Summer Freedom

Today was the last day of this academic year. As the summer stretches out ahead of me, I feel tremendous excitement and relief.

Now, don’t get me wrong. I love my job, and I’m a big proponent of hard work, schoolwork, homework, and all kinds of work. But by the end of the academic year, I’m totally and completely worn out. Schools are possibly the most structured and disciplined places on our planet. During the school year, faculty and students alike are governed by schedules, timetables, and syllabi. We think in terms of hour-long blocks that end with a loud bell. Our thoughts are always, necessarily, fragmented. Just as we’re working through a particularly difficult piece of poetry, the bell rings. All of a sudden, students have to march to a Chemistry class and wrestle with the periodic table, while I have to run to another class and teach a totally different text. And then, all year long, students and faculty alike march from one set of assignments to another, from one set of assessments to another, from one reporting period to another. Much as I love school, I do find the degree of structure overwhelming.

So, summer is a welcome break. As I contemplate two months of freedom, I realize how important unstructured time is for all of us: faculty and students alike. While structured learning is very important, a whole different kind of learning takes place in the summer. We can spend a morning immersed in a book, with no bell to interrupt the experience. We can immerse ourselves in a particular project or learning experience without the constraints and demands of school.  We can play! Play with ideas, play with words, play in the sand and play at the beach. We can engage in an activity for the pure pleasure of it, without worrying about external assessments and judgments. We can do what we love, what we want, instead of being forced to do what everyone else (administrators, exam boards, parents, teachers) tell us to do. Oh, the joy of summer!

Unstructured time is, I think, critical for deep thinking and creativity. All people, teachers and students alike, need long stretches of unstructured time to imagine, dream, and think. It is this mental space and time that allows us to be reflective and creative. Additionally, we all need downtime to recharge our batteries. And, very importantly, we all need time outdoors, time to connect with nature and our physical environment. The beauty of the academic year is that we have this time built into every year. Every academic year begins anew in August, with renewed vigor and intensity. And then every academic year winds down in June, giving way to the luxury and freedom of summer.

The Case For Homework or 'After-schooling'

A lot of Western research suggests that homework is detrimental in the early years. Kids should play and relax when they come home, and parents should not be “burdened” with the responsibility of homework supervision. Now, as a parent and a teacher, I don’t think this is true at all. I think that homework, whether it is mandated and prescribed by the school or simply created and planned independently by the parent is very important even in the early years, perhaps especially in the early years.

Why? Despite what Alfie Kohn and the other anti-homework guys say, I think that young kids (ages 5 to 10) benefit from twenty minutes to one hour a day of structured academic work at home (reading, writing, math).  The amount of time will obviously vary based on the kid's age. My reasons for this belief are listed below:

REASON #1: GROUP SETTINGS HAVE LIMITATIONS

·     In school, kids learn in a group setting. Whether the teacher engages in whole group instruction or breaks the class up into smaller groups and gives each group an activity to do, each student is rarely spending significant amounts of time working through a particular skill on his/her own. As a teacher myself, I know that I can introduce a concept or skill in class and I can get kids to think critically about a piece of text in a discussion. However, the actual mastery of the skill can only be achieved if the student spends a significant amount of time working with the material independently at a pace that works for him/her.  Now, the fact of the matter is that I don’t have enough class time to let kids wrestle independently with material as much as they should and practice skills as much as they should. They have to do this part on their own at home. 

Furthermore, this skill reinforcement works best at home because kids are less distracted and pressured by their peers. There are definite limitations to the kind of learning and the depth of learning that occurs in a large group setting (classroom setting).  Large groups are great for presentations, discussions, and activities. However, they don’t work as well for skill reinforcement and mastery of content and skills.

REASON #2: KIDS MUST MASTER FOUNDATIONAL SKILLS; PARENTS CAN'T LEAVE THIS ENTIRELY UP TO THE SCHOOLS.

·      In the early years, kids absolutely have to master a range of foundational skills. If they fail to master these skills, middle and high school are going to be nightmares for them. Between the ages of five and ten, kids have to become fluent readers, develop a substantial vocabulary, and master grammar and spelling conventions. In Math, they have to master basic numerical work and problem solving techniques (addition, subtraction, multiplication, division, fractions, decimals, time, money, percentages, basic geometry, word problems).  These foundational skills are necessary to survive in our complex modern world, and they are crucial for future academic success.  What I find as a high school English teacher is that many students lack these basic elementary skills. For example, I often have kids who don’t end sentences with periods (full stops).  Some of my high school students (and I teach at an elite private school!) still don’t understand when to use an apostrophe. Some of my students have very weak vocabularies. I believe strongly that all young kids have to spend time at home mastering these foundational English and Math skills, and while teachers should introduce these skills/concepts and provide activities and avenues for practice, ultimately, parents have to ensure that their kids master these skills. I use the word “master (mastery)” very intentionally. These skills have to be mastered and completely internalized; it is insufficient to merely expose kids to these foundational concepts/skills and hope that they “get it”.

REASON 3: HOMEWORK TEACHES STUDY SKILLS, TIME MANAGEMENT, AND ORGANIZATION

·      Homework is also important because it teaches basic study skills. I have students in high school who cannot get their act together and get down to work. One of my students, for example, told me that she doesn’t know how to organize herself and get her homework done. She literally falls apart when she is asked to read a book, write a paper, or study for a test.  Kids need to learn these skills early on so that high school doesn’t feel like a mad assault for which the kid is totally unprepared. The best way to teach kids how to work independently is to make sure that they sit down in a quiet space every evening after school and do forty minutes to an hour of structured academic work. They have to learn to focus their minds, practice their skills, and sit still.  And they have to learn that they can in fact control their time and get their work done.

While they do this, they will also begin to realize the high correlation between effort and achievement, and they will begin to understand the satisfaction involved in intellectual work. While advocates of a fun and playful childhood might lambast homework as a spoiler of fun times, I believe that learning can be extremely satisfying. I think that working through a math problem can be very interesting and fulfilling, as can reading a chapter of a book, or crafting a thoughtful response to a story. I also think that drill style learning in limited doses can be fun. When a student has to work through a list of math problems, they may seem dry and boring, but the child will enjoy his own sense of achievement as he figures out the answers. And he’ll be able to see that practice does, in fact, make perfect. There is something innately satisfying about learning, and contrary to the popular notion that all learning has to be a song and dance routine to be fun, I fully believe that many kids find real, challenging academic work satisfying, if not “fun.”

Even if a child does not enjoy homework, it teaches important study skills, and it makes a child realize that sometimes we have to get work done whether we like it or not. This is a real-world lesson that kids should learn early on.  I’m a teacher, and while I love being in the classroom, I find marking papers torturous. I absolutely hate marking. Yet, I mark every single piece of paper that my students turn in because it’s part of my job. Kids need to learn that they have to do all parts of their job, and some parts will be fun while others won’t. That’s life.

REASON #4: NO SCHOOL OR TEACHER IS PERFECT; PARENTS MUST GET INVOLVED.

·      A final benefit of homework: it allows parents to make sure that their kids get the education they need. I have worked in a number of schools, and I know that schools are not perfect. If a parent relies entirely on the school to ensure that her child is well-educated, she could be in for a rude shock. Parents have to be involved, and they have to supplement what the school does. If your child’s school is experimental and progressive, and if it espouses the ideas of experiential education and holistic education, then it is probably doing a great job of getting your child to think creatively and building your child’s self-esteem and confidence. These are very worthy and important skills and qualities, and the school should be congratulated and supported in what it does. However, the down side is that the school can’t do it all, and what gets shafted in the process is mastery of foundational skills and the development of hard-core discipline and work-ethic. In contrast, in a more traditional school (I’m thinking about Asian schools particularly), the school may focus so much on foundational skills that they neglect the more fun and creative projects and discussions that are so necessary to promote creative and critical thinking. Parents in this case might have to supplement in the other direction (more open-ended projects instead of drill).

The fact of the matter is that schools and teachers absolutely cannot reach every single child to the degree that they need to. What parents don’t realize is that their child is one of many at a school. Even the best, most expensive schools in the world have teachers that teach many children as opposed to a one-on-one tutoring system; at all the schools I’ve been in, a full-time teacher’s load is fairly overwhelming. An elementary school teacher, for example, teaches, on average, 20 kids in a class (and I’m talking about developed countries. In Indian schools, for example, classes can have over 40 kids.). There is no way that one teacher can give each student much one-on-one time.  Furthermore, she’s busy trying to make sure that the naughty kids stay in line and that the class is not overly chaotic. And she’s bogged down by report writing, lesson planning, and a whole host of nonsensical administrative tasks.

As a high school teacher, I often teach up to 100 students (four or five classes) each semester. And I am inundated with marking, report writing, and admin work. And when I’m in a classroom of 20 kids, I can’t possibly give each kid much one-on-one feedback. The number of kids, the constraints of time, and the demands of classroom management all preclude working individually with kids. If I assign an activity to the group and then spend time working individually with students, you can be totally sure that at least two kids are wasting their time updating their status on facebook or surfing the web (I teach in a one-to-one laptop school that chooses not to block facebook), and another three kids are chatting  (either out loud in the old fashioned way, or on their computers). So, the opportunity cost of one-on-one instruction in a classroom is relatively high. This one-on-one work has to happen outside of class, either at home or in a library.

So, in conclusion, I’m a fan of homework. It’s absolutely necessary, and all children should do it every day whether their school prescribes it or not. If the school doesn’t assign homework, then parents should.

Creating a Math Rich Home: Learning from Asian Moms

I’m an English teacher, so creating a language rich home for my young children came easily and naturally to me. And since most parenting literature emphasizes language (read to your kids, talk to them etc.) over all else, I always felt as though I was doing a great job on the cognitive development front with my kids.  Then I moved to Asia.

Asian moms care deeply about Math, and their goal seems to be creating a math-rich home for their young children, as opposed to just a language rich home.  Surprisingly, there’s very little literature/research on this particular topic. I’ve read tons of parenting books, and they all pretty much ignore the development of early math skills. Yet, in Asia, parents are very focused on cultivating mathematical minds from the get go. (Unfortunately though, they don’t formally research and publish their ideas.)

After a lot of searching, I found a few good academic resources on this subject. Jo Boaler’s book, What’s Math Got To Do With It, and the Sidwell Friends School Math website for lower schoolers, provide lots of good tips for parents. Neuroscientist Lise Eliot makes an interesting case for the early and deliberate development of visual-spatial skills in her book "Pink Brain, Blue Brain" and Stanislas Dehaene explores the way our brains process and understand numbers in his book Number Sense.

So, how should a parent go about creating a math-rich home? Here are a few suggestions, culled together from books, websites, and lots of informal discussions with Asian moms.

   Stage 1 – Ages 1 to 4
   Don’t just think books. Think blocks. Lots of blocks and building sets. Since a strong spatial ability is tightly linked to higher level Math proficiency, most researchers believe that block play will help kids in Math. In fact, there are studies that show a correlation between the sophistication of early block play and later Math achievement.

      Also get your kids to do puzzles since they develop both problem solving strategies and spatial skills.
 Play-doh, art, sand play, and general outdoor play are obviously really important at this stage as well. From the research that I've done, general manipulation of objects/play with objects helps children create a strong foundation for Math. Similarly, activities that involve sorting, classifying, and stacking/nesting of objects are great as well.

Count with kids A LOT.
If you live in a big city with lots of skyscrapers, get them into elevator math. Going up and down on an elevator is kind of like riding a number-line. Kids get to press a button and then see the elevator move up each floor. Talk to kids about the numbers on the elevator. Read the numbers. Calculate how many more floors you need to travel to get to the desired one.
Count when you grocery shop (I need five apples) and when you clean up (Let’s put five blocks back in the bin). Get them to help you cook (we need five eggs).  Count whenever you can.

Use Math talk when you can; for example, can you find me two blue blocks. Great, now find two green ones. How many blocks do you have altogether? Let’s count. See two plus two equals four. Use words such as add, subtract, half, one third, taller, shorter etc.

Don’t just think numbers. Think shapes and patterns. Get kids to draw and color shapes. Get them to identify shapes around them. Get them to look at and identify patterns with shapes.

And finally, let them measure stuff. For some reason, my kids love playing with measuring tapes. So get them to measure all the furniture.

Stage 2- Ages 4 to 6
This is when Asian moms start getting very serious about Math. They figure that kids are now old enough to start learning the real thing. So they introduce concepts, and then they do what Asians love to do: they practice A LOT.

Most Asian kids I know start a Math enrichment program like Kumon, Abacus, or Math Monkeys around age 4 or 5. The idea here is to get kids really familiar with numbers and mental math. I researched these programs and found that they are very, very drill based. Now, I’m all for some daily drilling, but to me Kumon seems mind-numbingly boring. As a result, I chose not to enroll my son in Kumon. However, I know several moms who swear by it, and it definitely makes kids very, very familiar with numbers and basic computations (add, subtract etc.) If, like me, you’re not willing to go the Kumon route, you can still buy the Kumon books and use them a few times a week so that kids get some amount of drilling/practice.

Other great ways to get kids to become very familiar with Math include board games. Play lots of Snakes and ladders and any other game that involves adding and subtracting. Play card games. Make up games with dice and cards. Games like Yahtzee and Ludo work well too. Play mental math games when you're in a car or bus.

Use lots of blocks, legos, jigsaw puzzles, and games that involve numbers and strategies (Connect Four, for example). All of these will help kids develop spatial skills, which are tightly linked to higher level Math proficiency.

Introduce the Tangram game – great for getting kids to disembed shapes, and thus develop spatial skills.

Stage 3: Formal School (Grade 1/Primary 1 onwards)

Now, when I think about Math in grade 1 and beyond, I think about it on three levels: Math facts, Problem Solving, and Spatial Skills. Kids need to work on all three levels throughout the year so that by the end of the year they have not only developed a mastery of math facts but also developed their problem solving and spatial skills. For most kids, Math Facts are the easy part; it's the more analytic problem solving and the more creative spatial skills that are harder.

Level 1 – Mastery of Math Facts - Procedural Knowledge.

Kids have to know how to add, subtract, multiply, and divide quickly and efficiently. This is stuff they will use all their lives, and even if a calculator can do it for them, it is essential that they learn how to do it themselves. This is really basic foundational stuff. And the only way that kids get really, really familiar with numbers is through daily practice. So, whether you go the Kumon route or not, you’ve got to give your first grader lots of daily drills on this material. In Singapore, kids in primary 1 are adding and subtracting multi-digit numbers with frightening speed. And by the end of the year, they all know all their times tables. You’ve got to admire the dedication that Asian moms have towards making sure their kids know their Math facts. The sheer reverence for Math is something else.

While many Asian programs (Kumon, for example) allow kids to use standard algorithms (stack and carry to add with regrouping, for example), many Western programs and many Asian mental math programs advocate solving complex computations by breaking numbers apart. For example: If you have to subtract 83 – 15, you could think of 15 as 10 and 5. First subtract 83 – 10 to get 73 (very easy) and then subtract 73 – 5 to get 68. You could even think of 5 as 3 and 2, so 73 – 3 = 70, and 70 -2 = 68. Kids need to work on decomposing and recomposing numbers quickly. They’ve got to be flexible with numbers. Jo Boaler’s book claims that this is a distinguishing trait of high achieving Math students in schools. I think that kids need to be taught both the standard algorithms as well as the "mental math" techniques so that they can use whatever works best given the situation.

Level 2 – Problem Solving - Conceptual Knowledge
Singapore Math workbooks are great for this level. They introduce kids to interesting and complex word problems that require good verbal comprehension and significant logical and analytic thought. These books are not for the faint-hearted. They are about two or three years ahead of your average American text book, but then Americans don’t seem to care about Math the way Asians do.

Jo Boaler advocates making problem solving more creative by offering kids “Math Settings” or a range of materials (for example, blocks or dice) so that the kids can create their own problems. They shouldn’t just be able to respond to a question, they should be able to ask their own questions too. Some of the Singapore Math books provide equations (14 + 8 = 22, for example) and then ask the kids to provide a word problem for the equation. Writing word problems is a great way to make sure that a kid really understands a mathematical concept.

Level 3 – Spatial Skill Development  - Creativity

So this is where I’m not so sure that Asian programs really work. They seem to be very workbook oriented and they need a more hands-on element. I’m terrible at spatial thinking, so I get worried that my kids may inherit my deficiency in this department. However, research suggests that spatial skills can be taught and improved with practice.

Activities to improve spatial skills include building models using directions or pictures (Blik Blok,  Lego kits, modeling clay, Origami) and understanding how to put shapes together or disembed shapes (Tangrams, measurement activities, building activities).

Additionally, video games (Tetris, action games) supposedly help in this department. However, video games seem to come with a whole slew of problems of their own, so I’d be careful about overdoing gaming.
According to Conrad Wolfram, director of Wolfram Research and author of an article on connecting Math to the modern world, "programming is the way you write down Math in the modern world." It makes sense to begin programming activities (lego-programming/elementary robotics, Scratch, Logo etc.) with kids in elementary/middle school. 

Kids need more opportunities to do hands-on stuff like taking apart a simple machine and putting it back together. Or simple carpentry projects.

Another great activity, which is very popular amongst Indian kids, is chess. I’m not a chess player, but it supposedly teaches spatial skills and problem solving skills simultaneously. This is an area that I find particularly challenging as a parent. It is definitely incredibly important in the 21^st century, where visual-spatial skills are absolutely necessary to understand and navigate the digital world and the real world.

 I think that creating a Math rich home and investing significant time and energy in Math from the get-go is a good idea. Just as early reading and talking help prime kids for success in school, I’m fairly convinced that early exposure to Math games and Math concepts help prime kids for success in Math. One more thing: in Asian families, succeeding in Math is not an optional thing. Just as kids have to learn to read fluently, they have to do well in Math, and that’s that.