Monthly Archives: May 2017

Mathematics is Everywhere And is Used for Everyone

The idea of “learning math” often conjures the image of a student hunched over his desk, solving problems using a set formula he copied down from his teacher. Math, we tend to think, is a strict set of algorithms, practices, and rules — all emanating from inside the classroom. New resources from the Harvard Family Research Project(HFRP), though, paint a different picture entirely — elevating the role of the family as a source of math knowledge.

In its latest initiative, HFRP is focusing on the idea that children’s knowledge of math is “broad and deep,” developing anywhere, anytime, and even starting at birth. Families are instrumental to their children’s success in mathematics, as they can help children recognize and use mathematical thinking in everyday activities.

But today’s math assignments can be confounding for parents who learned math in a pre-Common Core era, or in a different country — or who still harbor math anxiety from their own days at school, or never fully learned to connect the dots between everyday actions and math lessons. To ensure students are ready to thrive, educators have to partner with parents, acknowledging how diverse families already use math — and how they understand and grapple with math in their own ways.


To start, educators should keep in mind three broad ideas about mathematics and families, as explained by Diane Kinch and Marta Civil of the group TODOS: Mathematics for All.

  1. Mathematics is cultural. Families, especially parents who went to school outside of the United States, may have learned math differently than the way their children are learning it. They may have indicated decimals with commas instead of periods, or relied more on mental math in long division — and they may become confused (or confuse their children) when not introduced to the methods taught in their children’s school.
  2. Mathematics exists in many different ways in many different communities.Research often concludes that lower-income homes don’t do as many math activities as upper-income homes. But all families use math with their children, whether it’s through halving a recipe, calculating gas mileage, or figuring out the right angle to shoot a basketball. It’s up to teachers to connect with their school community and understand the practices and strengths of the families they work with.
  3. Students learn best when their families and teachers are co-learners.Teachers should help cultivate the mindset that everyone has different beliefs about what’s important in mathematics, and how that should be taught and learned.


How exactly can educators connect with families about mathematics? HFRP offers specific suggestions, drawn from TODOS, the case study “Daddy Says This New Math Is Crazy,” and the program Nana y Yo y las Mathematicas:

  • Leverage parents’ mathematical strengths. Seek out opportunities to identify math content and approaches with which parents are familiar. Look for and encourage instances of parents using math with their children, such as counting or noticing shapes, before asking parents to try out a new technique.
  • Make communication with parents the focus of homework. It’s easy for children and parents to grow frustrated when children can’t remember how to do their homework, and parents don’t understand the method that their children are supposed to use. Circumvent this problem by assigning students homework specifically asking them to teach the new method they learned that day to their parents.
  • Organize math discussions with families. Coordinate get-togethers to discuss content, ways to solve problems, and which skills are most important — meetings in which everyone is open to learning from each other.
  • Invite parents into the classroom. Ask parents to speak to their class about times that they have used math in their everyday lives. To demonstrate how mathematics is different — and the same — across cultures, invite parents to teach the class a lesson using the methods they learned in school, or using the same methods, but in another language.
  • Capture classroom lessons on video. Visits during the school day are not feasible for all families. Use smartphones to text short videos of lessons, to ensure parents feel included and aware of new learning methods.

Undocumented and Educated

In the four years since the Obama Administration launched the Deferred Action for Childhood Arrivals (DACA) program, young, undocumented immigrants have gained visibility, opportunity, and some measure of stability. But their immigration status, and that of their parents, still inflicts a corrosive burden, says Roberto Gonzales, who has chronicled their experiences before and after the DACA protections. For educators who work with immigrant students, the weight of that burden requires new support services and a distinctive kind of outreach, particularly as young people move through high school and become aware of the ramifications of their status.


“Kids grow up, from kindergarten on, with the idea that if you work hard enough and dream boldly enough, there can be something for you. You can be successful. That’s the ethos of this country,” Gonzales says. But as undocumented students move through the education pipeline, the broken mechanics of immigration policy gradually come to dominate their lives.

Gonzales explores the impact of that broken policy in Lives in Limbo: Undocumented and Coming of Age in Americaa book that pulls back the curtains to reveal a landscape of lost potential. He followed 150 undocumented young people in the Los Angeles metropolitan area over a period of 12 years, finding that even those with college degrees wound up on the margins of society, stuck in low-wage jobs, permanently constrained, and often raising their own children in poverty.

“For many of the kids I followed,” says Gonzales, “as they hit 13, 14, 15, years old — as their friends were taking after-school jobs, getting driver’s licenses, thinking about college — there was this dramatic awakening for them, that their futures were not going to be what they had been told. Even for the high-achieving students fortunate enough to get tracked positively and to get into good classes and get into college and have mentors — even for them, once they venture outside of this trajectory and get their first taste of the limitations their status imposes, they can fall off a cliff.”


Things changed in 2012 when President Obama created DACA. Under its protections, according to a new brief from the Migration Policy Institute (MPI), almost 730,000 people who came to the United States as children have received a two-year reprieve from deportation and a temporary eligibility to work legally in the United States and to get a driver’s license. Of the 1.3 million people that MPI estimated to be immediately eligible for DACA (those who met age, time of entry, and school enrollment criteria), 63 percent have applied (leaving a still-sizable percentage of eligible young people who have not). More than 90 percent of those eligible to renew their DACA status and extend the two-year benefits have done so.

Gonzales analyzed the transformational impact of DACA in a report published earlier this year, chronicling how it has expanded young people’s educational and work opportunities, resulting in better performance at school, increased wages, renewed hope, and a revitalized motivation to succeed.

But he found that significant obstacles remain, despite DACA protections. They include:

  • The significant variability of opportunity (or lack thereof) across localities and states.
  • The continued financial challenges of tuition, even in parts of the country where in-state tuition rates are available to DACA enrollees. (Undocumented people are not eligible for any federally funded student aid.)
  • Difficulties navigating the licensure requirements attached to many specialized vocations. Nearly 30 percent of all jobs in the US today require a license, and pathways to licensure can be uncertain or blocked for undocumented people, even if they’ve already received (and paid for) specialized training.
  • The lack of a permanent solution, making long-term planning a challenge.

Even as the country marked the fourth anniversary of DACA this summer, it was also absorbing the implications of a Supreme Court decision in June that blocked a larger Obama administration program to protect parents of citizens or permanent residents from deportation. For these adults, including many whose lives Gonzales had chronicled, who are now the parents of citizens, the decision is crushing. “It drives these parents and their children deeper into the shadows, where they will continue to suffer the effects of daily living that is narrowly circumscribed by legal limitations and the fear of deportation,” Gonzales says.

DACA survives, but its future is far from guaranteed. With the politics of immigration at the forefront of election campaigning, uncertainty about the future of the program is rising.


So what are schools, districts, and advocates doing to help DACA-eligible students navigate their complex situation?

Helping families and children understand their rights. All eligible students can and should apply for DACA while still in high school. In the wake of the Supreme Court’s ruling in June, some families may wonder whether DACA is still available, so additional outreach may be needed this year in particular. Undocumented adults may worry that there are new risks involved in enrolling their children in school.

Schools are legally forbidden from asking about immigration status, and some students may not disclose (or may not know) their status. Districts and schools with immigrant populations should communicate proactively with all families, with messages of inclusion and to encourage DACA enrollment and renewal, as modeled by this resource from the Boston Public Schools. From early on, they should spread the message to students that everyone can aspire to go to college and pursue interests and career goals. That message should include the fact that undocumented students can legally attend college in the U.S.

Ensuring that staff members know about the resources available to undocumented students, as well as the limitations. Variation at the state-level — involving tuition rates, state scholarships, and licensure requirements, among other things — makes it important for school counselors, teachers, and other academic advisors to be aware of the opportunities and restrictions available to DACA-enrolled young people in their localities. The DACA recipients that Gonzales interviewed said teachers and counselors had often encouraged them to pursue postsecondary education but knew little about the legal realities their students had to face.

Creating a strong mentoring system. Gonzales identified a single characteristic shared by each of the high-achieving undocumented students he followed: “To the person, they could name three or four adult mentors in their lives,” he says. “These were teachers, counselors, adults within the school community who really helped forge a pathway for them.”

Looking to colleges as a model for student services. At the postsecondary level, some colleges have taken the lead by creating resource centers for undocumented students, and these have been effective at providing the specific support these students need, Gonzales says. These resource centers include an identified staff person who acts as a liaison to students in navigating the bureaucracy of higher education. They also provide trainings for staff and faculty, and they convene support groups and clubs for undocumented students — creating opportunities for leadership and for civic and community engagement.

Without such targeted help, Gonzales says, undocumented students often get bounced among offices — the international office, the student affairs office, the financial aid office — “and they end up having to tell their story over and over again, often while standing in a long line,” which can raise fears of exposure.

This successful model is starting to be replicated in middle schools and high schools, Gonzales says — where the impact can be even greater.

Staying aware of the challenges of adolescence. Navigating adolescence is challenging for all children, but it’s uniquely so for undocumented children. Added to the typical turbulence is the stigma and exclusion associated with their immigration status, the self-seclusion or secrecy that families often feel compelled to impose, and feelings of depression that can arise as students come to appreciate the limitations of their status.

As kids come to see that they will have difficulties accessing opportunities their peers might take for granted, they begin “worrying about what teachers will say, what their friends will say,” Gonzales says. “Many of them choose to keep it a secret. So what does it mean to keep this big secret? Some kids separate themselves — from peer networks that have been critical to their success, from teachers, from clubs — because it becomes tiring to them to have to make excuses.”

DACA has helped to lessen what he calls “the mental health repercussions of being undocumented.”

“Today, there are more supports to prevent kids from falling off. There are new opportunities for guidance, allowing these young people and their families some breathing room — some chance to maintain their aspirations.”

Advocating for policy changes, starting with a pathway to legalization. Other needed changes include access to federal and state financial aid, and consistent access to in-state tuition rates. And there’s a continuing need to build organizations and systems that connect and share resources, leveraging the new awareness on college campuses and across society.

“When we get beyond rhetoric of campaign politics, I think very consistently our American public favors some kind of a pathway to legalization, especially for young people,” Gonzales says. “But what has been difficult is this very awkward marriage of policy and politics that’s really gotten in the way of us doing what’s best for kids, for their families, for their communities, and for this country.”

Learning in the Outer world

With the school year in full swing, it can be easy to forget one of the chief joys of the summer: Just being outside. Now, a growing number of researchers and educators are finding that outside time has benefits beyond leisure — and may be the key to happy and healthy children, schools, and communities.


Outdoor education encompasses a range of experiences, settings, and pedagogical goals. “Unplugged” sessions at overnight camp, or Outward Bound–type trips with classmates, are often the first images that come to mind. But outdoor education can be as simple as a lesson taught outside — entirely unrelated to nature, or using the outdoor landscape to teach sustainability or biology. Or it can be simpler still: playing outside, using free time to organize a game or investigate a wild section of the playground.

Each of these interactions has its own benefits, but the overall impact of time spent outdoors is clear: better physical health and wellness; increased environmental stewardship; enhanced creativity, concentration, and self-confidence; and stronger collaboration and relationship skills.

Environmental psychologist Louise Chawla has found that frequent contact with nature can reduce symptoms of attention-deficit disorder and increase memory; it’s also associated with lower rates of depression. Other studies have shown that time outdoors leads to lower rates of myopia among children, possibly because the high light intensity outside can stimulate retina growth. And more generally, exploring the outdoors introduces children to new sights and sounds and broadens their perspective beyond their immediate families and schools, says Jessica Parsons, who specialized in the topic while earning a master’s degree from the Harvard Graduate School of Education(HGSE).

Outdoor education can be as simple as setting aside a “wild” corner of the playground, where kids can make discoveries large or small.

Ben Wild, another HGSE alum, spent years leading teenagers on backpacking trips, helping kids become both self-sufficient and mutually reliant as they survived in the wilderness for a week. And because the students couldn’t bring any technology or reading material, they had ample time to set goals and reflect on the journey, skills they brought back to the classroom. They learned how to take risks responsibly, in a safe (and fun) context.

Working at a summer camp in Los Altos Hills, California, HGSE Lecturer Sarah Leibelnoticed other advantages. Her campers, who spent several weeks without cell phones, learned to make the most of the free time they had outdoors with their new friends, developing stronger conversational and interpersonal skills. And because they had so much time to run around and move their bodies, it became easier for them to relax and be still when it was time for a break.

But children and teens don’t have to travel far to benefit from the outdoors. In her research at HGSE, alum Erica Fine found that “frequent, close-to-home experiences are one of the best tools we have at connecting kids to nature.” Students who have a chance at recess to explore a tree or a wild patch of grass learn to be creative within their surroundings. Regular time outside gives kids more opportunities to exercise, and it lets them notice and appreciate all of nature — not just breathtaking views seen while camping, but also ants on the playground or a squirrel in the yard.


Compiling the advice of our experts, we offer seven simple suggestions for educators to integrate the outdoors into the school year:

  • Designate a “wild” area of the schoolyard for children to explore. Let the grass grow and animals make nests, and keep sticks and branches within reach of students. Encourage students to climb, discover, and play in the area.
  • Create an outdoor classroom where groups can meet to read, write, draw, or learn about the environment.
  • Let students eat lunch and do phys ed outside, weather permitting.
  • Foster partnerships between schools and local parks. Visit parks for outdoor lessons and free play, and offer to let the town use school playgrounds on weekends. These partnerships can be especially important for urban, low-income students, who may have fewer opportunities to visit green spaces on their own.
  • Take students for a walk during the day to make observations about the environment, to practice mindfulness, or to complete a teamwork activity.
  • Plan a fieldtrip where students can experience nature without technology.While immersive overnight programs can be transformational for students, they can also be expensive. Single-day adventures can be just as fun, with longlasting benefits.
  • Model the kind of engagement you want your students to have with nature.Explore new developments on the playground, play with fallen leaves, and vocalize what you notice and love about the outdoors.

Learning to Read to Learn

By middle school, typical reading curriculums assume that students have the necessary literacy strategies to decode the writing in front of them. Lessons have shifted from “learning to read” to “reading to learn,” with students using texts to make sense of unknown concepts.

But in a digital world, there are countless ways — books, newspapers, social media, blogs, online forums — to read information. This variety of sources can leave middle and high school students confused about which techniques to use to comprehend, analyze, and synthesize what’s in front of them, as well as which reading to use for higher learning.

Now, a study of three adolescent literacy projects reveals instructional approaches that can help teens develop the reading skills they need for consuming 21st-century texts.


“Middle and high school teachers could make their classroom activities more engaging by ensuring that students are focused on an organizing question or purpose for the activities. They could build time for peer-talk and purposeful classroom discussion more systematically into their lessons.”

The study, co-authored by language and literacy development expert Catherine Snow, looked at three multiyear adolescent literacy projects: Promoting Adolescents’ Comprehension of Text (PACT); Catalyzing Comprehension through Discussion and Debate (CCDD); and Reading, Evidence, and Argumentation in Disciplinary Instruction (READI). Each project focused on a different method of reading comprehension — for example, building vocabulary and knowledge central to a particular unit — and implemented a curriculum following that theory.

These three programs shared the understanding that adolescents face new challenges in reading, such as grasping unfamiliar content in complex language forms and integrating diverse forms of text. And while each project had its own model of building teenagers’ comprehension, all were successful in improving student outcomes.

Significantly, the researchers noticed three common practices in each of these projects. They found that building these practices in tandem into middle and high school reading lessons can help boost reading comprehension and build prepared, engaged learners.

Literacy projects are effective when:

  1. Students engage in active, purposeful, engaged reading.

All three programs emphasized the importance of students engaging with the textitself — rather than just learning the content, which they could have done through videos or lectures.

The projects also all included an explicit purpose for reading — answering essential questions or connecting content to students’ lives.

The projects all included non-textbook texts, such as short readings and background information, which helped keep students engaged.

  1. Reading involves various forms of social support.

Each program included group work, where students discuss, debated, and wrote together about the text. These projects also all used whole-class discussions to highlight ways of making meaning of a text. For instance, students could discuss the similarities and differences in their interpretations, or the teacher could model academic language and teach essential background information.

  1. Instruction leverages prior knowledge and introduces key concepts and vocabularies.

Just as younger students learn to read by connecting the words on the page to ideas they already understand, all of these programs introduced new content and vocabulary by connecting it with students’ prior knowledge. The projects then had students use that new knowledge in ways that activated higher thinking skills, such as making and justifying a decision or solving a problem.


“Our findings suggest that the distinction between learning to read and reading to learn no longer serves teachers or their students,” write the authors. While middle and high school students may have mastered the basic tools of reading, they still need help “learning to read” the increasingly complex and diverse texts of the digital age.

But that continued instruction has to be done in creative ways, says Snow, a professor of education at the Harvard Graduate School of Education. “Whereas first-graders are happy to devote themselves to learning to read because they are motivated by the accomplishment itself, older students who need to acquire more sophisticated reading skills are less likely to acquire those skills if they are taught directly.” Adolescents learn how to figure out complex language forms or to question characters’ perspectives “in the process of reading for authentic purposes,” she says.

To develop comprehension throughout middle and high school, then, reading and language arts teachers should give lessons a clear, useful, engaging purpose.

More specifically, suggests Snow, “Middle and high school teachers could make their classroom activities more engaging by ensuring that students are focused on an organizing question or purpose for the activities. They could build time for peer-talk and purposeful classroom discussion more systematically into their lessons. And they could teach vocabulary conceptually — focusing on the meanings of words related closely to their central curricular ideas, questions, and purposes, rather than teaching lists of words.”