged with your kids is worth much more than the 9% you save by doing it yourself!

Math in Preschool? Oh What Fun! (Really!)

Sarah — Wed, 08 Jul 2009 16:25:43 +0000

A new report from the National Research Council to Congress urges parents and teachers to help preschoolers learn more math. (Read the Education Week article, "NRC Urges Greater Focus on Preschool Math.") In preschools today, math is too often ignored. “It’s fair to say the attention is almost entirely on reading and literacy, without recognizing the importance of math,” said Christopher T. Cross, who co-edited the report and chaired the committee that produced it. Children entering kindergarten need to be “ready” in math as well as reading, and research -- and my experience watching my own preschoolers -- shows that preschoolers are as curious and interested in numbers and counting and measuring as they are with everything else.

Math learning games important at any age

Does this mean worksheets and flash cards? Of course not. Creative parents and pre-K teachers can easily incorporate math into the play activities they are already doing. Preschoolers can count how many rocks they collect, measure their feet, compare the size of two leaves, and discuss whether ladybugs are shaped more like circles or ovals. Sounds like fun to me!

Which Comes First: Education or Assessment?

Nigel — Wed, 10 Jun 2009 05:06:05 +0000

Recently an article in the Washington Post (46 States, D.C. Plan to Draft Common Education Standards) got my attention. No, I’m not going to get into the contentious issue of whether national standards are a good thing or not, because enough is written about that already. Instead I want to focus on educating students as individuals and how the article raised a number of questions for me. The following three paragraphs, in particular, got my attention:

"Led by the National Governors Association and the Council of Chief State School Officers, the states, including Maryland and Virginia, are aiming to define a framework of content and skills that meet an overarching goal. When students get their high school diplomas, the coalition says, they should be ready to tackle college or a job. The benchmarks would be "internationally competitive."

Once the organizers of the effort agree to a proposal, each state would decide individually whether to adopt it. …

[U.S Education Secretary Arne] Duncan and others also said that even the highest goals lose their punch if there's not an accurate way to gauge whether students measure up. That means revamping state tests -- a cumbersome and expensive process. So far, the states have committed only to working to develop the standards."

Does the assessment portion of this plan strike anyone else as being “too little, too late”? Darn it, if only there were a way to accurately assess a student’s knowledge and understanding at a very fine grained level that actually integrated with what and how they learned while they learned it! Then assessment would be neither cumbersome nor expensive. And the students might just be taught - and when necessary, retaught - what they needed to know when they needed to know it.

The DreamBox Learning K-2 Approach

Those of you familiar with DreamBox Learning K-2 Math know that our approach is to continually assess each student and individually adapt how we then present not just portions of the curriculum or individual lessons, but individual questions within those lessons. While DreamBox is based upon existing national standards, it teaches each student as an individual with their own strengths and weaknesses. In other words we continually assess then teach. Which is what good teachers have been doing for hundreds – perhaps thousands – of years. Children aren’t screws or widgets. Each one is uniquely different and may require specifically individualized teaching. While the debate about national standards goes on, let’s not forget that no matter which “standard” you adopt, if you consider assessment as an afterthought rather than an integral part of teaching, then you are forcing some students to continually play catch up. As I wrote in a recent blog (Sometimes Things Just Don’t Compute…): If you don’t know a student is having a problem, how can you address it in a timely manner? The success with which DreamBox Learning addresses students with widely varying skill levels has reinforced for me a variation of that old Chicago saying: If you want to provide a successfully individualized learning experience for a student, “assess early and assess often”! Let’s hope our politicians can be taught that as well.

Helping Young Animation Lovers Appreciate Math; and Vice Versa

Sue — Tue, 14 Apr 2009 14:43:14 +0000

Here at DreamBox, in our blog and in our monthly parent updates, we talk a lot about the importance of relating math to everyday activities with our kids. My own son has a gift for art and is especially interested in animation. (And while his math test scores are high he’s never been especially motivated to focus on math.) But a memorable way to help kids understand the connection between learning math concepts and something they enjoy in the real world is to ask them what their favorite animated movie is. The animated movies that younger kids love can be a good jumping off point for helping them understand the unlimited possibilities of learning math. If your child loved Finding Nemo or Toy Story, this Science Daily article might be a good read. Not all kids grow up with a love of math like Tony DeRose, a computer scientist at Pixar Animation Studios. He put the algebra and trigonometry he learned in high school to good use when he realized that “without mathematics, we wouldn't have these visually rich environments, and visually rich characters." The article includes a video clip of an interview with Tony talking about the connection between animation and math. You’ll also find a link to an article about the computer scientists who won an Oscar for developing the fluid simulation used in animated movies like Pirates of the Caribbean. Or take a look at this PBS Teachers site that suggests ways to help students use measuring, multiplication, division, and fractions to understanding what motion picture film is and how it is used. But we know that the best way to get kids interested in high school math is to make sure they’re engaged with math from the very beginning of school. And as a mother of an artist, in an environment where budget cuts have virtually eliminated art education from public school education, I was pleased to find someone like Wendy Jackson Hall. She was an animation artist and educator Seattle who used creative media like animation as a learning tool to help teach other subjects (and she introduced my son to stop-motion animation).

Relating Math Learning to Everyday Activities

In this terrific Stop Motion Works article, Wendy talks about teaching kids how to make flip books to relate math and aesthetics – with specifics for kids in grades 1 through 6. Helping children understand that 24 frames are combined to create one second of animation helps build comprehension of multiplication, division and fractions. And relating this to aesthetic principles of design, composition, contrast, and visual symbols, helps kids make the connection between the seemingly disparate worlds of math and art.

Does Mandating Higher Academic Standards Work?

Sue — Sat, 21 Mar 2009 20:15:21 +0000

There’s no question that a strong foundation in algebra is one key to raising academic standards, increasing the competitiveness of our future workforce and opening doors to broader career choices for students. But my attention was caught recently by the study of the effects of mandating algebra in 9th grade.

The Effects of Mandating Algebra in School Math Programs:

In 1997 the Chicago school district was one of the first to require that 9th graders take algebra to help ensure that its high school graduates would be ready for college. And many districts have followed—Minnesota and California even requiring it in 8th grade, assuming the California policy is implemented. However, researchers found rising failure rates, and the algebra mandate “did not seem to lead to any significant test-score gains for students in math or in sizeable increases in the percentages of students who went on to take higher-level math courses later on in high school.” (You can read the Edweek article I’m quoting here.) But isn’t it obvious that if algebra is the needed foundation for their future, kids need the right early foundation to be successful in algebra? All of which reinforces my belief in the importance of what we’re doing at DreamBox: helping more kids develop conceptual understanding and fluency with basics—like number sense and computation—and giving them engaging ways to develop problem solving skills. We're helping kids to be confident and well prepared for success with algebra.