Category Archives: Student Support

Students do not all fit into the same box. Therefore, they need the option of extra assistance or an option to move above and beyond the classroom curriculum.

Share the Beauty of Mathematics!

How our 1,000-year-old math curriculum cheats America’s kids

By hiding math’s great masterpieces from students’ view, we deny them the beauty of the subject

Rubik's CubeYou can use a Rubik’s Cube to explain symmetry groups: Every rotation of the cube is a “symmetry,” and these combine into what mathematicians call a group. (Jeffrey F. Bill / The Baltimore Sun)
By Edward FrenkelMarch 2, 2014

Imagine you had to take an art class in which you were taught how to paint a fence or a wall, but you were never shown the paintings of the great masters, and you weren’t even told that such paintings existed. Pretty soon you’d be asking, why study art?

That’s absurd, of course, but it’s surprisingly close to the way we teach children mathematics. In elementary and middle school and even into high school, we hide math’s great masterpieces from students’ view. The arithmetic, algebraic equations and geometric proofs we do teach are important, but they are to mathematics what whitewashing a fence is to Picasso — so reductive it’s almost a lie.

Most of us never get to see the real mathematics because our current math curriculum is more than 1,000 years old. For example, the formula for solutions of quadratic equations was in al-Khwarizmi’s book published in 830, and Euclid laid the foundations of Euclidean geometry around 300 BC. If the same time warp were true in physics or biology, we wouldn’t know about the solar system, the atom and DNA. This creates an extraordinary educational gap for our kids, schools and society.

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If we are to give students the right tools to navigate an increasingly math-driven world, we must teach them early on that mathematics is not just about numbers and how to solve equations but about concepts and ideas.

It’s about things like symmetry groups, which physicists have used to predict subatomic particles — from quarks to theHiggs boson — and describe their interactions. Or Riemannian geometry, which goes far beyond the familiar Euclidean geometry, and which enabled Einstein to realize that the space we inhabit is curved. Or clock arithmetic — in which adding four hours to 10 a.m. does not get you to 14 but to 2 p.m. — which forms the basis of modern cryptography, protects our privacy in the digital world and, as we’ve learned, can be easily abused by the powers that be.

We also need to convey to students that mathematical truths are objective, persistent and timeless. They are not subject to changing authority, fads or fashion. A mathematical statement is either true or false; it’s something we all agree on. To paraphrase William Blake, mathematics “cleanses the doors of perception.”

What distinguishes us from cavemen is the level of abstraction we can reach. Abstraction enabled humans to move from barter to money, and from gold coins to plastic cards. These days, what’s left of “money” is often just an account record we read on a computer screen, and soon it could just be a line of code in a bitcoin ledger.

Today, abstraction is all around us — and math is the language of abstraction. In the words of the great mathematician Henri Poincare, mathematics is valuable because “in binding together elements long-known but heretofore scattered and appearing unrelated to one another, it suddenly brings order where there reigned apparent chaos.”

For the next generation to operate effectively, they must gain proficiency with abstraction, and that means mathematical knowledge plus conceptual thinking times logical reasoning — all things that a wider view of math would bring to the math classes at our schools.

I recently visited students in fourth, fifth and sixth grades at a school in New York to talk about the ideas of modern math, ideas they had never heard of before. They were young enough that no one had told them yet that math was impenetrable, that they wouldn’t get it. Their minds were still uncluttered with misconceptions and prejudice. They hadn’t yet been humiliated by poorly trained math teachers for making mistakes in front of their peers. Every question I asked them was met with a forest of hands.

I used a Rubik’s Cube to explain symmetry groups: Every rotation of the cube is a “symmetry,” and these combine into what mathematicians call a group. I saw students’ eyes light up when they realized that when they were solving the puzzle, they were simply discerning the structure of this group.

We next studied the majestic harmony of Platonic solids using dice. And I told the kids about the curved shapes (such as Riemann surfaces) and the three-dimensional sphere that give us glimpses into the fabric of our universe.

These are portals into the magic world of modern math, starting points as surely as addition, subtraction and fractions are starting points. The added bonus is that they give us a perfect antidote to the common perception of the subject as stale and boring.

Of course, we still need to teach students multiplication tables, fractions and Euclidean geometry. But what if we spent just 20% of class time opening students’ eyes to the power and exquisite harmony of modern math? What if we showed them how these fascinating concepts apply to the real world, how the abstract meets the concrete? This would feed their natural curiosity, motivate them to study more and inspire them to engage math beyond the basic requirements — surely a more efficient way to spend class time than mindless memorization in preparation for standardized tests.

In my experience, kids are ready for this. It’s the adults that are hesitant. It’s not their fault — our math education is broken. But we have to take charge and finally break this vicious circle. With help from professional mathematicians, all of us should make an effort to learn something about the true masterpieces of mathematics, to be able to see big-picture math, the way we see art, literature and other sciences. We owe this to the next generations.

If we succeed, we will stop treating this crucial subject as if it were the equivalent of painting a fence, and we will do away with the question, why study math?

Edward Frenkel is a mathematics professor at UC Berkeley and the author of “Love and Math: The Heart of Hidden Reality.”

Copyright © 2014, Los Angeles Times

http://www.latimes.com/opinion/commentary/la-oe-adv-frenkel-why-study-math-20140302,0,5177338.story#ixzz2vOAPb66a

7 Board Games That Teach Math Skills (and are actually FUN)!

By: Samantha Oestreicher, guest writer

Editor’s note: Samantha is a college math teacher who also writes a blog entitled, “Social Mathematics.” She offered to share some of her expertise with us here at Engaged Family Gaming and we couldn’t pass it up! Read on for some excellent examples of board games that teach math concepts without being all “teachy” about it!

There is a lot of pressure from the media and from peers to believe that math is painful. Sometimes adults try to dress up mathematics to make it look like“a game”. As a gamer, I have been really disappointed in these dressed up math practice games because they miss the point of what a game really is. Instead they are loosely veiled attempts to manipulate kids to use math in a “fun” way.

All is not lost though, great games do exist that use mathematical thinking and math skills. The following is a list of fun games that can inspire mathematical thinking. I have compiled a list of seven wonderful board games for gaming families which can be enjoyed by parent and child alike which also include mathematical thinking.

  1. Set 5+ (grouping/sorting)

Set is an amazing card game! This is a game that your 6-year-old will be better at than you are. I’m not kidding; kids totally rock this game. This is a matching game that can be played solo or with any sized group. The rules are relatively simple. The cards each have a certain number of shapes on them of a particular color and pattern. A set is three cards which all have the same type of an attribute or miss-match an attribute. Perhaps a set is three cards all have ovals with a striped pattern on them but each card has a different number of shapes (1, 2, and 3) and different colored (purple, green and red). Pro tip: Sometimes there isn’t a set available in the cards on the table. When I play set with undergraduate math majors I ask them to prove to me why there isn’t a set. Challenging older kids to explain why is excellent mathematical practice! This game fits in your purse or stroller and is perfect for a quick distraction and only requires a small table (or floor) of space.

  1. Rummikub 7+ (Numerals/grouping/relationships)

Rummikub is a 2-4 player classic game with lots of tiles to play with and sort. While Rummikub is also about color/number matching, it is more advanced than Set because you can re-organize the board. The matching rules are similar to Set, but now all the collections of tiles stay out on the table and you can steal from already created collections to make a new one. Worst comes to worst, the tiles are fun to play with and you can build things with them! This is a great game to play at home or at the end of the day on a vacation.

  1. Connect Four 7+ (planning/pattern recognition/Loud pieces!)

Every family needs a noisy, clattering, pieces-get-everywhere kind of a game. Connect Four is a childhood classic that supports geometric thinking, planning and pattern recognition. It is a two player game and great for two children to play together. Basically, Connect Four is an advanced version of tic-tac-toe. I do not recommend taking this game out of your home as you will surely lose pieces. This is a great game to entertain the kids while you are finishing dinner or something.

  1. 20 Express 8+ (consecutive numbering/planning)

This game is great for parents to play with your kids! It’s a number game which focuses on consecutive ordering. The scoring may take parental involvement as it is a little weird at first sight. However, the cool part about this game is that everyone tries to organize the same numbers at the same time. So you, as a parent, can compare answers with the other players. “Oh, that was a good choice, I didn’t think to do it that way!” The only negative to 20 Express is that it obviously uses math and that may turn off some kids. This game is good for traveling as it doesn’t require a central table and any number of people can play at once. Each player just needs a pen and something to write on.

  1. Ticket To Ride 8+ (counting/planning)

This game is really fun! It is a time commitment (maybe an hour once everyone knows the rules) and requires a big table. There are lots of little train pieces that you get to place on the board when you build railroad tracks between cities on the map. I don’t recommend this game if you have a cat or child who likes to jump on the table and mess up the board. This 2-5 player game requires business optimization similar to operations research. There is no money, but you have to collect cards which include restrictions on where you are allowed to build. This game requires a longer attention, but is full of bright colors and will definitely be just as fun for the parents as the children!

  1. Rush Hour 8+ (problem solving/ spatial awareness)

Rush Hour is one player, portable, colorful, and mentally wonderful. The board is small and packed with vehicles which have set directions that they can move. The goal is to move the vehicles in a particular order to get the little red car out of the traffic jam. A negative is that every piece is important. Don’t lose them! This game is great for waiting rooms or car trips as it comes with its own board and it small enough to hold in a child’s hand or lap.

  1. Sumoku 9+ (addition/multiplication)

Sumoku is a math-centric game for 1-8 players. Think of it as Scrabble/Bananagrams for numbers. You add to the existing tile layout based on a specific mathematical goal. For example, every row must add to a multiple of 3. This is a great game to support a young mathematical thinker because along with practicing basic computational skills, the player is also planning and matching. Unlike Bananagrams, there is no element of speed, so young players may take as long as necessary to check their math before they place their tiles. Like 20 Express, this game obviously uses mathematics. But, I believe Sumoku is interesting and dynamic enough to provide entertainment to the whole family. This game is easy to transport and requires a central table.

My recommendation is that, if you only buy one of these games, get Set. Then I would pick up Ticket to Ride. After that your choices should depend on you and your children’s interests. And remember that your involvement always improves the quality of the game. Mathematical thinking requires self reflection and the ability to collaborate. Challenge your kids to explain why they made a particular choice or ask them to help you with your move.

Happy Gaming!

Math Games at Home

Looking for educational and fun computer games for children?

Here are a few links:

  • http://www.ixl.com/math/
  • http://www.coolmath4kids.com
  • http://www.mathplayground.com/games.html
  • http://www.hoodamath.com/games/
  • http://www.softschools.com/math/games/

Don’t let their brains turn to mush.  Brains need exercise just like bodies needs exercise!  Use this break to help students catch up or get ahead with math practice!

GO GO GO!

 

LEARN ABOUT CPM – College Preparatory Mathematics

  •  http://www.cpm.org for more information

CPM Educational Program is an educational non-profit organization dedicated to improving grades 6-12 mathematics instruction.

CPM offers professional development and curriculum materials.

CCA

CPM Educational Program strives to make middle school and high school mathematics accessible to all students. It does so by collaborating with classroom teachers to create problem-based textbooks and to provide the professional development support necessary to implement them successfully.

CPM (College Preparatory Mathematics) began as a grant-funded mathematics project in 1989 to write textbooks to help students understand mathematics and support teachers who use these materials. CPM is now a non-profit educational consortium managed and staffed by middle school and high school teachers that offers a complete mathematics program for grades six through 12 (Calculus).

CPM provides:

    • Professional development programs for CPM and non-CPM teachers
    • Curriculum materials (standards- and researched-based) that use problem-based lessons, collaborative student study teams and spaced practice with course concepts.
    • Learning strategies that are consistent with the CCSS “Standards for Mathematical Practices” and other models such as the strategies identified as effective by Dr. Robert Marzano at McRel.
  • CPM courses are used in 35 states. In the past 20 year more than 5,000,000 students have taken CPM courses and more than 10,000 teachers have attended CPM professional development workshops. CPM opens its workshops at no cost to everyone: teachers, administrators, ELL educators, student teachers, and parents. In a typical year workshops are held at about 40 national sites and one or more international sites such as Hong Kong. CPM teachers, current and retired, lead the seven days of implementation workshops that begin in the summer and continue during the school year. Additional workshop support, various coaching models and individual mentoring are available by contracting with CPM.

11 Virtual Tools for the Math Classroom

OCTOBER 25, 2013

More and more classrooms are gaining access to technology that can be used with students. Whether you’re modeling a lesson, creating stations or working in a one-to-one classroom, virtual tools can promote student engagement while increasing academic success.

Here are some free apps for iPads — along with a few other tips — that can transform your daily lessons and are definitely worth checking out!

Base Ten Blocks

Number Pieces is a great free app that allows every student with an iPad to have an endless number of base ten blocks at their fingertips. Whether they are learning basic place value, modeling how to add decimals or exploring expanded notation, this app is worth looking into. Children can write all over the iPad screen and demonstrate their thought process as they manipulate the virtual base ten blocks.

Protractor

Even on an iPad, a protractor can be used as a tool to measure angles. Children can simply practice making acute and obtuse angles by moving the line on the screen, or they can measure the angles in objects placed on top of their iPad. Try putting traditional pattern blocks or cutout paper shapes on top of an iPad screen. There are even a few apps that let you use the camera on an iPad or an iPod Touch for measuring angles.

Graph Paper

Geometry Pad lets children draw lines and shapes on graph paper. They can plot points on this coordinate grid and even add text to the screen. This app is easy to use and includes tons of functions to try out. Educreations also lets students change the background of their screen to graph paper before they start writing.

Geoboard

Say goodbye to rubber bands! This virtual tool is perfect for elementary and middle school classrooms. Kids can simply create polygons on their geoboardto show off different quadrilaterals and triangles. They can also find the perimeter and area of each shape.

Ruler

Ruler is a neat app to try out on your iPad — it simply turns your screen into a ruler. Students can measure items placed on their screen in inches and centimeters. They can solve perimeter and area problems with the information they gather using this virtual measurement tool. There are also apps that help children learn how to use a ruler properly.

Clock

Whether you’re teaching elapsed time or just helping students monitor their pacing and stamina, the timer built into the clock that comes with the iPad (or one of the many comparable options) is a great addition to your classroom. It’s perfect for teachers with one iPad or for children working in small groups, as they can now calculate how much time has passed or learn how to read a clockwith these virtual tools.

Glossary

The Common Core State Standards stress the importance of having children use math vocabulary in written and spoken explanations of their thinking.MathTerms Glossary can help students learn definitions of different words so that they can use them appropriately. It’s a great reference tool for students in a one-to-one classroom and even has Spanish language entries.

Want to learn more? Here’s a webcast from APPitic, a site maintained by Apple Distinguished Educator that focuses on using the iPad to teach Common Core math.

A quick substitution of a traditional tool can be a great way to experiment with new technology. Have you tried out any virtual math tools in your classroom?

Money 101: It’s Elementary

As appeared in Northern Trust – Wealth Magazine 

Once kids start asking for things they see in the store or on TV, it’s not long before most parents hammer home their first personal finance lesson: Money doesn’t grow on trees. From there, how can we teach them other basic money concepts?

Children as young as 3 can be introduced to money, and by age 10, they can even manage a simple savings account and budget, says Ann Freel, director of Family Education and Governance Services for Northern Trust.

Consider these eight ideas to teach your younger kids to save money, spend it wisely and watch it grow – just not on trees.

1. Use money to teach kids about math, and vice versa. Introduce your youngest kids to money as they learn to count. Once they can subtract, kids can make change. When they learn percentages, they can figure out an appropriate tip for a restaurant server. “This is also a great opportunity to share a bit of wisdom about financial etiquette and being gracious to those who provide service,” Freel says.

2. Help kids understand the difference between needs and wants. Be mindful of how you talk about purchasing decisions and your own wants and needs. As children get older, Freel suggests explaining the choices you make, including tradeoffs, from grocery staples to vacation destinations. This helps share your family’s priorities and values regarding money.

3. Don’t stop at just one piggy bank. As soon as kids start acquiring money from grandparents, the Tooth Fairy and other sources, they can learn to make allocation decisions instead of throwing it into one pot. “One way is to give them three separate banks for their money: one for saving, one for spending and one for charitable giving, if that’s a family priority,” Freel says. “Tell them what each bank is for, using specific examples that gently and positively reinforce family expectations.”

Around ages 8-10, some parents ask their children to contribute part of their savings for a special item they want. Others incentivize saving or giving by matching the amounts their children put aside for these purposes.

4. Give kids earning opportunities. However you feel about allowance, children should have opportunities to make money so they can learn how it relates to time and effort. Make a list of age-appropriate tasks – separate from normal household responsibilities – with corresponding dollar amounts children can earn. Offer a variety of jobs and amounts. Gathering laundry could earn some quick cash for the ice cream truck, while a larger job, such as weeding the flower beds, could help kids earn spending money and pad their savings. “One error families may make is creating all big earning tasks,” Freel says. “This age group has a short attention span. Keep the tasks relatively simple so kids find the experience of earning money a positive and achievable one.”

5. Address income discrepancies. At a young age, children start to notice the differences between their home and belongings, and others’ possessions. As they begin to associate effort with money, they might draw the conclusion that the less wealthy don’t work as hard. “Explain to them that some people take jobs that pay less for a lot of different reasons,” Freel says.

Explore some of the simpler ones, such as passions and preferences, with younger children. Trickier reasons like educational disadvantages can be addressed at an older age. “During these conversations, parents should also share their thoughts about what is more important than money in their family – for example, liking friends for who they are rather than what they have,” she says.

6. Open a savings account in your child’s name. This can be an excellent way to teach kids from 8-10 what interest is and how it works. Demonstrate the interest they will earn on their savings account – for example, 1% monthly interest – using a dollar bill and a penny. “Additionally, children should understand how important it is to save their money in a safe place like a bank,” Freel says. Explain that bank-related paperwork contains sensitive information that needs to be kept secure.

If kids want to occasionally withdraw a portion of their savings to buy something, discuss it but don’t forbid it. For kids under 10, making their account seem like a black hole might discourage them from depositing.

7. Introduce the concept of credit. When you swipe plastic, there’s no visible exchange of money for goods. Early on, explain to kids that the credit card substitutes for money you already have in the bank and that there’s only so much of it. Later, explain credit card payments as borrowed money you have to pay back with interest and fees if you don’t do so on time.

8. Involve kids in household finances. Kids as young as 9 or 10 can develop a sense of stewardship by managing, or at least keeping an eye on, parts of the family budget – particularly parts that are personal and relatable to them. For example, ask a child to help create a realistic budget for one of their sports or hobbies that the family can track together. Share the prior year’s costs, such as weekly lessons, uniforms and travel. Then have the kids factor in incidentals and optional expenses like concession stand treats, team photos and equipment upgrades.

Turn Family Time Into Financial Education

By setting aside time for family members to manage their financial lives together, you can reinforce practical skills and find more opportunities to instill your family’s “money values.” Consider these tips:
  • Make it normal, casual and regular. Some families designate one Friday a month as “budget night,” during which family members review their monthly saving, spending and giving over their favorite pizza.
  • Keep it age appropriate and engaging, using websites and worksheets for younger children.
  • Use these meetings to plan vacations, discuss major household purchases, and establish financial priorities and expectations as a family.

In short, help children learn about financial matters from an early age by looking for teachable “money moments” in your family’s day-to-day life. Give children plenty of financial practice when they’re young, rather than waiting until they’re older.

“Young kids are fascinated by how the adult world works, so parents can leverage this natural interest by starting financial education and financial conversations at a young age,” Freel says. “Children who have early, positive experiences building their own ‘nest egg,’ and then making choices about how to use it, tend to be more responsible with money as they grow older.”

– See more at: https://wealth.northerntrust.com/wealth-management/money-101-its-elementary#sthash.JIgvNfNe.dpuf

Schools Aren’t Teaching Kids To Code (Here’s Who Is Filling The Gap)

By Selena Larson | Business 2 Community – Mon, Oct 21, 2013 7:45 PM EDT

  • By Selena Larson | Business 2 Community – Mon, Oct 21, 2013 7:45 PM EDT

Learning to code is all the rage these days, but not in one place that matters a lot: U.S. schools.

U.S. students already significantly lag their global counterparts where math and science skills are concerned. But computer science is in even worse shape: Of 12 technical subjects Schools Aren’t Teaching Kids To Code (Here’s Who Is Filling The Gap) image schools arent teaching kids to code heres who is filling the gap

Schools Aren’t Teaching Kids To Code (Here’s Who Is Filling The Gap)examined in a recent study by the National Center for Education Statistics, computer science was the only one that declined in student popularity from 1990 to 2009 (p. 49).

Last year, just 1.4 percent of high school AP students took the computer science exam, compared to almost 40 percent that took exams in English. Far more students took AP exams in Spanish language, psychology, calculus, and history than in programming.

Insufficiencies in school can translate into a bigger problem on an economic level. Each year, U.S. companies need to fill almost150,000 jobs related to computer science and mathematics, but colleges and universities only graduate about 100,000 students with degrees in those fields.

Bridging the gap

Recognizing the need for an increased focus in computer science courses in schools, organizations like the nonprofit Code.org are teaming up with industry leaders to promote technology education in both elementary and high schools across the country.

Code.org believes all students in America should have the opportunity to learn computer science, and recently announced the first step in its plan to educate them. The Hour of Code initiative is a one-hour introduction to computer science, designed to help kids and educators understand coding. The organization will provide both online and “unplugged,” or paper, tutorials and materials designed to assist teachers with the education process.

“Bringing computer science to every kid is the gift the tech industry needs to give back to America,” Code.org cofounder Hadi Partovi said during the Hour of Code launch event on Monday.

The Hour of Code will take place during Computer Science Education Week, December 9-15, and will encourage teachers to include one hour of computer science in that week’s curriculum. The organization is using game-like tutorials including Angry Birds and Plants vs. Zombies to drum up excitement for coding in the classroom.

Code.org is supported by leaders in technology and education including Bill Gates, Mark Zuckerberg, former president Bill Clinton, NBA star Chris Bosh, and actor Ashton Kutcher.

Paypal cofounder Max Levchin said that teaching young students how to code is critical for maintaining economic competitiveness in the 21st century.

“I think learning how to code, learning how the vast majority of everything around them works, literally, that is to say Internet of Things, and many other trends like it,” he said. “Having that knowledge will prepare children in the generations to come to participate in the economic development of the world.”

A prep school shows the way

To meet the growing need for computer science literate individuals, Beaver Day Country School, an independent college prep middle and high school just outside Boston, now requires students to have coding experience in order to graduate. Rather than requiring students take a standalone coding course to graduate, Beaver’s educators are incorporating coding practices into classes like math, science and even English.

“We also recognize that coding is a mindset, so we don’t want our students to memorize a certain list of commands within a certain programming language,” said Rob MacDonald, the school’s math department head. “Instead, we want them to think about solving problems in innovative ways.”
Learning programming and computer science builds problem-solving skills and critical thinking that can inform other walks of life.

“We’re also planning an interdisciplinary project in which students will learn about the history of surveillance, including the recent controversies around the NSA and Wikileaks,” MacDonald said. “That project will incorporate history, English and math, and teachers from all three departments will work together on the curriculum.”

Beaver has witnessed the success of coding firsthand. Last fall, a group of students from the Beaver InvenTeam received a $10,000 grant from the Lemelson-MIT program to build “an automated robot vehicular independence system,” or a robot that can follow motion sensors while carrying up to 50 pounds of weight. The school will begin implementing the coding classes for upperclassmen, but will expand all the way down to sixth-graders in the future.

Of course, Beaver Day’s approach isn’t for everyone—tuition for the 2013-2014 school year is $39,950, and the school enrolls a total of 457 students—but it’s definitely an intriguing model.

A teaching shortage

While the idea of mandating computer science classes on the path to graduation is an impressive notion, many schools and organizations are finding it challenging to educate and keep teachers who develop technical skills. “I can say pretty confidently there are multiple challenges, but the biggest by far is the lack of teachers,” Code.org’s Partovi said.

To make up that shortage, many students turn to mentors or peers outside the classroom to assist with projects like building websites or mobile applications.

“I know some students that say, ‘I would have loved to learn more about technology, but my friends, teachers or parents didn’t know much about it’,” said Edward Jiang, CEO and founder of StudentRND. “Building an app was far off magic that no one understood.”

Jiang started StudentRND, an organization that inspires the next generation of technologists and encourages people to work on projects in their free time, after teaching himself how to build websites and online games in high school.

He noticed that many students don’t have the time or the place to explore topics like programming. So he created Code Day, a 24-hour event that brings together high school and college students to build projects.

Because of his program and others like it, students get the opportunity to connect with peers and mentors that share their passion for computer science and can build and develop projects they would have struggled with pursuing on their own.

StudentRND and Code.org both recognize the importance of qualified mentors as an impetus for students to pursue interests in computer science.

“My first exposure to code and programming was actually in a neighborhood workshop,” said Levchin, who grew up in the Soviet Union. “But it’s remarkable that a backwards country like the Soviet Union had [resources for] learning how to code. And industry people, and software developers from the defense program that were teaching kids how to code.”

By 2020, computer-related employment is expected to rise by 22 percent. That means students must be ready to enter a workforce that expects them to have polished technological skills.

Lead image via HackNY on Flickr, other media via Code.org

 

Broadening the view of differentiated instruction

  1. SETH A. PARSONS (sparson5@gmu.edu) and STEPHANIE L. DODMAN are assistant professors in the College of Education and Human Development, George Mason University, Fairfax, Va. SARAH COHEN BURROWBRIDGE is a 6th-grade teacher at Lynbrook Elementary School, Springfield, Va.

Abstract

Students in today’s classrooms vary greatly in background, cultures, language proficiency, educational skills, and interests. To best meet students’ diverse needs, teachers must differentiate their instruction. The authors argue that the current differentiation conversation focuses almost exclusively on lesson planning, but instead should include important adaptations made in the midst of instruction — an aspect frequently overlooked or discouraged.

Differentiation shouldn’t end with planning but should continue as teachers adapt their instruction during lessons.

Students in today’s classrooms vary greatly in background, cultures, language proficiency, educational skills, and interests. To best meet students’ diverse needs, teachers must differentiate their instruction. The research base justifying the need for differentiation is strong (Santamaria, 2009Tomlinson et al., 2003), and there is growing evidence that differentiated instruction has positive effects on student achievement (Rock, Gregg, Ellis, & Gable, 2008).

It is not surprising, then, that differentiation receives a lot of attention in teacher preparation programs, professional development efforts, and educational conferences. However, the differentiation conversation to date is missing a vital component, and we feel that current conceptions of differentiation are too narrow to capture the complexity of effective classroom instruction. Where the literature rightly details the role of planning in strong differentiated instruction, it almost wholly leaves out what can effectively happen during instruction.

Differentiation and planning

The educational literature on differentiation focuses on planning. For example, Gregory and Chapman described differentiation as “a philosophy that enables teachers to plan strategically in order to reach the needs of the diverse learners in classrooms today” (2001, p. x). Likewise, Tomlinson stated that differentiation requires an “alternate approach of instructional planning” (1999, p. 14). Lawrence-Brown conceptualized differentiated instruction as a “multilevel lesson planning system” (2004, p. 34). Moreover, foundations of differentiated instruction include such strategy created in instruction planning as curriculum compacting, flexible grouping, tiered activities, and student contracts (Brimijoin, 2005Tomlinson, 2001).

Indeed, these perspectives and techniques describe effective practices and are helpful for supporting teachers in thinking about different ways to offer content, engage students in learning, and provide opportunities for varied end products. However, they provide a narrow view of the complex work of instruction to meet students’ diverse needs. We argue that the adaptations made in the midst of instruction are an important aspect of differentiation that is frequently overlooked or discouraged.

FIG. 1.

View larger version:

FIG. 1.

A broader view of differentiated instruction

Adaptive teaching as differentiation

Thoughtfully adaptive teachers adjust their instruction in real-time to meet the specific needs of individual students or the demands of the situation in which they find themselves (Fairbanks et al., 2010Parsons, 2012). Therefore, teachers who effectively differentiate their instruction not only carefully plan instruction to differentiate for the variety of learners in their classrooms but also provide moment-by-moment adaptations to meet specific needs that become clear during instruction — needs that were not or could not be anticipated. Consider the following example.

The adaptations made in the midst of instruction are an important aspect of differentiation that is frequently overlooked or discouraged.

John Fox is planning to teach his 6th graders about adding and subtracting fractions. Aware of the curricula below his grade level, he knows students have at least been briefly introduced to this concept. To prepare for the unit, he gives students a preassessment to gauge their readiness. In planning the unit, he considers not only where students are academically, but also the multitude of learning preferences in the room. Based on this knowledge of students, he decides to begin with an introductory lesson on the basics of adding fractions and then sets up a variety of learning stations to practice the skill or deepen understanding. For the lesson, he groups students by their readiness to add fractions and assigns each to one of the following stations: using fraction manipulatives to solve problems, creating multistep fraction word problems, or playing fraction games. Fox feels satisfied in his differentiation of content and materials.

As students work in the stations, Fox circulates through the classroom observing and assessing students’ progress. Unanticipated issues arise. He immediately adapts instruction by pulling three students from two of the stations to correct a misunderstanding of the concept. Later, he notices that another student can’t match a written fraction to the corresponding fraction bar. He pulls this student for a one-on-one session on the basic concepts of fractions and then creates a simple task for the student to complete. Fox realizes that if the student does not understand the underlying concept of fractions, she isn’t ready to add fractions. This scenario shows differentiation in planning and in adaptive teaching.

Planning is the foundation of differentiated instruction, but a teacher cannot account for everything. Because student understanding is complex, even the most sensitive preassessment can only offer so much information. Teachers must be able to be responsive to unanticipated issues that arise when their differentiated plans are put into action. They must, then, be able to monitor student progress and adapt instruction based upon students’ needs and instructional situations (see Figure 1).

Advocates of differentiated instruction contend that reactive teaching is not differentiated instruction (Tomlinson et al. 2003), and we certainly agree. Instruction that is defined by a teacher planning one lesson for everyone and then trying in the moment to make adaptations when students indicate trouble is not differentiation; it is reaction. We agree with Tomlinson and colleagues that, “Effective differentiation will likely arise from consistent, reflective, and coherent efforts to address the full range of learner readiness, interest, and learning profile in presentation of information, student practice or sense making, and student expression of learning” (2003, p. 128).

Planning plus adapting

Teachers who effectively differentiate their instruction appear to possess three attributes. First, they consistently assess student progress in multiple ways. For example, in designing word study instruction, teachers typically administer a spelling inventory. The results of this inventory are used to create word study groups composed of students who are ready for instruction on particular word features (Bear, Invernizzi, Templeton, & Johnston, 2011). A 2nd-grade teacher, for example, may put one group of students to work on long vowel patterns, another group on blends and digraphs, and yet a third on compound words. Those groupings would have resulted from the teacher’s formal assessment and spelling inventory.

On the other hand, differentiating instruction by thoughtfully adapting during the midst of instruction requires teachers to use ongoing informal assessments to make informed instructional decisions. Wanda Jackson’s 8th-grade social studies classroom, which includes many Hispanic immigrants, serves as an example. She plans a lesson about Native Americans’ dependence on nature. Her objective is to illustrate how their surrounding environments shaped Native American cultures. She plans an introductory lesson followed by a read-aloud of an informational text on the role environment plays in our lives. She anticipates that the plan will engage students while meeting the objective.

Jackson begins the lesson with an orange, describing the trip the fruit took to get to their local supermarket. She wants to emphasize the stark difference between present-day life in America and the life of Native Americans during the 1700s. She asks students what types of food they would eat if they could only get food from the local area. A Honduran pupil who just entered the United States shares that she had never eaten an apple before coming to the U.S. The student explains that in her home country, very much like the Native Americans under discussion, people use strictly the material within close proximity to their village. Jackson asks if other students have had similar experiences, and seven other students raise their hands.

In this moment, she decides that these students’ stories are more powerful than the informational text she had planned to read aloud. She adapts her instruction by setting up sharing stations, where each of these students can share his/her experiences with other students in the class. This teacher has now differentiated the content of her lesson. This example demonstrates how informal assessments and spontaneous decision making help teachers differentiate their instruction to meet the unique needs of students and specific situations they confront.

A second trait of teachers who effectively differentiate instruction is that they have extensive knowledge about how students learn and effective pedagogy. Knowledge is frequently discussed in three dimensions: declarative, procedural, and conditional (Paris, Lipson, & Wixson, 1983Schraw, 1998). Applied to teaching, declarative knowledge refers to knowing what is taught; procedural knowledge refers to knowing how to teach it; and conditional knowledge refers to knowing why one is using particular instructional practices and knowing when to use them. Planning differentiated instruction relies most upon declarative and procedural knowledge. A popular planned differentiation technique, a tic-tac-toe board, for instance, requires the teacher to use declarative and procedural knowledge. Because it is created in advance, though, this and other planned differentiation techniques rely minimally upon conditional knowledge.

On the other hand, differentiating on the fly by adapting one’s instruction requires well-developed conditional knowledge. If a particular form of instruction is not meeting students’ needs or a different form of instruction would be better for a specific situation, teachers need conditional knowledge to apply optimal instruction. In the example above, Jackson demonstrated effective use of conditional knowledge by changing her lesson from reading a book to allowing students to share their life experiences. Jackson made this shift after observing immigrant students’ sense of inclusion and importance as they willingly

Teachers who effectively differentiate their instruction:

  • Consistently assess student progress in multiple ways;

  • Are very knowledgeable about effective pedagogy and how students learn; and

  • Are highly reflective.

shared their life experiences. She also saw the other students’ interest as they listened to their peers describe experiences similar to the Native American tribes they were studying. In order for all students to thrive, she knew she needed to foster a climate of acceptance in her classroom. Both lessons would have achieved the lesson objective, but Jackson used conditional knowledge to make a thoughtful adaptation that achieved much more.

The final characteristic of teachers who effectively differentiate their instruction is that they are highly reflective. Schön (1987) explains that practitioners, including teachers, engage in two types of reflection: reflection-on-action and reflection-in-action.

Reflection-on-action occurs after instruction is completed. Teachers reflect on what happened in the school day, and this reflection serves to inform subsequent instruction. Following a lesson, the teacher may reflect on what went well in her lesson and what challenges she faced. The teacher may choose to reuse strategies that proved successful or research new ways of teaching a topic area that created challenges for students.

On the other hand, reflection-in-action comes in the midst of teaching. This type of reflection informs adaptive teaching. Thoughtful adaptations require teachers to constantly observe student progress in order to make immediate changes or interventions. Teachers’ adaptability is honed by constant reflection: They enter each lesson with a clear plan to successfully teach a concept in a differentiated manner, but they are also ready to adapt if their best-laid plans are not sufficient for every child.

Teachers must be able and prepared to adapt their instruction in the midst of instruction.

Conclusion

As the diversity of the K-12 student population increases, it is critical that teachers differentiate their instruction to meet all students’ needs. Planning instruction that is based on individual student needs, interests, and learning profiles is crucial in differentiating instruction. Manipulating the content, process, and product of instruction facilitates differentiation. However, teachers also must be able and prepared to adapt their instruction in the midst of instruction. Exemplary teachers thoughtfully adapt their instruction to meet the diverse needs of students. Policy makers, administrators, professional developers, teacher educators, and school leaders can support teachers’ facility for differentiated instruction by valuing formal and informal assessments; emphasizing declarative, procedural, and conditional knowledge; and encouraging teachers to exercise reflection-on-action and reflection-in-action.

Five Research-Driven Education Trends At Work in Classrooms

 | October 14, 2013 | 21 Comments

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Increasingly, educators are looking to research about how kids learn to influence teaching practices and tools. What seemed like on-the-fringe experiments, like game-based learning, have turned into real trends, and have gradually made their way into many (though certainly not most) classrooms.

BRAIN-BASED TEACHING

Many educators are using researchers’ insights into how children best learn to inform their teaching practices. Stanford professor Carol Dweck’s research on encouraging children to develop a growth-mindset continues to grow in popularity, as educators try to praise effort, not outcomes. Dweck writes that if children believe their abilities are fixed — that either that they’re smart or they’re not — they approach the world in different ways and aren’t as able to face adversity. When they believe skills and abilities can grow throughout one’s lifetime, they’re better able to rise to challenges.

Brainology, Dweck’s program, is just one of many such school-based programs that teachers can use in classrooms, as is Brainworks.

Educators are also teaching learning strategies, helping students find out the best ways to not just learn content, but how to learn. Ideas like remembering facts when they are set to music. This practice has been employed since the days of oral storytelling, but teachers are reviving it to help students in modern classrooms. Recent studies show that adults learn new languages more easily when they are set to a beat. Some educators are even experimenting with breaking up classical literature into bite sized raps.

There are plenty more examples of brain-based research on learning making its way into classroom practices.

GAME-BASED LEARNING

Games have long been used to engage students. But as game-based learning becomes more prevalent in schools, researchers are interested in how game structure mirrors the learning process. In many games, students explore ideas and try out solutions. When they learn the skills required at one level, they move up. Failure to complete tasks is reframed as part of the path towards learning how to conquer a level.

Universities like HarvardMIT and the University of Wisconsin’s Game and Learning Society are studying how game-playing helps student engagement and achievement, and well-known researchers in the field like James Paul Gee and University of Wisconsin professor Kurt Squireshow are using their own studies to show that games help students learn.

Once the terrain of experimental classrooms, digital games are now becoming more common in classrooms. In a recent survey by the Joan Ganz Cooney Center, half of 505 K-8 teachers said they use digital games with their students two or more days a week, and 18 percent use them daily. Educators are using commercial games like MinecraftWorld of Warcraft and SimCity for education. The Institute of Play continues to study game-based learning and helps support twoQuest to Learn schools, which are based around the idea of games and learning.

POWER OF PERSEVERANCE

Paul Tough’s book, How Children Succeedpopularized the ideas of grit and perseverance. Now those ideas have made their way into a U.S. Department of Education’s Technology office reportas well as the Common Core State Standards, which many states are already implementing. The idea that failure is an opportunity to learn and improve, not a roadblock to achievement, is often referenced as one of the most important life skills a student can take with him beyond the classroom.

Angela Duckworth’s research on grit has shown that often students, who scored lower on intelligence tests, end up doing better in class. They were compensating for their lack of innate intelligence with hard work and that paid off in their GPAs. Duckworth has even developed a “Grit Scale” that allows students to self-report their “grittiness.”

QUESTIONING HOMEWORK

The growing movement against homework in the U.S. challenges the notion that the amount of homework a student is asked to do at home is an indication of rigor, and homework opponents argue that the increasing amount of “busy work” is unnecessarily taking up students’ out-of-school-time. They argue that downtime, free play, and family time are just as important to a child’s social and emotional development as what happens in school.

Some research has shown that too much homework has “little to no impact” on student test scores. Other research on how brains work challenges the common method of asking students to practice one discreet skill at home. Overall, there’s a push to reevaluate the kinds of work students are being asked to do at home and to ask whether it adds value to their learning. If the work is repetitive or tangential, it may add no real value, and teachers across the country are starting to institute no-homework policies. Even principals are starting to revolt and schools are instituting “no homework” nights or substituting “goals” for homework.

CULTIVATING CREATIVITY

Increasingly business leaders and educators are realizing that creativity is a uniquely human quality that will set future graduates apart from the ever smarter computers that are playing increasingly important roles in society. There’s been a focus on stimulating curiosity and creativity through Science Technology Engineering and Math (STEM) courses, including computer coding, as well as integrating art and design into courses. The design thinking movement is a good example of schools working to develop students’ ability to think for themselves, brainstorm ideas and execute them.

Many schools are also shifting towards project-based learning to help leverage student interestsand passions in their school work. Long-form projects often allow students to demonstrate their creativity more than assignments that every student must complete the same way. The trend towards project-based learning is one indication that schools are actively looking to build creativity into curricula.