While multimedia tools have been slow to penetrate instructional methods in some subjects, the math world is bursting with tales of teaching technologies that visualize concepts, adapt to students鈥� strengths and weaknesses, and align with state academic standards.
There鈥檚 adaptive-learning software that gears math lessons toward individual student progress鈥攁 concept that drew mainstream media attention when Time magazine named the math program in New York City as one of the top 50 inventions of 2009.
There are on-demand videos that give tutorials on nearly every concept in basic mathematics, algebra, calculus, and even applied math fields like accounting. For building one such repository, the Khan Academy, that now hosts more than 2,300 videos, Sal Khan made a name for himself and is now a featured speaker at innovation pow-wows like last summer鈥檚 Big Ideas Fest in Half Moon Bay, Calif., and this past March鈥檚 TED 2011 conference in Long Beach, Calif.
And there are Web-based tools that allow students and teachers not only to construct, but also to alter and examine the relationships in angles, shapes, and even quadratic equations. In some cases, those tools have reached more than half the nation鈥檚 high schools.
While educators in other subjects may still be figuring out how best to create multimedia tools for the classroom, math teachers appear to agree that their main challenges center around gaining access to already-existing tools and how best to weave them into students鈥� education. And just because there鈥檚 a lot to choose from doesn鈥檛 mean all the programs possess the same ability to teach math on a long-lasting, conceptual level.
鈥淏asically, the research says when students have the ability to engage with multiple representations of a problem, then they are better able to apply these tools with problem-solving and reasoning,鈥� said Mark W. Ellis, a board member for the Reston, Va.-based National Council of Teachers of Mathematics and the chairman of secondary education at California State University, Fullerton.
鈥淛ust having access to technology is not enough,鈥� Mr. Ellis continued. 鈥淚t鈥檚 the role of the teacher or of the curriculum that鈥檚 essential. Although kids are quick to pick [technology] up, they鈥檙e not that quick at learning to relate it to a mathematical concept.鈥�
Rules and Relationships
Many multimedia-tool developers have been striving to address the conceptual level of understanding that Mr. Ellis says is so important. But each one has a different take on how that鈥檚 done best. And sometimes it is the simpler tools that more easily enable comprehension of mathematical rules and relationships.
For example, online drawing programs that allow students and instructors to draw and manipulate shapes and graphs鈥攍ike the , made by Emeryville, Calif.-based Key Curriculum Press, or the independently run , which has established dozens of institutes across the globe鈥攊mmediately give users a sense of the relationships that govern geometry, algebra, and even calculus.
A student stretching an equilateral triangle can see that two sides and two angles remain equal no matter how the size changes. The same student can also adjust the rise, run, or intersecting points of a quadratic equation graph and see how the variables shift.
The downside is that, while allowing a teacher to demonstrate or a student to explore those relationships, it鈥檚 not something that鈥檚 embedded into a set of problems for a class or homework assignment.
But Elizabeth DeCarli, a managing development editor for Key Curriculum Press, says an instructor who thinks creatively can offset the tool鈥檚 stand-alone nature.
鈥淚鈥檓 modeling this as an exploratory tool. I really want students to be playing with this,鈥� Ms. DeCarli said of the Geometer鈥檚 Sketchpad, which she said has reached about 60 percent of the nation鈥檚 high schools in some form.
鈥淎s a teacher,鈥� she said, 鈥渨hat you want is for students to realize, 鈥業 don鈥檛 need to memorize a thousand different rules. I鈥檓 beginning to observe commonalities.鈥� I can import a picture and then say I want you to make this parabola and make the parabola match this fountain.鈥�
Reinforcing Concepts
Some adaptive-learning software, which tailors lessons and exercises to individual student progress, also uses visual representation to demonstrate relationships. Such programs appear to be in greater use in the lower grades.
For example, software designed by the , a Santa Ana, Calif.-based nonprofit group that focuses on how neuroscience links to education, uses virtual manipulative diagrams鈥攊n which quantities are represented by graphic units as well as numbers鈥攖hroughout its complete set of math content for grades K-5.
Throughout the software鈥攗sed as a curriculum supplement in about 1,000 schools nationwide鈥攗sers must solve math problems to help the character Ji Ji the penguin cross from one side of the screen to the other. Often there is more than one correct answer to the problem鈥攅specially when it involves teaching spatial orientation鈥攂ut users will typically be prompted to solve the same challenge using several different methods.
While the quantities and complexities of functions increase by grade, the framework and look of the character, landscape, and game-like nature of the content remain constant. And while Nigel Nisbit, MIND鈥檚 director of content creation, says the format is backed by neurological research, he admits the program鈥檚 appearance can initially be off-putting for teachers.
鈥淔or many teachers, when they see the games are purely visual, they鈥檙e sometimes very suspect of where this is going, so it鈥檚 trying to show them the why and how,鈥� Mr. Nisbit said. 鈥淚t鈥檚 about putting almost a sequence together. This is something, when we look at games in isolation, they don鈥檛 necessarily appreciate.鈥�
While software from Bellevue, Wash.-based also uses visual approaches, it differs from MIND鈥檚 software because it lets students in grades K-3 choose their own visual representations. After completing a problem one way, students will often be prompted to solve the same problem by choosing a different visualization to reinforce the concept.
Choice is important for student engagement, says Suzanne Farmer, a math intervention specialist at Toliver Elementary School in the 1,600-student Danville, Ky., school district, which uses DreamBox to aid students with special needs in math instruction.
鈥淭hey really feel like they鈥檙e in charge, like they鈥檙e controlling what is happening,鈥� said Ms. Farmer. 鈥淚 don鈥檛 think any kind of intervention should be punishment. 鈥� These kids are already feeling insecure in their mathematic ability.鈥�
(DreamBox鈥檚 chief executive officer and president, Jessie Woolley-Wilson, is a trustee of 澳门跑狗论坛, which publishes 澳门跑狗论坛 and Digital Directions magazine.)
Matching State Standards
But elements of adaptive-learning models still have to match with state standards and other demands, says Todd Hausman, a 4th grade teacher at Lowell Elementary School in the 11,000-student Bellingham, Wash., school district. He uses similar adaptive software made by Newton, Mass.-based .
Mr. Hausman, a former employee of the publisher Houghton Mifflin Harcourt and of the Bill & Melinda Gates Foundation, acknowledges that the software helps students gain conceptual mathematical knowledge.
But he adds that what 鈥渟ealed the deal鈥� on incorporating TenMarks鈥� content into his classroom, at the expense of other companies, was its ability to import data from thrice-yearly Washington state standardized testing.
Mr. Ellis, the National Council of Teachers of Mathematics board member, agrees that standards and other national, state, and district guidelines can shape decisions about procurement of adaptive-learning software as well as other multimedia tools. He says he鈥檚 hopeful that the Common Core State Standards Initiative will help enable more interested districts and individual teachers to use such tools while aligning with the standards, particularly the initiative鈥檚 eight standards for mathematical practice, which give broad goals for best practices in math classes across all grades.
鈥淲hat I like about them is they say, 鈥楬ere is what we want to see students doing in a math classroom,鈥� not 鈥楬ere鈥檚 how you teach math,鈥� 鈥� Mr. Ellis said of the common-core math standards, which he said stress broad principles and work habits over narrow learning goals.
鈥淚f you鈥檙e going to create an environment where it鈥檚 actually going to happen and students are going to be doing those things,鈥� he said, 鈥測ou鈥檙e going to need to bring in tools beyond pencil and paper.鈥�
Until then, teachers may continue to frequent resources that more easily align with their set district or state curricula and standards, such as video tutorials that break down specific math concepts, as well as related audio clips, audio files, or online diagrams.
Some content services like , from Woodbury, N.Y.-based AIM Education Inc., offer the ability to combine resources into playlists of media set specifically for the needs of individual students, to help give some of that multidimensional understanding of content. And while it may not be as high-tech as an online drawing tool or adaptive-learning software, the back button can still help foster student comprehension of complex concepts.
鈥淎 lot of the videos we have on our site are really addressing concepts from different forms of learning,鈥� said Anne Feldkamp, a content-acquisition and product-development manager for AIM Education Inc. 鈥淚 think that鈥檚 really the key鈥攂eing able to have those different approaches, and being able to say, 鈥業 still don鈥檛 get it; let me rewind it.鈥� 鈥�
