Different Ways to Solve the Problem of Algebra

Professor Jon Star of the Harvard Graduate School of Education, a former math teacher, has been working to make algebra instruction more effective. We know that algebra is a tough subject for many students and have written in the past about ways to make algebra more readily understood by middle and high school math students.

Professor Star’s project, as described in Ed. magazine and online in the Graduate School Newsletter, has two aspects: first, he is working with teacher volunteers to show them that providing more than one way to solve a problem is more effective than insisting that problems be solved in one particular way. Second, he is having math teachers include more discussion in their classrooms. The idea is not to just focus on getting the correct answer, but to discuss how that answer was found or why someone took a particular approach to solving a problem. 

Working with colleagues, Star has created a set of curriculum materials designed for middle and high school students, which incorporates these approaches to teaching algebra. The materials are available at no cost for teachers to use in addition to their regular modes of instruction. And the U.S. Department of Education’s Institute of Education Sciences has included this approach in two new publications, a problem-solving guide for grades 4-8 and an algebra practice guide for middle and high school students.

News Literacy Project

There’s been a concerning juxtaposition emerging over the last few years. As adolescents and young adults increasingly turn to social media for news and information, there has been a concurrent rise in the creation and widespread distribution of fake news. Much of this fake news is, not surprisingly, spread through the intricate webs of social media, like Facebook and Twitter. Students are not, however, routinely taught how to fact-check what they see and determine what is real news and what is meant to “persuade, sell, mislead, or exploit.” 

Fake news has come a long way from those magazine ads that look like real articles but say “Advertisement” in tiny print on the top. Now, there are whole sites dedicated to producing and distributing fake news, and many of them have names modeled after legitimate publications. Have you ever heard of the Denver Post, a reputable local paper? What about the Denver Guardian – sneakily named but completely fake (it was recently shut down after the Post exposed it)? Do you think a fifteen-year-old could tell the difference?

A recent podcast on National Public Radio (NPR) tracked down one fake news mogul and found out some very interesting and surprising information about one of the biggest fake news distributors out there. Even though it may seem easy for some to see the red flags – the missing byline, the lack of sources, the single-outlet coverage – millions of students are currently lacking the skills they need to discern real from fake on an ever-expanding internet. And when that means that young adults show up armed at local pizzerias that happened to be the unfortunate target of a fake news virus, it’s time to think about integrating fact-checking into the K-12 curriculum.

The News Literacy Project (NLP), which partners with reputable sources like The Associated Press, Los Angeles Times, and NPR, is hoping to help students change course. NLP’s education programs, including its "checkology" virtual classroom, is helping teachers, administrators, and students learn more about the rise in fake news and how to spot it. A typical three-week literacy course includes interactive lessons with journalists, student projects, and teacher-led lessons based on NLP’s curriculum. NLP believes that “knowing the standards of quality journalism empowers students as consumers and creators.” The coursework covers print, broadcast, and online reporting. Students are taught how to search for credibility, analyze primary and secondary sources, think critically about incoming information, and seek out different points of view. In the age of the echo chamber, where we typically surround ourselves with news that fits our own values and beliefs, learning to seek out valid, reputable sources that disagree with our own ideas is increasingly crucial.

We think The News Literacy Project has the right idea in mind, but talking about credibility with children can start with one discussion at the breakfast table. Consider sharing an age-appropriate article you’re reading with your pancakes and see if you can challenge your family to brainstorm why the article was written, what it hopes to achieve, and who it includes as credible sources. Then practice finding the holes, and see if you and your family can fill those holes with other credible information. Learning how to integrate lots of sources to get the full picture is a useful skill not just for reading the news, but also for navigating the complicated social world of childhood and adolescence.

Lessons on Immigration for Difficult Times

Where did your family come from?

Unless you are of Native American ancestry, your relatives came to this country from somewhere – or from many somewheres. It may have been a recent arrival, or may have taken place many decades ago, but all Americans have a story of immigration in their past. As immigration became a hot topic during the election and continues to be discussed in inflammatory terms now that the election is over, students and their families, especially those who have recently arrived in the U.S., deal with fear, uncertainty, and possible discrimination.

This may be a good time for teachers to examine immigration with age appropriate lessons for their students. A post-election blog titled, The Election Is Over, But for Teachers, Hard Conversations Are Just Beginning from Education Week asks the questions: How can teachers begin to unite their classrooms? How can they soothe students' fears? We have some suggestions for programs, readings, and classroom activities – some of long standing and some designed to respond to issues raised in the presidential election.

The Southern Poverty Law Center , whose mission is “fighting hate and bigotry and seeking justice for the most vulnerable members of our society … using litigation, education, and other forms of advocacy,” conducted a survey of nearly 10,000 educators – both before and after the election. Among the findings was that the presidential campaign “elicited fear and anxiety among children of color, immigrants and Muslims; emboldened students to mimic the words and tones of candidates and pundits; and disrupted opportunities to teach effectively about political campaigns and civic engagement”. Their response was to present resources for use in classrooms at all levels to help students recognize and respond to bias against immigrants and those of other religions or cultures.

PBS public television has extensive resources for grades 7-12 to use in connection with their documentary mini-series, The New Americans, which explores the immigrant experience through the personal stories of immigrants to the United States. There are 11 interactive lesson plans that help teachers connect their students with the historical and contemporary aspects of immigration.

Scholastic, publisher of books and educational materials, has 76 different resources, ranging from interactive white board lessons to paperback books on all aspects of immigration and the immigrant experience.

Although these lesson plans and other resources are designed for use in the classroom, many can be used by parents who want to help give their children a better understanding of the history of immigration in the United States and of people who may look, sound, or pray differently than they do. 

Teachers Pay Teachers

With the start of the new school year, teachers are putting the finishing touches on their lesson plans. Yellin Center Learning Specialist and blogger Renee Jordan shares her experiences as a classroom teacher creating and sharing her instructional materials.

As a new teacher, I spent hours roaming through local teacher stores and scouring education books at the library for activities, handouts, and materials for my students. I often found that so many of the reproducible materials had some great ideas, but they weren’t perfect and needed some tweaking.

I like to consider myself fairly tech savvy, so I began creating my own handouts and learning materials with my rudimentary InDesign skills. I doled out extra copies to interested coworkers who happened upon my materials on the photocopier. They were always so appreciative and it felt good to make the busy lives of my fellow teachers easier by providing them with materials that were tailored to specific student needs. It felt so good that I actually went on to study instructional and curriculum design in graduate school to better perfect my skills at developing learning materials. However, as the school year amps up, a teacher’s time becomes limited and there aren’t many hours at end of the day to spend creating and perfecting your own materials.

This is where Teachers Pay Teachers comes in to save the day. Instead of stumbling upon great learning materials in the copy room recycling bin, teachers are able to search for resources across age ranges and curricular areas that other exceptional educators have created.  Teachers Pay Teachers is the Etsy of the education world – an online marketplace for teachers to connect, both on and offline, and share the tools that have worked in their classrooms. Teachers are also able to sell their materials, garnering a supplemental income. As noted in The New York Times, some teachers are becoming very, very successful using Teachers Pay Teachers, with some materials having generating thousands of dollars of income for some truly innovative teachers. It is a sharing economy of high quality materials that have been created and vetted by seasoned, creative educators around the globe.

For me, Teachers Pay Teachers makes my life simpler by giving me easy access to exactly the type of learning materials I am hunting for. However, being a part of the Teachers Pay Teachers community is also inspiring. I love seeing the creative genius in my fellow educators across the continent; it fuels and spurs my own ideas of how to develop (and share) my own resources. When I share my materials in my Teachers Pay Teachers store I also benefit from the feedback other teachers provide on what worked in their classroom and what struggles they had with an activity I devised. This exchange of ideas helps me revamp and augment my learning materials. It may sound trite, but I truly become a better educator when I am able to connect and collaborate with the great teaching world through Teachers Pay Teachers. The Teachers Pay Teachers vision really says it all; they state that their “dream is to make the expertise and wisdom of all the teachers in the world available to anyone, anywhere, at any time." From my personal experience, they are really living that dream.

Design Thinking in the Classroom

In a recent blog, we wrote about how the maker culture is invading K-12 classrooms, and how design thinking is transforming traditional learning. We looked at how to get your kids making, creating, and designing. In today's post we are going to dig a little deeper into the “design thinking” buzzword and unpack what the integration of design thinking means for 21st century teachers, students, and schools.

Design thinking is a structured, but creative, approach to generating, rethinking, and tangible problem solving. It involves taking real-world problems and using research, analysis, and brainstorming to come up with solutions (Gerstein, 2013). Students then physically build and test their ideas through experimentation and product refinement.

Design thinking is supposed to be a messy, dynamic, and collaborative problem solving approach to real world problems. So, as students walk through each stage of the design process, it is important they remain flexible and return to previous steps if need be. Progression through the design process is not intended to be linear; it is fluid and creative in nature. However, a brief description of what occurs in the classroom during each step of the process is as follows:

1. Discovery
Students will discover a challenge or problem, and work to develop a clear understanding of the problem. They should research the problem and gather as much information as they can.

Example: College student is a very active marathon runner who loves to move around. She finds it very difficult to stay still in her chair but is expected to sit through a 75 minute math class without standing up.

2. Interpretation
Students will work to clearly articulate the problem they want to solve and why it is important to solve it. During this process students may need to go back and redefine the problem several times to further narrow the scope of their project.

Example: The student enjoys movement and needs to be able to move quietly, from a seated position, without distracting others in the classroom.

3. Ideation
Students will begin to brainstorm and come up with solutions for the problem.

Examples:

• The student could tap her feet under her desk (no, because that would distract others)

• The student could roll a wooden dowel under her feet (no, because the floor is hardwood and it would make a loud noise)

• The student could tie bouncy elastics to the bottom of her chair to press her feet on during the lesson.

4. Experimentation
Students will select what they think to be the best solution and begin to build a porotype of their solution. They will then test their ideas.

Example: Find a chair and test out different widths and types of elastics. Determine if there is any noise made or if other students are distracted by the noise made. Make sure that the elastics don’t break and are easily added and removed before and after class.

5. Evolution
Students will begin to evolve their ideas and refine what needs to be reworked. This may call for students to return back to the discovery, interpretation, or ideation steps of the design process.

Design thinking is an exciting concept, but it can be daunting to figure out how to integrate these ideals into your classroom routines. Thankfully, there are several resources out there to support interested educators who wanted inspire their kids to think, create, and experiment. Design Thinking for Educators is a great resource for educators who want to learn more.

Their website houses a plethora of videos that discuss the intricacies and rationale behind design thinking, while modeling real world examples of how the ideas are played out in a classroom. Design Thinking for Educators also has a downloadable toolkit to get you started in your design journey. Alternatively, Stanford’s School of Education has a wiki that outlines some great design thinking projects and challenges that innovative educators could attempt with their students.

Design thinking is a fascinating novel way to think about and engage students in the learning process. It gives the students autonomy over their learning, and teaches them how to find answers to their own problems through experimentation and research. Happy designing!

References;
Gerstein, J. (2013, March 11). "Hacking the classroom: Beyond Design Thinking." Retrieved from http://usergeneratededucation.wordpress.com/2013/03/11/hacking-the-classroom-beyond-design-thinking/.

Maker Culture in Schools

Maker culture is an off-shoot of traditional "do it yourself" (DIY) and craft culture. Adweek describes the maker movement as “…the umbrella term for independent inventors, designers and tinkerers. A convergence of computer hackers and traditional artisans…” Unlike the DIY movement, Maker culture is centered on tech; it involves computer programming, robotics, 3D printing, and digital and graphic design. The movement is so developed that it has its own magazine, Make, and hosts Maker Faires all over the world. Now, maker culture is pervading schools and your blogger is very excited about this creative shift in the education space.

Maker learning provides students with a hand-on, highly interactive way to explore the world around them as they engage with STEM concepts. Through a maker environment the learning a student does becomes intensely personal, project-based, and internally motivating. Maker culture is cross-curricular by nature and blurs the dichotomy between arts and sciences as students creatively design and construct novel technological products. Maker activities engage students in design thinking, a concept that is so powerful it is being integrated into curriculum at select schools. These schools are not alone. The Next Generation Science Standards advocates for computer science, engineering, and tinkering to be a part of every American child's education.

Maker projects can be as simple as using recycled materials to create a new toy. The materials used can be as basic as old cardboard to as advanced as 3D printers. Teachers could also have students explore stop motion animation by creating their own film to share. Or have students use MIT’s Scratch, a free computer programming tool, to create stories, games, or animations. Another way to infuse maker culture into a classroom is have students sew with conductive thread. This will allow them to make wearable electronic apparel or digital stuffed animals. Maker culture doesn’t have to be complex, it simply has to inspire students to invent, design, and create new products.

For teachers looking to bring maker culture into their own classrooms, an excellent resource is the book Invent to Learn: Making, Tinkering, and Engineering in the Classroom. The authors advocate that no matter your classroom budget there is a way to integrate maker principles into your students’ learning. They provide tips and ideas for students and teachers to learn together by interacting with a variety of high and low tech tools and materials. Edutopia also has a storehouse of Maker Education related articles that teachers can use to empower them to carry out maker projects in their classrooms. Maker Ed is another maker culture innovator where teachers can peruse their resource lists or get connected to maker events going on near them. It may feel daunting to take on such a large task in your classroom, but there are a lot of excellent resources out there to help support you in joining the maker movement. 

Happy Making!

Strategies for Promoting Self-Regulation in Children

We recently wrote about promoting mindfulness in children, which received a great deal of response and thanks from parents and teachers who were trying to address social and emotional learning with their children. They noted, however, that it has been hard for them to find tangible, effective ways to teach children skills like mindfulness and self-regulation. In response to their comments, we are going to dig a little deeper into self-regulation – the processes we use to calm ourselves down when feeling upset, angry, or overwhelmed or cheer ourselves up when feeling dejected or sad.

Social-Emotional Development and the Brain

Often, as parents or teachers, we think that children will be able to develop regulatory skills on their own. This is correct to some extent, as children do begin to develop self-soothing and self-regulatory abilities in infancy, and they continue to develop these over time. However, it can be hard for children to learn how to work through big, overwhelming feelings in a thoughtful, proactive manner. They often need to be explicitly be taught strategies for regulating their emotions and responses.

For more information, Dr. Shonkoff, Director, Center on the Developing Child, Harvard University gives a wonderful three-minute overview of the relationship between brain development, cognition, and emotional regulation in his video Brain Builders.

However, the salient question for many teachers and parents is how to translate all the information they know about the importance of fostering a child’s social-emotional development into fun and effective learning experiences. Luckily, we are here to help, and have outlined a few of our favorite resources and ideas for you below. 

Gross Motor Actives that Promote Self-Regulation

At The Yellin Center, we often recommend that students who are struggling with self-regulation or impulse control participate in gross motor actives that promote mind-body awareness. Examples of such activities are martial arts, ballet or yoga. A research study done by the University of Wisconsin-Madison supports this notion. Researchers looked at using a school based Tae Kwon Do training program to develop self-regulatory skills in students in kindergarten through fifth grade. They found that at the end of their three-month intervention the students in the martial arts program demonstrated greater improvements in “cognitive self-regulation, effective self-regulation, prosocial behavior, classroom conduct, and performance on a mental math test (Lakes & Hoyt, 2004).

Yoga is another activity that can help promote self-regulation in children. The children’s yoga and mindfulness program, Move with ME ™, provides video yoga classes to teach health and self-regulation skills to children through stories and pretend play. As children go through each video they will have fun pretending to be everything from a lion to a rocket ship. Beyond their yoga videos, Move with Me, also offers trainings, informative self-regulation activities, and other mindfulness curriculum materials. Best of all, Move with Me is constantly staying current on the latest research in social-emotional development in children and sharing that with their users.

Mind Up Curriculum

Scholastic has a curriculum called Mind Up that helps children “focus their attention, improve their self-regulation skills, build resilience to stress, and develop a positive mind-set in both school and life.” The lessons and curriculum are broken up by age group, and provide resources for children in grades kindergarten through eighth grade.

What we like best about the Mind Up curriculum is that it was created by neuroscientists, behavioral psychologists, and educators who use the notion that knowing one’s own brain can empower students to learn complex skills and overcome challenges. When developing their instructional strategies they integrate the latest neuroscience research on how our brain works and how it impacts learning. Here at The Yellin Center, that is exactly what we do and believe in. By knowing how their brain works, and what parts of their brain control their actions, feelings, and learning, students are often better able to overcome their challenges. If you head over to the Scholastic Website you can download a sample lesson plan and excerpt from the program to determine if the materials would meet your needs.

References
Lakes, K. D., & Hoyt, W. T. (2004). Promoting self-regulation through school-based martial arts training. Applied Developmental Psychology, 25, 238-302.

Fun Ways to Build Numeracy with Number Lines

A recently published study has got us thinking about number lines. German researchers taught first graders to walk along an unmarked number line on the floor to show where certain numbers (78, 15, etc.) would be. Compared with a group that learned simply to point to the right place on a smaller number line, the group that used gross motor movements performed better on various addition tasks afterward.

Used creatively, number lines certainly have a lot of potential.

Number lines are often used in classrooms, particularly with young children learning early math skills or middle school students working on negative numbers for the first time. But number lines’ potential for helping students develop numeracy skills (sometimes called “number sense”) is vast, and we think they deserve to be a bigger part of math education for learners of all ages. Here are some fresh ideas that will help unleash the power of number lines:

• Want a simple way to make number line use more tactile? Draw a number line in permanent marker just under the closure of a slider Ziplock bag. Students can move the slider from one number to another as they use the line to help them solve problems. Sandwich bags work well for lines showing 0-10, and gallon-sized bags can be used for longer lines with more numbers.

• Help a younger child draw a number line on the sidewalk using chalk, or on a big whiteboard or butcher paper with markers. Show him how to make the distance between numbers uniform by using the length of his foot or the width of his hand to measure.

As the study above shows, movement can help lots of young children grasp concepts. Engage an energetic child by making a giant number line to use on the floor. Write the numbers with sidewalk chalk or write on separate pieces of paper that can be taped down. (Plan to use this a lot? Get a scrap of carpet or an inexpensive carpet runner and make the number line with duct tape or paint, then roll up your reusable number line between uses.) There are almost endless ways to use this; here are a few ideas:

• Ask the child to hop along the line in a pattern: land on odd numbers with one foot and land with two feet on even numbers.

• Show/say a simple number sentence (e.g. 5+2 or 7-4) and ask her to “jump it out” or “stomp it out” by starting on the correct number and hopping or stepping to the next number in the equation. She should count aloud as she moves along the line to find the answer. Note that this will require some pre-teaching.

• Ask student to jump along the line while counting by 1’s, 3’s, etc. Help her to recognize that she has to make bigger and bigger jumps as she counts by bigger and bigger numbers. 

A tailor’s measuring tape makes a great number line. Unroll it and ask the student to place paper clips along it at intervals as he skip counts. Colored paper clips can be used for different skip counting intervals (e.g. 2’s vs. 4’s). Ask the child to remark on how the different intervals look and, through questioning, try to help him make generalizations. For example, he might notice that the spaces between the paper clips are larger when he skip counts by bigger numbers. Or he might see that the space between clips when he counts by 4’s is twice as wide as the spaces when he counts by 2’s, and 4 is twice as big as 2. Keep a record of these observations. There are also commercially available number lines.

Give a student a blank number line with only the first and last numbers labeled. The scale can be varied according to the student’s experience with number lines. Ask her to estimate the placement of various numbers by drawing a dot and labeling it. She can check her own work with a master number line drawn or printed on a transparency that she can lay over her work; punch and label holes in the transparency so that she can mark the correct placement on her paper.

Help a student see the relationship between a pictorial fraction (e.g. a “pie” with some of the slices shaded in) and a fraction on a number line. Present a student with a shape shaded to show the fraction 1/2 and a number line that goes from 0 to 1, and ask him to estimate where to place the fraction on the line. Help him to understand that half of the shape means he should move halfway along the line. Try the same exercise with other pictorial representations of different fractions.

Students often understand fractions more readily than decimals. A number line can be used to harness a child’s understanding of fractional quantities to help her grasp the correlation between fractions and decimals. Help her construct a number line that goes from 0 to 1 with important benchmarks written as fractions above the line, like 1/3, 1/2, 3/4, etc. Underneath each benchmark, ask her to write the corresponding decimal (0.33, 0.5, .75, etc.). Help her to notice trends; for example, the number closest to the decimal point gets larger as the decimal gets closer to 1. Keep the number line to use as a tool for homework assignments.

Number line at top from Wikkispaces Classroom

New Study on Impact of Influential Students on Bullying

Reducing and abating bullying within schools is a focal point for teachers, parents, and policymakers. There are a plethora of programs, tools, and research into the topic and yet little significant evidence has been yielded on how to definitively curb bullying. A new study from researchers at Princeton University (working with colleagues from Rutgers and Yale) suggests that key, influential students may be able to hone and shape a school culture that is intolerant of bullying. Theories of human behavior posit that individuals often attend to and emulate the behavior of people within their community in order to learn the social norms and constructs. Researchers used this notion to identify, often through social media, key influencers in the social network of 56 middle schools in New Jersey, and analyzed their ability to reduce bullying and school conflict.

Current anti-bullying programs are constructed by adults to address adult defined problems. The distinguishing feature of the program model used in this study is that researchers trained the students on anti-conflict ideologies and then let them independently lead their own messaging campaigns. This gave the autonomy to each student to change and shape their school culture by addressing the problems they saw using their own voice. Students were encouraged to make their anti-conflict stance well known through social media posts, and printing posters they designed, while also suggesting positive ways to resolve issues they confronted in their own smaller social circles.

The report, “Changing climates of conflict: A social network experiment in 56 schools,” found that the middle schools who used social influencers saw a 30% decrease in student conflict over the course of the year. The rate of decreased student conflict also appeared to be correlated to the number of social influences each school had; the more social influencers present in a community, the higher the reduction in bullying behavior.

For more information about the program used in this study or to review the anti-bullying curriculum they used, head over to the Roots program. The researchers at Princeton’s Woodrow Wilson School of Public Health have generously made their anti-bullying curriculum open source for anyone interested in using their ideas in their own communities. The curriculum is "user friendly" and uses specific examples and illustrations to explain how communities of influence work,

For example, the Hoberman Sphere functions as both a toy and a visual reminder of social networks. When expanded, it represents the way in which communities of influence can have an expanded impact.

.. 

We are excited to see a program that empowers students to make a tangible change in their own communities, using their own grass roots ideas of how exactly to affect that change. We believe there is a lot of power in a program that tackles bullying from the bottom up, rather than the conventional top-down approach.

The Best Evidence Encyclopedia

The phrase "research-based" is thrown around a lot, these days, but what does it really mean? And how can one be sure that educational programs and policies are soundly based on reliable research? Those without easy access to professional journals will find the Best Evidence Encyclopedia  to be an excellent resource for answering all manner of education questions.

You may be familiar with other resources for evaluating educational programs and policies. Our blog has featured posts about the What Works Clearinghouse, operated by the Institute of Education Sciences at the U.S. Department of Education and Usable Knowledge, a new initiative from the Harvard Graduate School of Education. The BEE is designed to be an especially accessible resource of this kind.

The Best Evidence Encyclopedia, or BEE, is a free site created and maintained by the Johns Hopkins University School of Education's Center for Data-Driven Reform in Education (CDDRE). The goal of the site is to provide teachers, principals, policy makers, and researchers with balanced, authentic information that will help them choose curricula and tools that are most likely to work in K-12 classrooms. The BEE, which is organized by both academic discipline and grade level, is easy to navigate. Users can also search for a specific term, or browse the sections on early childhood education and comprehensive school reform.

In addition to being valid, the information shared by the BEE is refreshingly easy to understand. CDDRE staff members write summaries of the studies that meet the BEE's strict criteria, then send them to the studies' authors for approval before they are posted on the site. Not only can users read the summaries for free, but they may also access the full texts of each article.

A strong background in upper-level statistics is not needed to make sense of the BEE's conclusions. Their program rating scale is simple and straightforward; programs and curricula are rated based on the overall strength of the evidence supporting their effects on student achievement. For example, programs with sufficiently large treatment groups and significant effect sizes are described as having "strong evidence of effectiveness." Programs rated as having "limited evidence of effectiveness" are ones for which no convincing studies demonstrating their merit have been published. It should be noted that this doesn't mean the programs are poor, only that no substantial research has yet shown that they work.

Want to stay in the know? Sign up for the BEE's bi-weekly electronic newsletter. The Best Evidence in Brief offers a quick round-up for current news in education research. It's an excellent resource for those who want to look behind the headlines to learn practical information about what works in schools.

Educators and others who are interested in sound teaching practices couldn't ask for a sounder, or more useful, resource.

Algebra in the Real World

A couple of years ago, Queens College Professor Andrew Hacker wrote a provocative piece in The New York Times entitled, "Is Algebra Necessary?". In it, he notes that completing required high school or college algebra courses is a significant bar to graduation for many students. He explains that it is not the useful aspects of mathematics that are the problem; instead, it is the way algebra is taught and the tenuous connection between classroom formulas and real life applications that raise questions about the usefulness and necessity of algebra courses.

We have seen a number of students, with and without math disabilities, struggle with this subject matter and are not surprised by Dr. Hacker's statement that in the City University system in New York, where he taught since the early 1970's "...57 percent of its students didn’t pass its mandated algebra course. The depressing conclusion of a faculty report: “failing math at all levels affects retention more than any other academic factor." "

There are many excellent tools, books,  and games that help students build algebra skills and support the importance of mathematics and algebra as part of school curricula and as a life skill. Take a look at the "tags" along the right hand side of this blog page for the subject "algebra" to see our relevant posts.

Following up on Dr. Hacker's article, the Times came up with suggestions for using algebra within the context of the subjects covered by the newspaper. In a post on its Learning Network titled, "N Ways to Apply Algebra With The New York Times", Patrick Honner lists numerous ways to apply algebraic formulas. These include:

• Exploring the housing market, including the impact of changing mortgage rates and whether it is less expensive to buy or rent an apartment
• Reviewing the numbers used in college rankings and creating an individualized formula for ranking colleges
• Looking at the costs of owning a car and exploring depreciation rates
• Determining whether it pays to buy a seven day, 30 day, or single ride MetroCard

Whether you and your students agree or disagree with Dr. Hacker, we can all agree that algebra is not disappearing from high schools and colleges any time soon. If you love it, or just want to get it over with, spending some time applying algebra in the real world may be a useful way to use your brain this summer. 

Questions for the College Bound

Whether you are a graduating senior who already knows where you will be attending school next year, a high school junior who is starting to get serious about the college application process, or a younger student or a parent who has questions and concerns about college, there are a few things to consider that might not be on your radar.

Retention Rate
You probably would not want to take a job in a company where most people quit after the first few months. You might rightly be concerned that there was something about that company that was problematic. In the same way, it is important to ask about the retention rate at any college you are seriously considering. How many students come back for their sophomore years after their first year? How many continue on to complete their junior and senior years as well? While some top universities have almost a 100 percent retention rate, others lose up to a third or more of their students from freshman to sophomore years. The reasons for this can vary and can include economic, social, and academic readiness factors, although some research has demonstrated that lack of retention may not have anything to do with whether students have learning disabilities.

What a low retention rate should do is prompt careful questioning about why students don't return and to weigh these factors into your own equation of what is important in a college. Is the school too isolated or does it empty out on weekends, leaving out of town students with little to do? Are the course offerings too sparse? Are there limited opportunities for research or advanced work for serious students? Is it a bit too much of a party school for you or your student? While it is always possible to transfer to another school, checking out your college choice carefully may enable you to avoid this process.

Time to Graduate
The four year college degree is not always a four year process. According to a Time analysis of U.S. Education Department figures, four year completion rates for a B.A. or B.S. degree can be as low as 30 to 40 percent, with the lowest rates in public colleges. There can be many reasons for this -- and most students do finish within six years of matriculating. But difficulty registering for courses needed for their major or switching to a different major and thus needing additional courses are two prime reasons for these numbers. Given the extraordinary expense of college, with no discount given if you can't get into the specific course you need, students and their families should give considerable thought to what majors are available and what percent of students are able to register for their first choice of classes. Note that many schools permit students registered with the Office of Disability Services to have priority registration, which can be huge benefit and can also allow students to select professors whose teaching style will best align with their learning needs.

Requirements
This is a subject we have written about before and is explored at some length in my book, Life After High School: A Guide for Students with Disabilities and Their Families, but it is still an area that trips up some students. Colleges almost always have two kinds of requirements: high school courses they require to admit a student and the courses students are required to complete to graduate. If you or your student has a particular area of difficulty, such as a language based learning disability that makes it extremely difficult to learn a foreign language, or a math disability that makes completing a math requirement just about impossible, it is crucial to be aware of the requirements of your chosen college. Your high school may have waived or modified certain courses because of your learning disabilities, and the college may have admitted you because not all majors require a foreign language or a math sequence. But, depending on what course of study you choose, you may find yourself required to take courses in which you are not able to succeed. Keeping this issue in mind can avoid this problem.

Interleaving Can Lead to Improved Outcomes

Here at The Yellin Center we have long suggested that students benefit when their assignments are designed with the concept of "interleaving" in mind -- where no two problems or questions of the same kind appear in order. So, for example, a homework assignment might include newly learned long division problems, but also some multiplication and even addition and subtraction. This is different from more traditional tests or problem sets, where the questions follow the blocks of the curriculum and material from earlier lessons is only reviewed when it is time for year end tests.

Photo: Silenceofnight/Flickr

A recent discussion of this practice was included in an excellent Science Times section of The New York Times which focused on "learning what works" in education. The article looks at research from a team at the University of South Florida which looked at interleaved math instruction in a small sample (140 students in all) in a Tampa middle school. The students found that interleaved problem sets took a bit longer to do, at first, but that when they needed to study for a test they could spend less time reviewing because all the material they had learned was still fresh in their minds.

Furthermore, the results when the students took tests were remarkable. The scores on problems presented in the traditional manner averaged 38% -- but they scored an average of 72% on the material they covered through interleaved problems. The Times discussion included opinions of various psychologists and learning researchers as to why interleaving is beneficial, which ranged from noting that it engaged particular kinds of memory (something we call "paired associate memory"), to opining that since students need more time when they are first working with interleaving, the additional assistance they may get from their instructors makes a difference in how much they learn.

The research team plans to expand its investigation to see the impact of interleaving when it is used more broadly, with a far greater number of students. We will be interested to see the results.