Teaching the hardest-to-learn math concepts

What are the concepts within core math topics that students struggle to understand in particular?

Under the direction of Melendy Lovett, president of education technology for Texas Instruments, that was the question TI recently set out to answer.

The company partnered with Gail Burrill, an instructor in the department of teacher education at Michigan State University, and Thomas Dick, a professor of mathematics and coordinator of collegiate mathematics education at Oregon State University, to find out which math topics students traditionally struggle with more than others.

Burrill and her team of researchers at Michigan State, and Dick and his team of researchers at Oregon State, examined all of the high-stakes assessments they could find in all 50 states and looked at how well students performed on each individual item.

“We tried to categorize items in terms of whether students were succeeding, and we looked to see, across the space, if there were clusters [of difficulty] around the same mathematical topic,” Burrill said.

Algebra is one common area of difficulty, and Burrill said it was clear that students struggled with the notion of equivalents, equivalent expressions, and other algebraic concepts.

The researchers weren’t able to do a full item analysis for every state, but for those states that made performance data available for each individual test item, Burrill and Dick said they saw a common pattern of math struggles emerge.

“The research we did really was around trying to get a better handle on what were those problem topics that kids were having difficulty with,” said Dick. He noted that the research “set the stage for us to think [of] ways that we could use [the TI-Nspire] to target these topics.”

Based on what they learned, Burrill and Dick—who both are project researchers and academic advisors for TI’s Math Nspired initiative—brainstormed ways of using the TI technology to help students master these hard-to-teach concepts.

The researchers brought their ideas back to Lovett at TI. The company gathered a group of educators to evaluate these prototypes, and the educators, researchers, and TI team members shared their thoughts on addressing tough-to-teach areas using the TI-Nspire system and the prototypes.

“One of the things we’ve been thinking about is that technology serves two roles. It serves as a mechanism for doing the operations, performing the calculations, and freeing up kids to think about what is actually happening mathematically,” Burrill said. “Its other role is to develop understanding. We really focused more on developing understanding—not ignoring its ability to do things, but we were really trying to help address the [mental hurdles to understanding] that surfaced in the tough-to-teach, tough-to-learn areas.”

Dick said that because the TI-Nspire lets students play with equations and see corresponding changes immediately, it opens up a chance for teachers to ask students not just what happens, but why—and students can explore the math however they please.


An essential tool for teaching

The National Council for Teachers of Mathematics holds that technology is “an essential tool for teaching and learning mathematics effectively” and that it extends teaching and learning opportunities.

Tools such as interactive graphing calculators and computer software not only help in collecting and analyzing data, but also help students “extend the range and quality of their mathematical investigations and encounter mathematical ideas in more realistic settings,” according to NCTM’s math position.

When properly implemented and supported, technology can help students increase achievement and grasp complex math concepts that might otherwise be too obscure for thorough understanding, the organization says.

Because technology is an essential tool in the math classroom, educators must be adequately prepared to know when and how students can most effectively use technology to boost learning, according to NCTM.

NCTM’s recommendations for technology in the math classroom, posted on the organization’s web site, include:

•    Every school mathematics program should provide students and teachers with access to instructional technology tools, including appropriate calculators, computers with mathematical software, internet connectivity, handheld data-collection devices, and sensing probes.

•    Pre-service and in-service teachers of mathematics at all levels should be provided with appropriate professional development in the use of instructional technology, the development of mathematics lessons that take advantage of technology-rich environments, and the integration of technology into day-to-day instruction.

•    Curricula and courses of study at all levels should incorporate appropriate instructional technology in objectives, lessons, and assessment of learning outcomes.

•    Programs of pre-service teacher preparation and in-service professional development should strive to instill dispositions of openness to experimentation with ever-evolving technological tools and their pervasive impact on mathematics education.

•    Teachers should make informed decisions about the appropriate implementation of technologies in a coherent instructional program.

The Center for Implementing Technology in Education (CITEd) conducted seven focus groups in 2005 to examine the challenges facing schools and districts when it comes to implementing technology.

Some common challenges emerged, including funding and professional development needs.

The two are somewhat linked: Many focus group members said that limited funding means limited professional development opportunities. Tight school budgets also mean outdated computers, software programs, and internet connections.

In addition, educators said time constraints often limit the extent to which they integrate technology into their instruction. CITEd reports that teachers said they don’t have the time to find technology resources online or in professional learning communities.

Limited time and funding contribute to what many in the focus groups said is an urgent need to help math teachers experience professional development that uses the technology teachers already have access to in their own classrooms. Because such opportunities often are not available, teachers are left to determine how to integrate technology into their teaching without support.



Putting our ideas of assessment to the test


How we evaluate students, and teachers, is at a crossroads.

How we evaluate students, and teachers, is at a crossroads.


Default Lines column, October 2010 issue of eSchool News—Here’s a pop quiz: What are the skills that today’s students will need to be successful in tomorrow’s workplace?

The answer to this question has enormous implications for the future of education, including what we teach our students—and how we test them.

According to an Associated Press story published on Labor Day, economists fear that many people will be left behind even when this historically bleak job market begins to turn around.

As our economy continues its shift from a manufacturing-driven economy to one fueled by service industries, the number of lower-skill, middle-income jobs will shrink, AP reports. Any job that can be automated or outsourced overseas will continue to decline.

Of the 8 million-plus jobs lost to the recession—in fields such as manufacturing, real estate, and financial services—many aren’t coming back, economists warn. In their place will be jobs in professions like health care, information technology, and statistical analysis—and most of these new positions will require complex skills or higher education.

The AP story validates a theme common to many advocates of education reform.

In his best-selling book A Whole New Mind, author Dan Pink writes: “Thanks to an array of forces—[including] globalization that is shipping white-collar work overseas, and powerful technologies that are eliminating certain kinds of work altogether—we are entering a new age.” Pink argues that right-brain skills such as creativity, innovation, collaboration, and empathy are what will distinguish the workers in this new age and allow them to succeed.

Education consultant Alan November agrees. During the Florida Education Technology Conference earlier this year, November said he was talking with a senior executive at a global investment bank recently, and he asked the executive: What is the most important skill for today’s students to learn so they are prepared to succeed in the new global economy?

To his surprise, the executive replied: “Empathy”—the ability to understand and respect different points of view.

Most of today’s companies do business with customers all over the world, November explained, and several also have branches in multiple countries. Chances are good that when students enter the workforce, they’ll be working with—or doing business with—someone from another nation, with its own culture and its own unique perspective, at some point in their career.

It’s not hard to find people who are smart, the executive told November. What is hard to find are employees who have to ability to empathize with, and be sensitive to the needs of, people from other countries. (See “Four things every student should learn … but not every school is teaching.”)

I don’t mean to imply that traditional areas of learning aren’t important. But it’s becoming increasingly obvious that these don’t go far enough in preparing students for the new challenges that await them when they graduate.

So, if it’s true that our economy is changing, and that the skills that will define success in this new economy are changing as well, shouldn’t we be rethinking the skills we’re teaching students—and the abilities we’re testing them on?

That’s what the federal government is encouraging states to do with $330 million in new Race to the Top grants, as we report here. Two large coalitions of states have won grants to design new exams that (1) are better able to assess important 21st-century skills, and (2) are aligned with the Common Core standards that the Obama administration also is pushing.

Because these projects are in their early stages, it’s too early to tell how effective they’ll be in meeting the need for a new generation of assessments. But educators will be watching closely to see how these experiments fare.

Whatever their outcome might be, it’s bound to be controversial, as change often is. Take Oregon’s experience, for instance. In this story, we report on how a decision by the Oregon Department of Education to let students use a computer spell-check feature when taking an online version of the state’s writing exam has raised concerns among stakeholders, prompting a larger discussion about the skills students should be tested on in the digital age.

State officials say the controversial move comes after consulting with local school systems and ed-tech experts, and they argue that it’s a natural evolution that more accurately reflects how students compose essays today. To some critics, however, the decision spells the end of society as we know it.

Oregon’s decision is the latest response to an increasingly important question in education: With such powerful technology now at our fingertips, do we really need a command of all the facts—or do we need to know how to call up those facts when we want them?


Taunt them with technology and they will not resist the fever

A new program helped a district keep its parents in the loop.

A new program helped a district keep its parents in the loop.

As unusual as it may sound, I used a new technology to attract teachers’ interest when our district approached implementation, rather than face pushback when we implemented the new technology, and they quickly took the bait.

When our district, Bossier Parish in Louisiana, decided to implement a new online program, I began eMailing staff daily about an individual feature included within the program. I made the eMails simple, such as, “Wouldn’t it be great to put an assignment online and have it automatically integrated into your grade book and posted online on student profile pages?” A second eMail would tease, “Wouldn’t it be great for parents to get instant access to student grades without you ever making a phone call or setting up a meeting?”

As you can imagine, our teachers were intrigued. I also placed small clues in the eMails. For instance, instead of signing the eMails with my normal signature, I would place the ‘loop’ symbol at the bottom of the eMail. For more than two weeks teachers were begging me to tell them what it was all about.

When it came time for the new product implementation, teachers knew it was going to be something positive. I already knew they liked the idea and wouldn’t really fight the new technology, because they said how much they wanted to have the tools I mentioned in my eMails. Once we had teacher buy-in, we at the district knew the overhaul would be positive and that the technology would drastically change the way things were done.

When Bossier Parish Schools needed an updated web site system that allowed us to communicate with parents and manage data across programs, we turned to School Loop for help. School Loop’s programs help school districts enhance communication between school administration, teachers, students, and parents. With more than 20,000 students to ‘track’ in the district, it can be extremely difficult to ensure that all parents are kept informed and involved with their children’s learning, especially on a daily basis. Yet parental involvement has been proven to be a strong factor in student achievement.

What began as merely a search for an improved way to host and update our web site for better communication to students and parents quickly grew into implementing a site that included data management of grades, intervention capabilities, and daily notifications to parents or guardians. We upgraded our district and school web sites to School Loop Plus when we learned that the system offered all that we wanted, plus it could be connected to our student information system (SIS) for more seamless data management.

Every morning the School Loop program and our SIS talk to one another and update changes to student information, so each day teachers have fresh, current data. These changes could include parent contact information, changes in teachers, or home contact information. The School Loop Plus Gradebook feature allows teachers to manage all their students’ grades online and easily transfer them from or into our SIS. These updates happen immediately.

In addition to this ability to transfer data in and out of our SIS, School Loop Plus allows Bossier Parish Schools teachers to effortlessly and automatically send parents daily personalized eMails about homework assignments, test schedules, grades, and general school news. Some might think this allows parents to constantly nag for data, but this has not been the case for Bossier.

Some parents are less needy because they know the information will come to them on a daily basis. They expect the data and can find it without ever needing to make contact with the teacher. To acclimate parents to the new system, we hosted small sessions during the schools’ summer open houses so parents could register and learn more about the School Loop features. Many parents say that School Loop has lowered their need to ask teachers for feedback on their student(s).

Administrators, educators, and parents use the system’s Loop Mail to communicate about all sorts of information, from a simple fund raiser to daily test grades.  With the ReachOut Report, schools are able to save paper and ink by sending progress reports only to parents who don’t have eMail access.

This data management system has also been helpful for the middle-of-the-road students. As administrators and teachers, we often we find ourselves overlooking the students that do well or improve only slightly. Yet with School Loop, parents and teachers can see even small improvements and focus on those positives with students.


Free online learning coming to some in Haiti

Most of Haiti's campuses were destroyed in January's earthquake.

Most of Haiti's campuses were destroyed in January's earthquake.

The founder of the tuition-free online University of the People said providing an education for Haitians after a massive earthquake destroyed most of their country’s colleges could demonstrate the value of a web-based university infrastructure targeting those in developing nations.

The university, launched last year by founder and president Shai Reshef, announced Sept. 20 that it would join the Clinton Global Initiative (CGI) in the organization’s efforts to help Haiti recover from a Jan. 12 earthquake that killed between 200,000 and 300,000 people, according to government estimates.

University of the People committed to enrolling 250 college students from Haiti into its free online programs, including computer science or business administration, over the next three years. The 600-student university is not yet accredited, but officials have pledged to achieve accreditation in the coming years.

Twenty-eight of Haiti’s 32 universities were leveled during the earthquake, which registered a 7.0 on the Richter scale. The four universities that weren’t completely destroyed were severely damaged…

Read the full story on eCampus News.


FCC opens up unused TV signals for broadband

In a highly anticipated move that could lead to faster, more robust Wi-Fi networks in schools, the Federal Communications Commission is opening up unused airwaves between television stations for wireless broadband networks that will be more powerful and can travel farther than today’s Wi-Fi hot spots, reports the Associated Press. The five-member FCC voted unanimously Sept. 23 to allow the use of so-called “white spaces” between TV stations to deliver broadband connections that can function like Wi-Fi networks on steroids. The agency is calling the new technology “super Wi-Fi” and hopes to see devices with the new technology start to appear within a year. Leading technology companies, including Google, Microsoft, and Dell, are eager to develop the market. They say television white spaces are ideally suited for broadband because they are able to penetrate walls, have plenty of capacity, and can travel several miles. Just like the spectrum used by Wi-Fi, the white spaces will be available to all users for free, with no license required. The FCC hopes they will help ease strain on the nation’s increasingly crowded airwaves as more consumers go online using laptops and data-hungry smart phones. Although the FCC first voted to allow the use of white spaces for broadband nearly two years ago, the plan ran into serious opposition from TV broadcasters and wireless microphone manufacturers worried about interference with their over-the-air signals. The FCC has taken steps to mitigate these concerns, including setting aside at least two channels for users of wireless microphones…

Click here for the full story


Education Department grants $442M for teacher merit pay

The federal Education Department is giving school districts and nonprofit organizations from across the country $442 million to create merit pay programs for teachers and principals, reports the Associated Press. The Teacher Incentive Fund is aimed at attracting and rewarding high-quality educators and encouraging them to work in the country’s highest-need schools. The programs will create performance pay systems based on evaluations of educators, among other incentives. Winners include school districts such as Wake County, N.C., and the New York City Department of Education. State education departments in Indiana, Tennessee, Ohio, and Louisiana also won grants, as did private companies such as Uplift Education, which has five charter schools in Texas. This is the first phase of the larger teacher incentive program, which has $1.2 billion in funding over the next five years. But the effectiveness of merit pay has come into question after a study from Vanderbilt University’s National Center on Performance Incentives showed that offering bonuses to teachers didn’t improve test scores. The study, released earlier this week, is billed as the nation’s first ever scientific look at merit pay for educators…

Click here for the full story


New software can help ‘proofread’ Wikipedia

A new tool might help fight malicious editing that introduces incorrect or misleading information in online sites such as Wikipedia, UPI reports. University of Iowa researchers are developing a software tool that can detect potential vandalism and improve the accuracy of Wikipedia entries, a university release says. The tool is an algorithm that looks at new edits to a page and compares them to existing words in the rest of the entry, then alerts an editor or page manager if it senses a problem. There are existing tools that spot obscenities or vulgarities, or major edits, such as deletions of entire sections, or significant edits throughout a document. But those tools are built manually, with prohibited words and phrases entered by hand, so they’re time-consuming and easy to evade, the UI researchers say. Their automatic statistical language model algorithm works by finding words or vocabulary patterns that it can’t find elsewhere in the entry at any time since it was first written. For instance, when someone wrote “Pete loves PANCAKES” into the Wikipedia entry for Abraham Lincoln, the algorithm recognized the graffiti as potential vandalism after scanning the rest of the entry and not seeing any mention of pancakes…

Click here for the full story


South African students study math via cell phone

A South African think tank said Sept. 23 that it has lined up volunteers to tutor on a popular mobile phone platform after a nationwide teachers’ strike left students unprepared for final exams, reports the Associated Press. With exams for graduating students a month away, the Council for Scientific and Industrial Research is concentrating on math. Students can download study materials from MXit and exchange messages with tutors. “MXit is cheap and efficient,” said Laurie Butgereit, who is overseeing the tutoring effort, called Dr. Math. More than 1,000 MXit messages can be sent for one rand, about 15 U.S. cents. “It is a perfect opportunity for South Africa to roll up its sleeves and help” final year students, she said. “Dr. Math is currently helping 12,000 learners on MXit, but we could be helping so many more if we had additional volunteer tutors.” More than 100 Dr. Math volunteer tutors have been screened and registered. Ishmail Makitla, a master’s student in information technology, is among the tutors. “It is a great experience to chat with students and to help them with their problems,” Makitla said. Butgereit said Dr. Math is only available outside school hours. She came up with the idea when she helped her son and a few of his friends with their math homework using MXit…

Click here for the full story


Japan to pilot digital textbooks in classrooms

Japan soon will start piloting electronic textbooks in its primary schools, enhancing the role of IT in the classroom for a generation of “digital natives” born in the wired age, reports the Economic Times. Under the “future school” project, 10 elementary schools will give all their under-12 pupils tablet PCs and fit their classrooms with interactive electronic whiteboards starting as early as next month. The networked devices boast software that lets them trace complex Chinese characters on-screen or exchange ideas on a virtual white sheet of paper in real time, while a teacher digitally monitors their work. Japan, despite its status as a high-tech pioneer, lags behind South Korea, Singapore, Britain, and other countries in IT use in education, said an official with the communications ministry, which is running the pilot program. To change that, a newly adopted government growth strategy aims to give every student a computer by 2020. Publishers of textbooks, software, and other educational materials showed off their latest cutting-edge goods for the wired classrooms of tomorrow at the New Education Expo in Tokyo this week. Toshiba has developed a tablet PC designed for educational use called the CM1, together with U.S. microprocessor giant Intel, which will be used in the “future school” project along with devices made by Fujitsu. One of the software programs for it is “CollaboNote,” by JR Shikoku Communication Ware, which allows pupils to share a virtual sheet of paper to write, read, and share information in real time. It can link students within the classroom but also in remote locations, allowing them to discuss and study a common subject…

Click here for the full story