In a recent article from the Associated Press, 8th grade math teacher LaMar Queen explained his approach to teaching algebra: “Math is a bad word in a lot of households, but if we put it in a form that kids enjoy, they'll learn.” The form that he has chosen is rap. Students love his unique method, and many have improved their grades since encountering math rules through music. The songs get “stuck in your head,” said one student, and so does the math.
How better to engage students and promote their understanding than with music? Each of Queen’s songs presents a concept and goes through sample problems to solidify students’ knowledge. (Check out his website, MusicNotesOnline, where you can listen to clips of his songs, download lyrics, and purchase his CD)
Two of the greatest challenges of teaching elementary mathematics are making the subject seem appealing to students and finding a way to explain math concepts that will stick with them. Students have no trouble memorizing raps, even when they are replete with math terms and functions, so Queen seems to have found an optimal solution to both of these obstacles.
After visiting the website, I, for one, found myself singing along to “Distance, Rate, Time.” It’s no wonder that math students are so excited about this new form of learning. What are some creative ways that you engage your students in math? What math topic do you think Queen should sing about next?
Photo Credit: Associated Press
Recently I have been reading Robert Ashlock's book, Error Patterns in Computation, which discusses common errors made by students in elementary and middle school mathematics. Most of these mistakes seem to arise from misunderstandings students have accumulated based on their experience. For example, many students believe that multiplication always results in a larger number. Their confusion is understandable. When people refer to objects multiplying outside of math class, they almost invariably mean increasing in number. Therefore, when students encounter a problem in which a whole number is multiplied by a fraction or a decimal less than one, many will automatically assume that the whole number will grow or multiply. (It doesn't, but the fraction does.)
In his book, Ashlock presents a series of computation errors made by students and asks the reader to find the patterns in order to uncover the students' thought processes. The best instruction should target each student's specific misunderstanding, whether it be computational or conceptual. Only when students have been redirected towards a fuller understanding of the material can they effectively move forward in math.
After diagnosing student errors, Ashlock recommends using a variety of tools and strategies to enrich instruction in basic math. By using manipulatives, such as Base 10 blocks, students develop a richer understanding of place value. Diagrams of mathematical vocabulary help eliminate confusion caused by arithmetic syntax. Ashlock focuses on experiential learning because it is the most meaningful to students. Experience is, after all, how they have accumulated most of their knowledge in the first place. Furthermore, when students can understand and make connections, they will be more motivated to learn.
How can teachers correct student misconceptions while still encouraging them to learn from experience? And in increasingly diverse classrooms, how can teachers find and address these "error patterns"?
Photo Credit: http://www.amazon.com/Error-Patterns-Computation-Using-Student/dp/0135009103/ref=sr_1_1?ie=UTF8&s=books&qid=1277152676&sr=8-1
A new study by a team of researchers from University of Massachusetts at Amherst is testing a math software program, called Wayang Outpost, which aims to take cues from students' emotions to determine where they need help in the problem-solving process. Studies have found that girls especially lack confidence in their math ability and report feeling "more frustrated and anxious than boys" when faced with math problems, according to Ivon Arroyo, a research scientist at UMass. The software program would offer hints and encouragement in response to cues from students' facial expressions as well as movement in their chair and grip on their mouse in order to boost confidence and thus improve performance.
Furthermore, researchers want to test whether environmental factors can have an effect on student performance in math. Some are investigating "stereotype threat", in which people submit to a stereotype and suffer a decrease in performance as a result. Others want to determine how the physical environment might affect a student's sense of "fitting in" and their subsequent interest in the subject.
All of the research seeks to look at the problems students encounter in their heads as they attempt to tackle math. If educators can identify some of these issues and eliminate the cognitive and emotional road blocks that prevent students from recognizing their full ability, overall student performance in math should improve.
How does emotion factor into your students' achievement in math and other subjects? What can schools and teachers do to build a more encouraging environment for their students?
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The latest American Educator issue has several articles on 21st century skills: its history (it's not a new idea at all), its benefits (clear preparation for the working world), and its shortfalls. The potential danger in shifting the attention from the academic curriculum to real-world interactions is a perspective that I have not heard much about.
Diane Ravitch pointed out the following in her article:
"The problem with skills-driven approaches to learning is that there are so many things we need to know that cannot be learned by hands-on experiences. The educated person learns not only from his or her own experience, but from the hard-earned experience of others. We do not restart the world anew in each generation. We stand on the shoulders of those who have gone before us."
There is a need for a skills movement as well, however, because taking in knowledge and then using that knowledge to learn and innovate - with critical thinking and problem-solving skills - is how society advances.
The importance of achieving this balance of 21st century skills and academic knowledge has been echoed in my interactions with teachers and educators through focus groups and advisory board meetings here at our office. Some teachers have shared that they felt their teaching materials were too discovery and theory-based while others wished there were more real world applications available. Teachers with the former resources fell behind in covering enough content standards while teachers in the latter condition found that students lacked motivation to learn.
How do you think the teaching of 21st century skills and academic knowledge in math classes should be balanced? Should it be 50/50 or should one element be more of a focus?
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I found a pleasant surprise in, of all places, the appendix of the final Common Core Standards for math. Tables 1 and 2 describe common addition and subtraction situations and common multiplication and division situations, respectively. The situations Add To/Take From, Comparison, Put Together/Take Apart, Equal Groups, and so on -- are embedded in the elementary standards themselves under the heading Operations and Algebraic Thinking. For Example, the grade 2 standards state:
"Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem."
We started tracking the research on schema-based instruction, upon which these situations are based, a number of years ago. In fact our program GO Solve Word Problems teaches students to do exactly what the above standard requires. The Report of the National Mathematics Advisory Panel recognized the potential of this research and it's great to see it fully incorporated into the Common Core.
The evidence for the effectiveness of this approach continues to grow. You can read more about it in the GO Solve white paper. Or search for "schema based instruction" on the web. Pay particular attention to the work of Asha Jitendra. Interesting stuff.