NOTE: This post is written by Brad Fulton, Mr. L’s coauthor and partner from Teacher to Teacher Press.
Many factors go into creating a successful program for preparing students for 8th grade algebra. Here are ones we feel have contributed to the success of our program. While you may decide that some of these strategies may not work at your site, the more of them you implement, the more results you should see. You may be able to put into practice your own ideas which are not on this list.
1. Expose as many of your 8th graders as possible to an algebra program in the 8th grade. Include ELD and resource students. When in doubt as to whether a student is ready to take algebra, let them try the course.
2. For students who require more support, avoid pull-out programs. All remediation should be in addition to not in place of regular instruction. Dovetail intervention classes to support the instruction of the regular algebra program.
3. Use collaborative time to develop continuity along grade levels for algebraic instruction. Use common vocabulary, strategies, and teaching techniques to avoid students having to memorize extraneous information. For example, how do you teach students to approach solving equations?
4. Begin early with preteaching of concepts. Encourage teachers to look at the standards their students will face in subsequent years. How can we lay the foundation for these future skills?
5. Teach algebra concepts to all 8th graders. Teach the rigor of Algebra 1 to the students who are ready for the traditional course. For many struggling students, it is not the algebra itself that creates problems, it’s the mathematical rigor of negative numbers and fractions. Read the rest of this entry »
Tags: 8th grade algebra, algebra 1, algebra concepts, algebra program, research
Rubik's Speed Cubing - from the New York Times
Dr. Jessica Fridrich likes to tackle problems that might seem impossible to others. Rubik’s Cube is an example. She has created what is possibly the world’s most common strategy for speed-solving the popular puzzle, and is the subject of a YouTube video.
The Fridrich Method deals with more than 50 algorithms, which are rotations of the cube, and herein lies the mathematics of her method. Many of the world’s fastest speedcubers know more than 100 methods, and can solve a scrambled cube in mere seconds.
Here’s the link to the New York Times article about Dr. Fridrich.
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Tags: algorithms, fridrich method, jessica fridrich, Problem-Solving, Puzzle, speed cubing
Mathematics news items from Google News, Science Daily, Scientific American, New York Times, and over twenty math-related blogs can be found in one place on the web, Alltop - Top Math News.
Each source found on Alltop shows five stories/blog entries, and by hovering your mouse over the source you can see a quick intro to the material found there; then it’s only a click away. The home page of Alltop has a Tutorial Video for new users describing the features of the site.
This is a site teachers can use for “Current Events/Activities in Math”. It’s a great source for ideas and potential Extra Credit assignments for students, as well as showing them mathematics in the real world (outside the classroom).
Take a look - I’m sure you’ll find something of interest!
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Tags: alltop, current events, google news, Mathematics, mathematics news, Website Resource
Here’s a neat challenge for your students: Ask them to find a way to represent each of the positive integers from 1 through 12 using exactly three 9’s.
This puzzle is a variation of the Four 4’s puzzle: Write each of the positive integers using exactly four 4’s. Some sample answers include the following.
1 = (4+4)/(4+4)
2 = 4/4 + 4/4
3 = (4+4+4)/4
This clock can actually be found online for purchase at cafepress.
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Tags: cafepress, Math, Math Activity, math challenge, Mathematics, numerical reasoning, Problem-Solving, Puzzle
NOTE: This is the text of an article written by Rob Stein, a Washington Post Staff Writer, on Monday, September 8, 2008. Here is the link to the article found on the Post’s Website.
Scientists have for the first time established a link between a primitive, intuitive sense of numbers and performance in math classes, a finding that could lead to new ways to help children struggling in school.
A study involving 64 14-year-olds found that the teenagers who did well on a test that measured their “number sense” were much more likely to have gotten good grades in math classes.
“We discovered that a child’s ability to quickly estimate how many things are in a group significantly predicts their performance in school mathematics all the way back to kindergarten,” said Justin Halberda, an assistant professor of psychological and brain sciences at Johns Hopkins University who led the research, published online yesterday by the journal Nature. “It was very surprising.”
Other experts agreed.
“The link between math achievement and number sense is really stunning,” said Peggy McCardle of the National Institutes of Health, which funded the research. “The potential here could be very important.”
Researchers have long known that people are born with the ability to quickly estimate relative numbers of objects, with studies finding the skill in children within months of being born and across cultures. It is what people use in day-to-day life to estimate everything from whether a stack of paper plates will suffice for a backyard barbecue to whether they have picked the best spot to squeeze onto a crowded train. Read the rest of this entry »
Tags: brain, brain sciences, cognitive skill, intuitive sense, Math, Mathematics, research
Here’s a wonderful method that will enable your students to write (and THINK!) about the mathematics they are learning. Ask them to write a short explanation of the main concept/skill covered in class that day and the results will be that they understand it better and will remember it longer!
Students can use a single piece of binder paper per week. The teacher will collect these EZ Writes once a week and grade them as an assignment. The students are asked to reread their weekly entries and select the one they feel is their best, and then place a STAR by that entry; this is the one that the teacher reads first and most carefully. Comments/corrections/suggestions can be made by the teacher and then the EZ Writes are returned to the student. These are saved by the student and become a source of study material and also a source of important concepts. Since these are written by the student, they are in the student’s own language and therefore communicate the information well.
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Tags: language, Math, Mathematics, writing
Hundreds of papers you can download and print for free. Here you can find graph paper, lined paper, financial paper, music paper, and more.
Here are some of the Categories of interest to math teachers:
Graph Paper, Lined Paper, Logarithmic Graph Paper, Polar Graph Paper, Isometric Graph Paper, Hexagon Graph Paper, Octagon Graph Paper, and Dot Paper. There are many other categories available - something for everybody!
To give you an idea of the large variety of options found at this site, there are 130 types of Graph Paper in the Graph Paper category alone. From the website, “This printable graph paper (also known as grid paper) features squares of various sizes, from 1 line per inch to 16 lines per inch. Variations include index lines (heavier grid lines) and the size of the paper (legal, letter, ledger, and A4). Click any paper to see a larger version and download it.”
Printable Paper has been featured by LifeHacker, Kim Komando, Woman’s World magazine, and elsewhere.
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Tags: dot paper, grid paper, Math, math classroom, Mathematics, printable graph paper, Treasure Trove, Website Resource
NYTimes KenKen graphic
Here are twelve ready-to-hand-out masters you can use to teach your students numerical and logical reasoning skills while they solve these intriguing puzzles. Students love these puzzles, view them as games, and enjoy them tremendously. Classroom management problems are almost nonexistent; one of the only issues is that some students want to keep working on the puzzles rather than doing “regular math”. But that’s a great problem to have.
The puzzles are from the New York Times KenKen site. I made a screen capture using SnagIt, pasted them into MS Word using text boxes, and formatted them so three fit nicely on a page. They are great for introducing students to the world of KenKen. Students can then graduate to the 6×6 puzzles found online.
I’ve left the download files as a Word document so you can modify it to fit your needs. Here’s the file:
kenken-puzzles-4×4-from-nytimes
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Tags: games, intriguing puzzles, KenKen, logical reasoning skills, Math, Math Activity, Mathematics, numerical reasoning, Problem-Solving, Puzzle, Website Resource
This post features a video and some excerpts from the article “Lebanon schools turn algebra into child’s play”, by Betsy Hammond, The Oregonian.
While most high schools in Oregon and across the nation struggle to get freshmen to pass algebra, one school district is trying something very different. Lebanon, which educates 4,000 students in eight schools, is pushing algebra on students as early as first grade. And the kids are getting it.
| Riverview elementary really teaches math |
Visit a Lebanon elementary math class, and you will see:
First-graders set up and solve formulas such as 9 - x = 5, as they did when Raylene Sell talked with her class about “some teddy bears” walking away from the classroom rug, leaving five behind. Students don’t do worksheets, use flash cards or memorize multiplication tables. Yet by third and fourth grade, most of them add, subtract and multiply quickly and accurately.
Lebanon officials are loathe to proclaim their program perfect, noting that math instruction is evolving, that some teachers still use traditional methods and that the biggest payoffs are yet to come.
But they say they are confident that their new approach to teaching math is the way to go.
Among the key elements: Begin simple algebra and multiplication by first grade; have every child talk extensively about his or her mathematical reasoning; let students set up their own problems and equations and allow them to use big numbers if they choose; cover few topics in great depth; use lots of visual and hands-on modeling to make math ideas concrete.
Other tools in the Lebanon math toolbox include lots of visual modeling of math ideas. Plastic blocks represent hundreds, tens and ones; kid-sized balances show ways make both sides equal to balance the scale; number lines make it easy to see that 3/4 and 0.75 mean the same thing.
Lebanon’s approach is in line with recent national reports about what’s wrong with U.S. math classes and how to fix them.
The Center for Data-Driven Reform in Education at Johns Hopkins University reported this month that getting teachers to change their daily teaching practices does more to raise math achievement than buying new textbooks or computerized math programs.
Link to the original article:
Lebanon schools turn algebra into child’s play
Tags: algebra one, intuitive sense, Math, math classroom, math instruction, mathematical reasoning, numerical reasoning, teaching math, visual modeling
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