Math Tips

Written by a teacher, this article has some great tips for teaching math.

Teaching Secrets: Making Math Meaningful for All

Published: August 18, 2010

By Cossondra George

While it is considered unacceptable for the average person to lack basic reading and writing skills, people often brag about their inability to “do math.” It is almost a badge of honor to be numerically challenged.

As classroom teachers, we must overcome this attitudinal acceptance of not being successful at math before we can create numerically literate students. We must learn to teach in ways that make mathematics accessible to every child and build our students’ confidence in their capacity to master the knowledge and skills associated with our important—and intriguing!—content area.

Here is a quick list of her ideas:

1. Purchase a set of student whiteboards for your class. (Thanks for getting us a class set, Steve!)
2. Create real-life examples of concepts you are learning.
3. Use small groups and presentations where students teach each other as well as the entire class.
4. Teach the power of “Is your answer logical?” (essential in math)
5. Integrate technology to capture student interest. (check out her links)
6. Encourage, require, demand re-do’s. (this, along with number 2 and 3 should be done in all areas).

You can read the full article by clicking here.

Can you find the math in this 2nd grade activity?

Top 20 Reasons for iPhones in the Classrooms

Late last week even after the iphone 4 antenna fiasco, Apple posted an incredible quarter. They also mentioned that for some reason they couldn’t get the white plastic right until the end of the year. I was waiting for that one, but decided that was too long to wait and got myself the new one. What to do with my old one, I thought. It’s headed to my classroom. Here are my top 20 reasons for having iphones in the classroom. If you have more, I’m all ears!

1. It’s an ipod after all – kids can listen to audio books (formerly called books on tape) – and it can play music
2. It’s an e-reader – even though I can’t read for too long on those small screens, kids can.
3. It’s a recorder – kids can record themselves reading
4. It’s a camera – kids love taking pictures and from their perspective, there are always interesting shots. Unfortunately my phone is 2 versions old and doesn’t do video (but I hear there may be a way to do this)
5. It’s a drawing pad – just think, no messy fingers full of paint, no wasted paper, and a gallery of kid art
6. It’s a calculator – you can even geek out and get one in reverse Polish notation
7. It’s a clock – and a timer, stop watch, alarm – you can even get a binary clock.
8. It’s a dictionary
9. It’s wikipedia
10. Kids can watch BBC or PBS clips on youtube (National Geographic, Nasa, and Discovery have great apps too)
11. It’s a web browser
12. That means it’s also a writing tool (zoho.com is a good example – a mobile google docs is coming soon)
13. It can still be used as a phone without a plan over wifi (skype)
14. A lot of educational games – Scrabble, chess, sudoku, tangrams, pentominos, (and a lot of games that aren’t) – there are also flashcard games, memory games, strategy games, puzzles, mad libs, etc.
15. It can be used as an FTP server (if you don’t know what this means, ignore and read the next one)
16. It can be used as a remote for your slide shows, used as a mouse, even be a remote desktop for your pc!
17. It can be a translator or converter (imperial to metric, dollars to euros)
18. Kids can use it to roll dice or flip a coin
19. It’s great for mapping – google earth is amazing
20. It can be used as a flashlight/level/ruler (you get the idea)
21. (bonus) – it’s a musical instrument too.

If anyone reading this has an old iphone 3g or 3gs sitting around in a drawer somewhere, I am accepting donations for my classroom. I’ll also be accepting any old Kindles that would otherwise be unused.

Interesting story here – don’t know how legit it is, but a $35 tablet computer? I’ll believe it when I see it.

We Need More Patient Problem Solvers

I’m not a big fan of text books. Good tools, perhaps and also convenient. Still, it doesn’t make us better teachers. Furthermore, textbooks in many ways dumb down ideas. In math, textbooks tend to encourage the “one way to get to the right answer” kind of questions. I was great at at decoding textbooks and thus was very successful in high school. But how does someone get an A in a subject like physics and have no clue how the world works? Kids really need to understand how things work rather than learn to manipulate formulas. Students have to come up with problems, reason, and have patience.

His wonderful TED talk explains the problem with math in this country today. Making math real is what it’s about. In second grade, when a child asks, “How many more minutes to recess?” resisting the temptation to tell them and saying instead, “There’s the clock,” provides a real need to learn how to do it.

When you dine with friends and its time to split the bill, it’s amazing how often people pull out their calculators to divide and then calculate the tip. Often they are the same people who knew how to use the quadratic equation at one time. Something is not right in the way math is taught. Hopefully, we as educators learn how to it better.

He’s got a good blog: http://blog.mrmeyer.com/

Differentiating by Ability and Heterogeneous Grouping: Aren’t These Conflicting Terms?

Differentiating curriculum by ability and having children work in heterogeneous groupings are considered two important strategies in meeting learners where they are. I’ve always struggled with this, especially in math. Can both strategies be utilized simultaneously? A child entering second grade who is still counting on his fingers needs very different instruction from another who can use repeated addition to multiply 3-digit numbers by a single-digit number (in his head). How can you group these students so their learning is maximized?

First, I’m learning that not everything has to be differentiated, nor does every grouping need to be heterogeneous. Knowing the objectives and your students are key. Second, depending on the lesson or concepts being taught, one strategy may be better than the other. There are times, however, when you can do both.

As a culminating math activity, we adapted a unit where the second graders had to set about building a village. Reusing half-gallon milk cartons, brown paper bags, scrap paper, students created their homes, businesses. They had to create budgets in order to get supplies, work together to solving the problem of how lay out their own town quadrants based on very strict city codes. Throughout this unit, they were working in heterogeneous groups. As the unit progressed, we started to differentiate the math. While some were figuring out the area and perimeter of a piece of land 2 square units by 8 square units, others measured each square unit to find out their actual size (4″ by 4″) and found the area and perimeter of the same piece of land using square inches. 2 x 8 is quite different than 8 x 32. It was great to see one student count out the actual squares and to observe the other solve the problem by writing 64+64+64+64 vertically and begin to solve.

Not every math lesson or unit lends itself as well, but the same two children were able to work cooperatively to create and solve problems together, and yet were still given math learning opportunities that suited their learning needs. Differentiation and heterogeneous grouping are not mutually exclusive of each other, but they often seem that way. Hopefully, when I recognize those two strategies working together, I can make a few notes with the chance that I may replicate it elsewhere.

To Infinity and Beyond

Steven Strogatz’s column in the nytimes sadly came to an end earlier this week with yet another great explanation of complex math ideas, like differing magnitudes of infinity, made simple. His idea of writing a column explaining math concepts starting with the pre-K and counting all the way through grad school mathematics was a lofty goal, and so incredibly well executed. In his first post, he says “our freedom lies in the questions we ask — and in how we pursue them — but not in the answers awaiting us.”  One of my favorites of his posts is titled Division and its Discontents.

After reading it I posed the question, what is one fourth of one fourth to a few of my second graders. They didn’t know anything about multiplying denominators and numerators, but what a few did, was draw a square or circle,

and divide it into four pieces. Staring at their drawing one child began dividing one of the sections into four more section. Another pause ensued (and I’m guessing he was mental

ly figuring out the four sections of four), and suddenly he said, “one sixteenth.” Although that wasn’t what got me excited. After I acknowledged his response one of his peers said to him, “How did you get that? Can you show me?” I don’t know about most teachers, but for me, when students start asking other students to teach them something, I do a happy dance.

If you’re an elementary school math teacher, I highly recommend the first 5 in the series, who knows, you might end up reading them all and perhaps when Buzz Lightyear from Toy Story says, “To infinity and beyond,” it might make some sense.

You can start at the beginning of the column by clicking here.

K12 Common Core Standards for Math (I’m Glad It’s a Draft)

I’ve been trying to make sense of the draft of the K12 common core state standards for math. These are different from the National Council of Teachers of Mathematics (NCTM)’s standards. Trying to line up what children should be able to do based simply on the grade they are in is not realistic. Staying close within the age range of the children I teach, I found it interesting that for Grade 1, they include “Tell time from analog clocks in hours and half- or quarter-hours,” yet there is no mention of introducing or teaching fractions until the Grade 3 standards. Then for Money, the Grade 2 standard reads, “Solve word problems involving dollar bills, quarters, dimes, nickels and pennies. Do not include dollars and cents in the same problem. So I suppose asking a kid to add $1.50 and $1.50 is something I shouldn’t do? There’s no mention of learning about money again on these standards. Hmmm?

Math is a cumulative subject, but it isn’t linear, and like all things we learn, the more we use it, the more internalized it becomes leading us to be able to construct new concepts. While the standards and scope and sequence of most standards in math are linear, math itself is not. The subject of time involves many skills and for a second grader who doesn’t know how to read time on an analog clock, learning what skill or underlying concept is keeping them from moving forward.

Reading a dial is one skill.

Knowing that there are two separate dials (one divided into 60 parts and the other into 12) is another.

The one dial affects how the other dial moves.

The passage of time is another concept kids need to learn. How long is 5 minutes? Using and hour glass is a great visual for kids.

They need to be able to understand half and quarter of a circle and what that looks like.

They need to be able to count by fives as many clock faces don’t number the minutes.

AM and PM (many kids associate one with night and the other with day).

Time is not something that should be introduced in chapter 5, taught intensly for 2 weeks, assessed, and then done with. Kids should be asked to tell time out of necessity.

Student: Is it recess time yet?

Teacher: You tell me. There’s a clock over there.

The way your student responds can tell you a lot.

And for the children who already know how to tell time on an analog clock. Start preparing them for the problem that begins: A train left the station in New York at 3:30 PM …

Curricular standards (and how they are assessed) have been argued for decades. And they continue to be debated. Free creative commons digital textbooks, where students get to customize their own subject content and download it, are just starting. CK-12 is a good example (still mostly high school content).

Understanding Math

Teaching kids to use algorithms in math often provide them with a useful tool, but without understanding how things work, tools aren’t very helpful. I’ve always thought that calculus was a complete waste of my time in college. Even though I thought it was easy for me (or so I thought), it’s something I never thought I’d ever use in my life. 20 some years later, a wonderful, short, simple opinion piece in the NY times about calculus has completely changed my mind. Definitely worth the five minute read and perhaps relearning a few things this summer. I realize now that I was just good at following procedures without any real understanding. I wasn’t taught to understand. Many continue to criticize how we assess our students like AP tests. Tony Wagner suggests many can get through AP programs without actually having to do any real thinking. Algorithms and math text books can be good tools if accompanied by understanding. As teachers, we just have to be careful to balance those two things.

Board Games: The Next Generation

Scrabble is one of my favorite board games and one of those games that is great to have on your phone when you’re waiting in a long line somewhere. There are several downsides to board games that become electronic, especially for young children. For one, the simple arithmetic employed to keep score is done for you. Whatever the video game, the math is done for you. You don’t even need to compare numbers at the end, the computer declares who won.

Last month Monopoly released a new electronic banking version. The dollar amounts are adjusted to be in the millions, but there is no cash to handle. Everything is done via a plastic debit card. One push of the button and the math is done for you. The handling of cash and counting back change are missed learning opportunities.

When kids use technology, we have to be careful to asses whether or not they’re using skills we assumed they were.

March Madness: You Do the Math!

In a recent in-service for our advanced learners of math, one of the recurring ideas was to get them to create the math problems. Here are some examples one can clip out of a magazine or find online and then ask the students to come up with the math – it’s also a great tool in helping kids work backwards through a problem.