Supporting Struggling Students

I was recently reading a teacher’s manual for fourth grade.  It suggested if students were struggling with a particular concept that the teacher should “make the font bigger.”  I don’t think this strategy is going to help for most students but it does bring up the question,  “How can I help students who are struggling?”

Development of math concepts proceeds along a continuum from concrete to abstract.  When students are first learning, they should start with a concrete representation of the concept.  As their skill grows, they can move to a more abstract understanding.  For instance, when working on a subtraction problem such as 32-19, students should first work with unifix cubes or other objects so that they can count out 32 cubes and then take away 19 of them.  As they develop more proficiency, they can move on to using more abstract manipulatives such as base ten blocks.  These blocks include a stick with marks on it to show that it is a stick of ten.  Unlike the cubes, however, one cannot break it apart and take some off.  To solve 32-19, one can take away one stick of ten.  Then to subtract the nine, one needs to take away another stick of ten and trade it in for ten units in order to be able to take away nine units.  Once students have worked with the blocks enough, physically trading in the ten stick for ten units, they will then understand why we “cross out the 3 and make it a two” when using the algorithm. 

Often when students struggle it is because they haven’t spent enough time at the concrete stage or they have been shown the algorithm directly and haven’t spent any time at the concrete stage.  They have memorized a procedure but there is no understanding about why it works.  If they are presented with a problem that doesn’t fit their memorized procedure exactly, they cannot solve it. 

To support these students in building their understanding, you need to go back to a more concrete representation, such as manipulatives.  These will provide a visual model of the concept.  Students can work through problems by creating models.  They will physically move the materials and be able to see what happens to the numbers as they work.  If they do this they will be using their kinesthetic and visual modes of learning.  If they then discuss what they are doing they will be using their auditory sense as well.  By approaching the problem using so many pathways, they will develop a deeper understanding.  They will see that math makes sense. 

Consider an example from middle school.  When I have worked with middle school students and brought up the concept of trapezoids, I am often met with many blank stares.  It is difficult for some students to remember what a trapezoid is and how it is different from other quadrilaterals.  On the other hand, students who have used pattern blocks a lot in their earlier years know exactly what I am talking about.  When they were young, they had the opportunity to hold trapezoids often.  They built designs with them.  They put two trapezoids together to build a hexagon.  They fit the acute angle of a trapezoid between two equilateral triangles to make an interesting design.  (Though they had no idea about this terminology when they did it.)  When I mention trapezoids to middle school students who have had these concrete experiences they have a physical reaction to the word.  They often exclaim, “the red one!” (In a set of pattern blocks the trapezoid is red.)  Many hold out their hand as if they are remembering what a trapezoid feels like.  They can also tell me that it has two sides, two sides are parallel, two angles are acute, two angles are obtuse.  They can work from this specific information to generalize a definition of a trapezoid.  They are building on a solid foundation of experiences with the shape and expanding their understanding with new experiences.  The students’ early activities with the manipulatives have an effect on their math understanding, even many years later. 

Often students begin to struggle with math in fifth grade.  Up until this point these students may have been good at memorizing algorithms and teacher instructions.  Their math experiences did not include early experiences with manipulatives and problem solving that helped them make sense of the math.  Fifth grade is when students need to start applying algorithms, often in sequence.  If they do not have a firm understanding of what they are doing, the process falls apart for them because they do not have a firm enough understanding of what is happening to be able to follow the numbers and make sense of the work.  It is like building a house on sand.  The foundation is not firm enough to support the weight of the heavier math.  More often than not, this results in a frustrated student who says, “I hate math.”  This student often starts to turn away from math at this point and is unlikely to pursue math challenges and courses in the future. 

We need to go back and shore up the foundation for these students by helping them build their understanding from concrete to abstract.  By using manipulatives and helping students make sense of the math then they will be able to move forward with a more positive attitude.  They will be more likely to stick with math and gain skills that are needed for the jobs of the 21^st century.

Communication In Math Class

I once had a parent very upset with me because I gave her son a math assignment to do with a partner.  “Are you trying to teach my child math or are you trying to teach them social skills?”  Well, both.

Times have changed since I was a student and since many of today’s parents were students.  It is true that my middle school math class was silent.  No talking was allowed.  We all sat in rows alphabetically.  I sat behind the same boy for all of 6^th, 7^th, and 8^th grade.  I never talked to him or any other students in class nor did we ever share our ideas in front of the class.

If one talks to adult mathematicians, however, it is clear that the work of a mathematician is social work.  Solutions are rarely arrived at on one’s own.  It is through collaboration and discussion that solutions are found. 

The new Common Core Math Practices reflect this.  One of them reads: “Construct viable arguments and critique the reasoning of others.”  Students need to learn to clearly explain their thinking to others.  They also need to learn how to disagree with and question the work of others in a tactful manner.

My husband and I recently remodeled our 50 year-old kitchen.  He was very invested in the color of the new floor.  He really wanted a deep reddish color.  I wasn’t focused on the floor at all and was ready to go with the first color suggested by the contractor.  I was focused on the backsplash and what kind of tiles to use there.   My husband wanted the backsplash to be plain white.  By bringing our two different perspectives together, we were able to create a finished product that is more complete and more elegant than we could have done on our own. 

I know you have had this experience too.  You worked on a work project, a house project, or had a discussion with someone.  By bringing your ideas together the final result was much stronger.

A math problem flows in the same way.  Yes, we can often solve a problem by using algorithms to get the solution but another person might have a more elegant way of getting to the solution.  Their path might take into account patterns or ways of grouping numbers thus making the problem so much simpler than you originally thought.  They might have attended to a piece of the problem that you hadn’t considered carefully enough, making the final solution more complete.  In addition, the sharing of ideas makes each person reconsider their perspective in light of new information and either reject their first idea or add to it.

By talking about math with our children, we can also help them see new connections in math and think about concepts in ways that may be different or new to our children.  We also help them learn that math is part of the real world.  It is not just something that is done inside of a math classroom.  We can work together on sudoku puzzles on an airplane or play Blockus together in the evening.  It is more enjoyable if it is shared.

It is funny to think back to my middle school math classroom.  In addition to regular math class, I was on the math team.  The same teacher practiced with us after school, solving complex problems together as a group but during our regular class time we were in those rows.  Why did the teacher teach the two groups so differently?  The implication was that kids who were good at math should talk about it and those who weren’t should listen quietly to the teacher’s ideas.  Maybe those of us on the team got better at math BECAUSE we talked about it after school.

Common Core directs all students today to be doing math like mathematicians.  We want them to talk and share ideas and learn from each other.  Not only will this prepare them better mathematically but it will make math feel like math is a part of their whole lives, not just their school lives.

Watching Our Language

I often give talks about math to groups of parents.  So often parents come up to me afterwards with a question or a comment.  They preface it by saying, “I’m not a math person.”  This comment always makes me wonder, “Have you figured out how to double a recipe?  Do you manage your bank account?  Can you tell how much the pants will cost if they are 25% off?”  Yes, you are a math person.  You may not love math, but you are a math person.

We cannot deny how much math affects our modern lives.  Each morning when my son wakes up he checks the temperature for the day and compares it to the day before.  “Oh, mom, it is going to be 13* cooler than yesterday.”  My daughter collects snacks for her Girl Scout troop.  “If we have 12 girls and each box of granola bars holds 8 snacks then I need to bring two boxes.”  We get in the car and I calculate if ¼ of a tank of gas will get me the 30 miles to school and back.  Every hour of the day we are involved in some sort of math.

Two hundred years ago women were considered too delicate to think about math.  We need to stop perpetuating this idea and give our daughters (and sons) the confidence that they CAN do math.  It is OK to say, “I don’t know how to do this problem,” but follow it up with, “Let’s figure it out together.”  Your child will get the idea that they can do math if they stick with it and talk about it.

Most parents know that it is important to read to their children at night but so few parents know that it is also important to do math with their children.  No, I don’t mean worksheets.  I mean, real-life math.  First you need to realize when you are using math in your life and then you need to talk about it with your children. 

Has the price of gas gone up?  If it goes up five cents per gallon how much does that change your weekly gas bill?  Talk about it. 

Are you wearing a fitness tracker?  Have you hit your 10,000 steps for the day?  How far do you have to go?  Talk about it. 

Just this morning the DJ on my radio said that she didn’t like doing math.  Talk about it.  Break down those perceptions.

My children are now in middle school so they are studying decimals and percents.  I have been using that language to give them answers to their questions.  How much longer until we get to the birthday party?  We are 50% of the way there.  Do we have any cake left?  75% of it is gone.  Talk about it.

So many of the jobs of the 21^st century require math skills.  We are doing our children a disservice when we set them up to think that they are not a math person and thus cannot do many of our modern jobs.  Change the language in your house.  Change your child’s attitude and tell them we are all math people.

Building a Strong Mathematical Foundation

Before the days of GPS systems if you needed to go somewhere in a new town you would get out a map and take a look at what route you might take.  You might decide to take the freeway.  You would do that route for many days since that was the one route you had learned and each day it would get a bit more comfortable and familiar. 

After many days of following the same route, you would move to an abstract level.  You wouldn’t need to consult your map anymore to double check the name of the exit.  You would be sure to turn right at the T in the road rather than turning left.  If you wanted to stop and get a coffee on your way, you would know how to alter your route slightly to hit the Starbucks.   If you were on the freeway one day and there was a traffic jam, chances are you would have a good sense of how to exit and take some side streets because you had studied the map and had an idea of the surrounding area. 

Building a strong mathematical foundation with students proceeds in much the same way.  We want them to move from a concrete understanding to an abstract understanding but this process takes time.  We start with the students using tools and building models to develop their understanding of a concept just as you used a map to plan your route.  Once students develop some comfort and skill at this concrete level we can start moving them to more and more abstract levels of understanding just as you did when you were able to alter your route to grab a coffee on your way.

We want students to have a good sense of the surrounding area.  If they get stuck in one place, they should have ideas for how to go in another direction.  The new math practices call for students to “Use appropriate tools strategically.”  In order to chose a route and decide upon the best course of action, students need to have options available.  When we were in school most of us only learned one method for solving a problem.  Teachers have learned, however, that we do students a disservice when we only teach them one method of solving a problem.  If they get stuck or want to check their answer, they don’t have any other tools to choose from.

Additionally, teaching multiple strategies helps to meet the diverse needs of a class.  At any point in time students will be spread out along the continuum of understanding of a concept from concrete to abstract.  All students can be working on the same problem but they might not all be working on it in the same way, at the same level.  Students can learn from their classmates’ methods and ideas about solutions.  The whole group grows mathematically stronger as their consider the problem from different perspectives.

Recently I have been studying some of the math programs that are available for elementary schools.  Though Common Core standards are very clear about having students work at a concrete level before moving on to an abstract level, most of the math programs are not aligned with this thinking.

One program I reviewed had pictures of a few models but then when it came time for students to work independently, all of the work was abstract.  It takes time for students to move from a concrete to an abstract understanding.  Considering the example of the route in a new town again, you might have needed to consult your map each day for a few days before you could travel the route unassisted.  You traveled the route over and over and soon you became very comfortable with it.  We cannot just show students a few pictures of objects and assume that they are now ready for abstract thought about the topic.  Students need to build, model, and discuss their ideas.  They need to consider other students’ models of the concept and look at theirs in light of the new information.  The only way that students can build a strong foundation is to move through these steps from a concrete to an abstract understanding of the concept.

I see too many fifth graders who tell me they hate math.  It doesn’t make sense they say.  It isn’t interesting to them.  When I talk with them further I realize that most of these students never had an opportunity to explore concepts at the concrete level.  They were given algorithms and told to memorize them.  They were then able to apply those algorithms if the new problems looked just like the problems they had practiced.  If they hit a problem that looked slightly different or asked them to use their skill in a new way, they did not have enough of a mental image of the concept to be able to choose a new route.

Teaching students multiple ways to solve problems gives them a stronger mathematical foundation.  They can consider new problems from different perspectives and then choose the best method for solving them. They are flexible thinkers who can try new approaches when the one they are using doesn’t work out.  Teaching in this way also helps to meet the diverse needs of a group of students.  This is one of the strengths of the new Common Core Standards.

Scarcity

Wow, thank you Lynne Twist for giving us a lens through which to view the current culture in many schools.  In her book, The Soul of Money, Ms. Twist writes about the culture of scarcity. “No matter who we are or what our circumstances, we swim in conversations about what there isn’t enough of.”  Parents devote great amounts of time to avoiding scarcity by filling their children with extracurricular activities and tutoring, worried that their children are not getting enough education at school.  Parents are working so hard to make sure their children are at the top of the pack in academic subjects.  They are also driving hither and yon to make sure that their children are well rounded and skilled in many areas.  Will the extras be enough for my child to get into a good college they wonder?  Perhaps we could do a little more.  So they push and sign up for one more activity, all at the expense of family time, friend time, and play time.

What if we didn’t need to do all of this?  What if we just said, “This is enough.”

Angelique, a good friend of mine, with children the same age as mine once said, “They don’t need that much, Alison, they really don’t.”  In so many ways she is right.  Our children don’t need five winter jackets.  One will do.  They don’t need birthday parties with 30 friends who each bring a present resulting in a mountain of new toys they won’t have time to play with.  They don’t need special activities every day of summer.  Time spent reading books, digging in the dirt with friends or sorting collections of coins can be just as fun as a big trip to a museum. 

Lynne Twist writes, “Scarcity is a lie.  Independent of any actual amount of resources, it is an unexamined and false system of assumption, opinions, and beliefs from which we view the world as a place where we are in constant danger of having our needs unmet.”  Let us think more deeply about what we want for our children.  Parents of school age children voice great concern about getting their children into the “right” college.  Is that our end goal?  Will life be glorious if our children get one of the coveted spots?  Perhaps our energies would be better spent teaching our children how to build and sustain relationships with others. 

Dan Buettner has studied people who live 100+ years.  He went to “blue zones” around the earth.  His goal was to figure out what lifestyle habits the people followed.  Sure, there were the expected habits of eating healthy food and exercising but he also found that putting family first, celebrating elders, and laughing with friends were key to a long life.   Today’s family time has been so chopped up by our focus on extracurricular activities and academics.  We would develop healthier habits and save money if we dropped some of the extracurriculars and spent more time with our families.

We need to move from a you OR me culture to a you AND me culture as suggested by Buckminster Fuller.   In this kind of environment children would be supporting each other and looking out for one another rather than competing with each other for coveted spots at Stanford and Harvard.  In a you AND me culture people will use their time, energy, wisdom to work towards common goals.  In every classroom we teach that two heads are better than one. People working together create something greater than one person can working alone. We need to carry this through to a life view that people working together are better than people competing with one another.  We all will be better off if we can make this change.  There is enough for everyone.

  

Plan For Success

The new school year is almost upon us.  As you are helping your child pick out a new binder and highlighter markers for the new year, there is something that you can do to get ready for the year too.  Think about your goals for your child for this year.  How do you want them to grow this year? 

You might chose something academic like, “I’d like my child to consistently use capital letters appropriately 90% of the time.”  It might be something more metacognitive like, “I’d like my child to manage their homework time independently.”  It might even be something about friendships like, “I’d like my child to broaden their friendship circle by playing with two new friends this year.”  Whatever you choose, make it something small enough that your child can accomplish it in the next few months.  You may want to pick more than one goal but don’t pick more than three.  Your child can only stay focused on a few goals at a time and it will help their teacher be focused in their efforts as well.

Once you have your goals, be sure to share them with your child’s teacher.  If you have an intake conference early in the year this would be the time to share your goals.  If your school does not have intake conferences then you can either send the teacher an email or request a conference (you would want to choose this option if you have a fairly large or serious goal you are working on). 

At the end of my daughter’s second grade year we received her standardized test scores.  Oh boy, did she struggle with the writing mechanics section of the test.  Yes, I saw this at home too.  Her use of capital letters and punctuation was haphazard.  At the beginning of her third grade year I shared my goal of focusing on punctuation with her teacher.  This teacher had a more holistic approach to teaching writing but she knew this aspect was important to me so she was sure to spend time working on it with my daughter.  By the end of year, through work at home and at school, my daughter’s skills had improved a great deal.

I always reach the end of the school year and think about how much my children have grown.  They will grow in so many ways that we cannot name them all but by picking a few goals you can focus your energy as well as build a strong connection between the classroom and home and ensure that those particular goals receive attention. 

Dr. Phil McGraw discusses the importance of knowing where you want to go so that you can get there.  Without a clear goal, it is hard to know where you are going or even if you arrive.  “People that are successful have a strategy from getting where they are to that success. The difference between goals and dreams is a timeline. “Someday” is not a day of the week. You have to work for what you want; not for what you don’t want… every day.”

I think we do children a disservice when we don’t teach them how to work towards goals.  I am NOT recommending that you pick huge, lofty goals and have your child work many hours a day towards them.  A balanced approach is necessary. I do think, however, that it is healthy for children to learn to work towards goals.  This is a life skill that you can help your child develop now.   There is a great deal of discussion in education circles now about the importance of grit in helping children become successful.  Working towards goals, facing setbacks, and forging ahead towards those goals are ways of teaching students grit. 

The beginning of the school year feels like a new beginning each and every year.  What new things do you want to begin with your children?

Plan for success this year.

We Need A Food Revolution

In a few short weeks we will get the emails from my children’s soccer coaches inviting them to show up for the first practices of the season.  As I sit here eating a peach that I plucked from the tree in our garden I am thinking again about the food paradox that exists at so many of my kids’ events.

Everywhere I take my kids they are getting filled up with unhealthy food choices.  When we go to a birthday party the kids are usually served pizza, which is full of saturated fat, sugar, and sodium.  Then they fill up on birthday cake or should I say frosting with a little bit of cake beneath it.  A party at school often involves lots of cookies and candy.  A sleepover with a friend once resulted in my child having eating nothing but banana bread for 24 hours. 

Don’t get me wrong, I like a slice of pizza and a piece of chocolate as much as anyone but I do think we are sending the wrong message to our kids when we are feeding them empty calories at every turn or not encouraging them to eat a wider variety of foods.  My son is twelve and we have only once been to an event where the host provided a healthy spread for the children.  All of those years of birthday parties, school celebrations, and sporting events add up to a lot of missed opportunities to teach children about healthy food choices.

Children’s sports are an arena where I feel we are particularly remiss in the messages we are sending around food.  I sign my kids up for sports so they can get exercise.  I want them to learn new skills and make new friends as well.  I want them to feel strong.  Blocking that shot, making a goal, or swimming a faster time in the pool are all ways they can build their confidence and feel their own power.  All of these are elements of a healthy lifestyle.

I assume many parents have these same goals in mind.  So, if our goal is encouraging healthy behaviors, why are the children given snacks at the end of the event that run so contrary to this goal?  What message are we sending to our children when we teach them to replenish their bodies after a workout by eating all of this unhealthy food?

When my son played baseball each game ended with all of the players sitting in the bleachers sharing a meal together.  It was actually a really nice time.  The players got some time to just hang out and it built community among the parents as we struck up conversations too.  Each family would take a turn bringing the snack/dinner.  My son and I would start discussing our snack weeks beforehand.  My goal was to bring some healthy food that would appeal to the kids.  His goal was to make sure I didn’t embarrass him. 

We watched to see what the families ahead of us in line would bring – Costco pizza, Caesar Caesar Pizza, Round Table Pizza.  Hmm, we were sensing a theme.  The pizzas were often accompanied by huge Gatorades in shocking colors and topped off with a bag of Chips Ahoy or Oreos.  Could we turn this around and create a snack that would appeal to the players but would fit my desire of encouraging better eating habits?

We decided upon hot dogs (nitrate free!) in whole-wheat buns.   Only one kid complained about the whole-wheat bun.  Then we popped popcorn ourselves and added just a touch of salt and butter.  It tasted good but was not overwhelmed with fat like some of the microwave popcorns in a bag.  Lastly, we had 100% apple juice.  Still thirst quenching but free of red dye #40 and yellow dye #5, which are both banned in a number of European countries.  This meal passed my son’s cool test and satisfied the players’ hunger in a healthy way.

During soccer season there is a different protocol in our town.  The kids don’t eat a meal together but instead get snack bags that they take away and eat on their own after the game.  Often my kids get bags that are so full of candy they seem like a trick or treat bag from Halloween.  I don’t think a bag of M and Ms or a Ring Pop really has anything to offer a body that has been running for an hour straight yet family after family follows this model when they put together the snacks.

One year my daughter had a great soccer coach who brought orange slices to every game.  My daughter doesn’t even like oranges but since everyone else was eating them she did too and by the time the snack bags came out she was too full to eat anything in them.  Yay, a little victory for fruit!

A friend of mine has two boys who are actively involved in sports as well.  When it is her family’s turn to do snack my friend makes up a huge batch of smoothies.  She brings those to the park and serves them up.  Thirst quenching and healthy!  She has also done fruit kabobs, which the players gobble up after the games. 

Oprah once said, “… better food is the foundation for a better life.”  We need to show our children the way.  The habits we help our children build now may well last a lifetime.  If we let them eat a steady diet of chicken nuggets, pizza, and sports drinks now these will be the foods they turn to when they are adults.  We need to start seeing the act of providing healthy food choices as important to our job of parenting as helping with homework and encouraging them to play sports.

Culminations

Welcome back to school everyone! I am sure you have been busy preparing your children for school or preparing your classroom to receive new students. Bulletin boards are hung, curriculum has been planned, and nametags have been written. As part of your beginning of year preparations, I urge you to take some time to think about how you will celebrate learning with your students and families this year.

When I first started teaching, I invited parents into the classroom for everything. Every month we held an author’s tea and invited parents in to hear the writing we had done. Every time we ended a big project, we put on a show for parents. One year we studied the Olympics so we had a day when we dressed as the ancient Greeks did and held a party with traditional foods. Another year the students had learned some new dances in PE so we invited parents to picnic on the lawn with us and watch the new dances. Another time we had Book Character Day. Students dressed as characters from their favorite books. Parents came and read stories with us and we all tried to guess who the visiting characters were. I still have fond memories of those events. Parents loved them and students enjoyed them. It gave the students something to work for and livened up our routine.

It was, however, a lot of work. I began to wonder if all the time we spent preparing for these special activities might not be better spent on learning new things. When we practiced our dances for the 50th time, we weren’t learning anything new. We were perfecting our dances but we weren’t learning new steps. When we practiced performing our poems over and over for the author’s tea, we weren’t learning to love the language more or learning new vocabulary. We were learning to project and enunciate but was that worth the amount of time we put into it month after month?

In recent years I have done fewer and fewer big class events, preferring instead to push the student’s minds in new directions rather than perfecting known routes. I often found, also, that parents often didn’t see the genius that went into a story that was being shared or the amount of effort it took to get that sculpture to stand up. Those of us in the class knew because we had been there for the experience. It was more difficult to share this with parents who hadn’t been on the journey with us every step of the way.

Now that I am a parent, however, I see the deep pride on my child’s face as he shows me around his classroom during his school’s Open House. I see the excitement in his body as he prepares for his class’ Irish Dancing Performance for St. Patrick’s Day. I notice the sense of closure in the classroom as everyone closes up a chapter of learning and prepares to open another.

I sit in the audience and think, “What a wonderful teacher to bring this special experience to my child. Look at my child up there with all of his classmates. He will remember this.” I feel good that he has been part of this.

So, as you begin your year, be sure to plan in time for culminations. Celebrate all of the work you and your students have done together. Share your accomplishments with the parents, even if they don’t see the details that are meaningful to you. One teacher I know planned a “moon party” with her students complete with hot chocolate and telescopes to culminate her class’ astronomy work. Another teacher invited parents to attend the burial of a chicken her class had mummified as part of their study of Ancient Egypt. Another class dressed in period costume as they shared the work they did as part of their study of the turn of the century. How will your class celebrate their learning this year?

Differentiation in First Grade Math

Sometimes it is hard for teachers to know exactly how to differentiate in a classroom. This post explains what a series of differentiated lessons in math looked like in a first grade classroom.

I have been working with a group of gifted first graders for a few months now. From some early assessments, their teacher and I knew that they were working at a higher level than their classmates. We decided to put seven students in my group. The teacher took the rest of the students. The teacher’s group has been walking through the textbook. In this particular unit on addition, they are solving problems with regrouping such as 14 + 7= __________.

My group of students needed more challenge but I didn’t want them to stray too far from what the topic their classmates were studying so we started by solving regrouping problems with larger numbers such as 48+37= __________. We used place value mats and base ten blocks to model each problem. We have been doing lots of trading this year (trading pennies for dimes, dimes for dollars, etc.) so once I reminded them that they would need to trade, it was easy for them to solve these problems which all involved trading units for longs (ones for tens).

The next day the teacher’s group practiced different strategies for solving their two digit plus single digit problems (counting on and building with blocks).

My group was already proficient at counting on and building the easier problems with blocks. The next challenge for them was to solve problems that involved two trades – units for longs and longs for flats. These would be problems such as 129 + 83= ______________.

Before we started, however, I wanted to check that the students knew how to build the larger numbers. The students were confident using the base ten blocks to build numbers up to 100. With larger numbers, their understanding was not as solid. We practiced building and writing numbers such as 110. Many students built it correctly but then wrote it as 10010. Once they saw that their model only used three columns, they realized that the numbers they wrote down needed to correlate to their place value mat. They had one flat in the hundreds column, one long in the tens column and zero units in the ones column. They could then record this as 110. Next they were challenged to build 203. Some built 230 and some built 203. We continued to practice until they could build numbers up to 999 with accuracy. They were then able to solve the more complex addition problems confidently.

Throughout this process, one student correctly built and recorded each number without fail. I made a note of this student’s solid understanding of place value. This would help me plan next steps for him in math.

The next day the teacher’s group continued to need more practice with regrouping. It was clear, however, that my group did not need this practice. What they did need was to solidify their understanding of the place value of larger numbers that they had been building over the past few days.

I decided to have them work on counting strips. If it had been the beginning of first grade, I would have had them start their counting strips at number 1. Since we had been working on numbers over 100, I had them start with 100. They placed one flat on their place value mats. Then they added a unit and recorded 101. They then added another unit and recorded 102, etc. Soon the students were able to work abstractly and did not need the blocks to represent every number but used them at tricky times such as going from 149 to 150.

For the past few days, the class had been benefitting from the two math groups. At this point, it became clear that we needed to split yet a little bit more to meet everyone’s needs. The one child who had a solid understanding of place value from the start did not need to do a counting strip in base ten. I did, however, want to keep him on the same topic so I started him on a counting strip in base five. This would test his understanding of place value and strengthen it. He was thrilled to be working on something at his level and actually went home and asked him mom if he could do counting strips in bases two and three as well!

The day we started working on counting strips, the students in my group were beaming. They were so happy to be working on work that was just at the right level for them. They asked me why the one child was working in base five and the others were working in base ten. I told them that everyone’s brain was getting what it needed. They accepted this idea and continued to work quietly and happily for the rest of the period.

While this level of differentiation was achieved by having two teachers in the classroom, it could have easily been done by one teacher. One group could have worked with the teacher while the other group did some independent work (Marcy Cook math tiles, playing math games, reading, etc.). The teacher could then switch groups.

The biggest hurdle to differentiation is realizing that different students have different needs. Once a teacher acknowledges this, meeting those needs does not mean creating twenty different lessons. It does mean having two or three different levels of a topic available to meet the range of needs in the class.

5 Ways to Differentiate

In response to Rebecca Alber’s blog in Edutopia (http://www.edutopia.org/differentiated-instruction-definition-strategies-alber) about defining differentiation, there has been some discussion about how to differentiate for GATE students.

Often when I am out working with teachers, I hear it is the GATE students they struggle with the most. Many teachers have ideas about how to meet the needs of students at the other end of the spectrum but they aren’t sure what to do with GATE students. Many teachers tell me they differentiate by having the GATE students help other students. Other teachers allow the GATE students work on more difficult material but those students must teach themselves since the teacher is busy teaching others.

To help those teachers who are wrestling with this issue and to help those parents who want more for their GATE children, I hereby offer five quick suggestions to help GATE students in the elementary school classroom. My hope is that every day every student will be given the chance to move forward on his or her own learning journey. GATE students need opportunities to learn, just like other students.

1.Curriculum compacting. This concept is simple. Give the posttest for a unit before you teach the topic. Maybe you only give it to five students whom you suspect already know the material or maybe you give it to the whole class. If any student scores 90% or above on the post-test before you have even taught the material, that student already knows it and can “pass out” of that unit and work on material that is more meaningful to them. (See suggestions below for what that might entail.)

2.Writer’s Workshop. I thought word about Writer’s Workshop had spread and everyone was using this for his or her writing program but I have recently learned that is not the case. Many schools are still using formulaic writing frames in which there is little room for a gifted student to go beyond the boundaries of the assignment or let their imagination soar. Writer’s Workshop allows students to work at their own pace and on material of their own choosing. Students can often choose what kind of text to write and how to put their piece together. Teachers conference with students individually about their writing. In this way, the individual needs of gifted students can easily be met. Perhaps one student is working on using quotation marks while others in her class are still working on periods. Or perhaps she has a great idea for a poem even though most of her classmates are writing narratives. There is room for these variations in Writer’s Workshop. If you have not yet read a book about writing by Lucy Calkins or attended the Teacher’s College Reading and Writing Project summer courses, do so!

3.Math binders. Math seems to be the subject that is the hardest for teachers to differentiate. It may be that a student’s strength in math is often very visible. They can compute faster than anyone in the class and with bigger numbers too. Teachers then feel a pressing need to provide work at the appropriate level. In my classroom I met this need by keeping a math binder for every student. Inside that binder was work appropriate to their level. Students could reach for their binders any time they were done with other work or needed different work from the rest of the class. (These were also great for substitute days too – everyone just worked in his or her math binder, no prep required!) . I filled the binders with work as I came across it. Maybe we didn’t get to spend enough time on measuring. Then I would put some extra work in everyone’s math binder. Maybe Josh is really struggling with his addition facts. Then I would put some of that work in his binder alone. Perhaps Rose really enjoyed the 100s chart puzzles we did. I would xerox a few extra and stick those in her math binder. Sometimes students would ask me, “Can I have some work on division? My big brother is doing it and I want to do some too.” That would go in their binder as well. Each student then had a personalized collection of math materials at their disposal. At the end of the school year, I would send these binders home. Parents were thrilled to have some summer work for their children that was “just right” for them as opposed to a workbook they might buy.



4.Choice. Provide choice within units of study such as individual research projects or choices about products students will use to show what they have learned. This is a place where gifted students can soar. We have all seen those classrooms where there are 22 clouds on the wall and each one has a poem about a cloud on it that starts exactly the same way. Let’s shake it up some more and challenge the students to bring themselves to the assignments! What about a research project into the different types of clouds? Or a month’s log about the weather and a discussion about what this might mean for this year’s peaches? How about an interview with a meteorologist and a report back to the class about their job. Gifted students love the depth and complexity of these kinds of assignments. Teachers can control the choices by offering just a few for students to choose from or they can let students write a contract about what they want to do. Teacher and student then sign this before the student takes off. All of this work can be displayed around the classroom in a poster, photographs, a Powerpoint, lyrics to a song, or an essay. It will be so much more interesting to view than 22 cloud poems.


5.Computers. OK, I must admit that I am not a big proponent of computers for young children. However, that they can be a great differentiation tool. Programs such as Renzulli Learning and Stanford’s EPGY program are specifically designed for gifted learners. They can be used by students on their own to learn about things at his or her level, at his or her own pace. Renzulli Learning works to pinpoint a student’s areas of interest and then provides activities related to those interests. Stanford’s EPGY program also offers courses in a variety of different subjects. I have used it with students mostly for the math portion. I wouldn’t park a student on the computer for large portions of the day but I do think for a small amount of time each week, this could be an area where a student really feels like they are working on something that is meaningful to them.

Math binders, writer’s workshop, research projects, and computer programs are all things that will challenge gifted students. They are also projects that students can work on independently, with some teacher check-ins along the way. Get these things rolling in your classroom and when a student “passes out” of a unit, send them to do work in their math binder, write a story, do more research into their topic, or work on their Renzulli activities. This will keep them moving forward on their own learning journey.

See my next post for two more complex ways teachers can create a classroom that will meet the needs of ALL students!

Why Should We Care About the Gifted Kids?

Most people would agree that all children are entitled to an opportunity to learn. What then does it mean to learn? The dictionary defines learning as “acquiring knowledge or skill.” When gifted students are sitting in a classroom being taught material that they already know can we say that they are “learning”? Aren’t they then being denied a basic right that we believe all young people are entitled to?

I have been stunned lately by the disregard for gifted students in our public schools. I hear, “But they can already pass the tests.” or “ We need to focus on the lower students to bring our test scores up.” I even heard, “Let’s just have the gifted students teach the struggling students. That will give the gifted students something to do and will bring up our test scores.” It is well known that people learn material better when they need to teach it but if our gifted students are spending their time being ignored and teaching others, when are they given the opportunity to learn? This goes beyond funding and test scores. This is a civil rights issue and it criminal to have these students sitting in classrooms day after day spending their time doing work that keeps them busy but does not contribute to their learning.

The San Bruno Park School District has budgeted over $300,000 dollars for Special Ed Funding for the 2010-2011 school year. Special Ed. Funding is federally mandated so the district must follow the guidelines and the money must be spent. Funding for gifted education is not currently federally mandated. Guess how much the San Bruno Park School District will spend on gifted education next year. The answer is $0. I do not deny that students in special ed. need special services but it neglect to have so many services for those students and none for the gifted students.

If we think about 100 as a median IQ, students who are two standard deviations below the mean (IQ of 70) are required by law to have special services. Students who are two standard deviations above the mean (IQ of 130) have no federal protection and thus have no services. If a student has an IQ of four standard deviations below the mean (IQ of 40) they would be in a special day class and it would be unlikely that they could be mainstreamed into a regular classroom. For students with an IQ of four standard deviations above the mean (IQ of 160), they are usually stuck in regular classrooms doing the same work that their classmates are doing. Or they are home schooled because parents cannot find a place that will work for them in the school system. Laws have been enacted to make sure that some students are given the opportunity to learn but they have neglected to extend that right to all students.

Underachievement is the number one problem facing gifted students and it comes from the students being denied the opportunity to learn important skills such as perseverance, study skills, and the value of practice. These skills would be learned by engaging in challenging work that is commensurate with a child’s academic needs.

The bigger issue for me is the waste of these young minds. Imagine what a gifted student could do with years of learning under their belt. If they were given the opportunity to make continuous progress in school year after year imagine what they would be capable of by the end of high school. Now imagine the opposite, what they will have gained from years of classroom experiences in which they haven’t been challenged in the least? Gifted students are going to be movers and shakers in our world. They are bright. They are intense. They are able to take many different parts of a problem and put them together in a coherent whole. Why aren’t we shaping this and giving them the tools to learn to be leaders in our world?

This week a group of gifted first graders dutifully completed the page in their math book. They had to circle whether the crayon was “next to” or “far from” the glue bottle. Then they had to circle whether the marker was “in front of” or “behind” the scissors. These are words these students learned when they were two and three years old. I don’t see how this work guides them on their educational path. I don’t see the critical thinking skills and higher order thinking that I would hope would be part of the tool box of tomorrow’s leaders.

I fear for our future. If our students, all of them, not just the gifted ones, are only being taught the most basic material and how to be experts at filling in the blanks, I don’t know how they are going to solve problems in our world that are big and messy and don’t have simple solutions like a fill-in-the-blank worksheet. As we sit and focus on test scores we are losing sight of the fact that we need to teach students to think.

Creating the internet, inventing a computer, developing a hybrid car. I can guarantee these were not things people learned how to do from a worksheet. Who knows what challenges we will face in the next thirty years as the world becomes increasingly complex but I know that I want creative, bright, resourceful people leading the way. It is essential that we fight now for all students to have the opportunity to learn so that we will have skilled leaders to guide us in the future.

Ingredients for a Great School

I know that my ideas about what one would find in a great school are not unique but I have been touring schools this year and have been so surprised to find that very few schools actually employ current methods and thinking about education. So, I hereby submit my list of ingredients for a great school. I hope my children have the opportunity to attend a school like this some day.


1. A clear mission and vision. A clear mission and vision are the steadying forces that guide a school. When a parent advocates for a special program or desired additions, the mission and vision can help a school decide whether these new additions make sense. Without them, schools try to become all things to all people and end up with frenetic programs. Be clear about what kind of school you are. If parents aren’t interested in what you offer, they will go somewhere else.

2. Faculty and staff who act with integrity. The adults in a school environment should be models for the students. It’s as simple as that.

3. Involved parents. There is such a thing as parents who are too involved. However, I have also seen the other extreme where a school has too little energy because of the lack of parental involvement. Parents are needed to help in classrooms, plan science fairs, bring in speakers, and create community events like the pancake breakfast. In this tough economic time, parents are also essential for raising money to bring programs to the school.

4. Respect for students. OK, doesn’t this seem obvious in a school? Recently a first grade boy asked the principal of his school for some new balls to use at recess. The balls were promised. Two weeks later the little boy still skipped to school each day, eager to see the new balls but they had yet to arrive. Adults who work in schools must always remember that they are creating an environment for little people. Things that may not matter much to us mean a lot to them. A gentle tone of voice, promises kept, a celebration of student work on the walls, all of these things mean a lot to a young child. They want to be proud of their school. They want to feel like they belong. They want to feel like they matter.

5. Teachers who are learners. Colleagues who want to learn from each other. I swim on an adult swim team. I am quite good at all the strokes but my backstroke has never been fast. I recently took a swim lesson to improve my technique. It was so hard for me to do all the things the coach was asking me to do. It was a great experience as a teacher, however, to be in that position again and realize how it feel to my students day after day as they try to do things that are challenging for them. In addition to empathy for our students’ experiences, teaching is a profession that is always changing. Teachers must continue learning to do their best to meet the needs of their students.

6. High expectations for students. Jaime Escalante and Erin Gruwell have proven that if we hold high expectations for students, they can do more than we have dreamed. Maintaining low expectations only ensures that our students achieve at a low level. Even high test scores do not mean that we can now sit back and relax. There is so much more to learn than those items that can be tested. We must expect that each student will move forward on their educational journey every day and we must create the conditions for that to happen.

7. Small enough class sizes that each teacher can truly know their students. A teacher cannot teach students whom they do not know. They need to know what their students already know about a topic under discussion. They need to know their students’ motivations for learning. They need to know a bit about what their students do outside of school. They will bring all this information to bear as they design the most effective lessons for these students. Without this information, the teaching will be flat and less effective.

8. Curriculum based on essential questions. If you haven’t yet read the work of Grant Wiggins and Jay McTighe, do so. In their book, Understanding by Design, they lay out the simple, yet often ignored idea that teachers should be clear what they want their students to learn and work towards that end. They state that we cannot teach every fact or detail so we must teach larger enduring understandings which students can them use as a framework for understanding new ideas.


9. Creativity. In A Whole New Mind, Daniel Pink advocates that we emphasize creativity in our classrooms. In the near future, jobs such as computer programming will be shipped overseas. What will be needed are people who can solve problems, work well with other people, and design new products and processes. We need to start teaching our students these skills when they are young. Everyone can fill in the blanks on a worksheet. Learning to use our creativity to solve problems takes more practice.

10. Differentiation. The best classrooms are those in which teachers are able to differentiate to meet the needs of different students all within the same room. It takes experience to do this. Without it, a group of students is always left out. This group is often the gifted students.

11. Something extra. Every school should offer something extra to its students. It could be a focus on science or a second language or a large arts program. It could be a focus on learning about the world or a focus on social and emotional learning. These things do not necessarily cost a lot of extra money but they do make the families feel like there is something special about their school. It helps families feel like there is a reason to be at that school rather than the school down the street.

12. Opportunities for inspiration. Authors who visit and share about their work. Conservationists who talk about their work with orangutans. Artists who show us how they create their paintings. A book arts class led by someone from the San Francisco Center for the book. A field trip to help at a shelter. All of these out-of-the-ordinary events feed the mind of a young child and open them up to possibilities. Last year my class was able to hear a conservationist speak. This inspired a group to have a bake sale to raise money for the orangutans. They decided this all on their own and with a little adult guidance, were able to pull it all off. We never know how these “extras” will resonate with the students. They might be the seed that blooms into something great later on.

13. Space. Children need lots of room to run and play. State regulations require a certain amount of outdoor space for children to play. School-imposed rules about the space, however, often leave children with little else to do than sit quietly. In addition to needing space to unleash one’s wiggles, children also need natural spaces. In Last Child in the Woods, Richard Love tells us about how children have lost their connection to nature and it is actually leading to increased levels of ADHD and depression. One school in Palo Alto has a whole garden and a farm. They are growing vegetables and welcoming bees into their hive. They have two goats, chickens, two sheep, and a duck. And yes, the rest of the playground is a blacktop playground but a corner of it has been cut out for the farm. At that school there is lots of room to connect with nature and lots of room for wiggling.

Training the Teachers

This month the principals of the seven schools in the San Bruno Park School District were all offered an opportunity to have training for their teachers in meeting the needs of gifted students. The training would be funded through a grant so would come at no cost to the schools. Not one principal jumped at the chance.

The same offer was going to be made to the principals in the Burlingame School District but no one there responded to letters and e-mails.

A principal of a school near Menlo Park attended a meeting with the parent of a highly gifted child. The principal told the parent that the teacher had direct orders from him not to modify the curriculum one bit for the child.



A traditional career path for a principal is a few years in the classroom, then an administrative position, then perhaps a move to a supervisory role (such as assistant superintendent) at the district office. When we consider that 61% of public school teachers have had no training in gifted education, then it comes as no surprise that principals are putting up barriers for gifted students.

It is very clear that teacher education programs need to include classes in gifted education. I have heard so often that we need to train teachers to work with inner city kids, not with “easy” gifted students. What this does not take into account is that there are gifted students in every school. Joy Oatman from Tilman High School in Chicago Illinois states, “People need to know that there are children with talents here. People who live in the inner city in the barrio, or on the reservation need to know that their children are smart. There’s too much raw ability going through the cracks. If a child we might lose had the ability to cure cancer but ends up joining a gang or dealing dope, that’s a double loss to the country.”

Yes, teacher education programs need to change but one area that we can start to change right now is to educate our teachers who are already in the classrooms. The parents of gifted students can do this. All parents of gifted students need to learn to advocate for their children. We need to start teaching the teachers that the needs of gifted students are different. We need to ask for enrichment programs, depth and complexity in the curriculum, and practice with critical thinking skills. We need to go into the classrooms and share our talents with the students and through our modeling, hopefully change the thinking of the teachers, a little bit at a time.

I recently suggested the idea of “compacting” to a teacher. This is a method often used to meet the needs of gifted students. She hadn’t heard of the term so I explained that she would give the post-test to her class before teaching the next unit. If any of her students scored 90% or above on the test, then they already know those skills and should be given the opportunity to move ahead with their learning rather than required to do the work as outlined in the textbook. She followed through with my idea and was surprised to realize that half of her class scored 90% or above on the post test before she even taught the unit. Wow!

What would it be like if we changed our goal from “high test scores for all” to “continuous academic progress for each student”? Many of our students are already performing well on the tests. How can we really say our students are “learning” when they are just doing work that they already know how to do? What could they do if we made sure that each day they learned something?

The San Bruno Park School District spends a huge portion of its budget on special education funding and roughly 1/15 of that amount on education for gifted students. Is it fair that all of these resources are being poured into some populations of students and not others? Let’s make “continuous academic progress for each student” our mantra and work together with our teachers make this a reality for our students. A few years down the line, this may pay off as one of these teachers becomes a principal and searches out programs for the gifted students, as well as the other populations in his/her school.

Underachievement

I recently had the pleasure of attending a few workshops taught by Sally Reis from the University of Connecticut. She was in California for the CAG conference and I went to every session she offered!

My favorite was a session on underachievement. Dr. Reis feels that this is the biggest problem facing gifted students and it is on the increase today because bright kids are not learning to put forth effort. I can only infer that this is due to the unchallenging curriculum offered in schools due to NCLB.

Dr. Reis encounters many gifted college students who have not yet learned to study because they have cruised through school. They have gotten 100% on every test with minimal effort. Due to classrooms aimed at students who are struggling, gifted students have missed out on learning study habits as well as things such as perseverance and resilience. She told the story of a pharmacology student who got an “F” on his first test, decided he was stupid, and was then ready to drop out of school. What he needed instead, however, was to learn how to study to improve his grades. It was the first time he had received less than an “A” and he just didn’t know what to do, attributing his difficulty to his intelligence rather than a missing skill.

I was grinning broadly as Dr. Reis said that activities outside of school teach that effort matters. For years, families of second graders have come to me frustrated because their children are having a hard year. These young children often learned to read early and so kindergarten and first grade, where much of the focus is on reading, came easily to them. It is not until second grade that they realize they really need to work in school and this feels hard to them. At this point I like to recommend piano lessons or sports activities so that students can learn the value of practice. We also need to help parents understand that it is actually a blessing if schoolwork feels hard (within reason). It means that their children are being challenged and are learning life skills in the process.

Dr. Reis’ definition of “achievement” is “the act of accomplishing something of merit by means of effort, skill or perseverance.” If we use this definition, many students still have not yet accomplished anything by second grade. Though they may have gotten good grades, they have not yet accomplished anything.

Some of the most successful students I have known have been gifted students with learning differences. They have had to work hard from the beginning. They are bright but they also know how to study and they know how to put forth effort, often producing great results.

In her research on underachievement Dr. Reis found that “busier adolescents underachieve less” and that “students with regular patterns of work in music or athletics develop positive self-regulation strategies in academics.” She also found that underachievement can be reversed in 70-80% of kids. Two important factors in this reversal are parental interaction and involvement in enrichment opportunities.

So, how can we use this information to guide younger students? Acceptance and rejection letters were sent out by Nueva School last week. I have received many phone calls from parents whose children did not get in. They are at a loss as to how to proceed. With all of California’s budget cuts, GATE programs have been eliminated in many districts in the Bay Area, leaving parents of gifted students with few options. Parents feel a responsibility towards their gifted children but feel frustrated about how to meet their needs in this economy. Listening to Dr. Reis made me realize that there is one big thing we can do. We can involve our children in learning the importance of effort and perseverance. Sign your child up for music lessons or a sports team. No one gets to be an expert piano player by just sitting down at the piano. They need to put in the work to improve. This is an important lesson we can give our children at this time.




For more on this topic read, Work Left Undone: Choices and Compromises of Talented Women by Sally Reis.

How to Advocate for Funding for Public Schools

Recently I feel like I am seeing the widening of the gap between the “haves” and the “have nots.” Last week parents in San Bruno were out on El Camino waving signs and gathering at City Hall to protest cuts to education. I called my friend in Palo Alto to ask if she was going out to protest and she didn’t know what I was talking about. Then I called a friend in Burlingame to see if she was going out. She didn’t know what I was talking about either. I thought since the budget cuts are going to be statewide it would affect all districts equally but apparently it doesn’t.

I was at the California Association for the Gifted Conference in Sacramento this weekend and I purposefully attended two workshops with a woman named Teri Burns. She is the Director of Legislative Advocacy at School Innovations and Advocacy. I wanted to understand what is going on with the California budget and I wanted to understand what the vehicles are for effective action.

Ms. Burns explained that there are statewide cuts of about $225 per student in the new budget but the cuts come from a pot of flexible-spending money. Districts can choose how they want to cover that shortfall. Many districts are in danger of losing their GATE programs. San Bruno wants to lay off teachers, eliminate class size reduction, close our school library, eliminate PE, and eliminate art. It was eye opening to realize that we don’t have to eliminate class size reduction. Yes, we only have so much money to spend but there has not been a statewide declaration that class size reduction will end now. It is our district’s choice.

To be fair, Ms. Burns pointed out that the Governor still owes the schools money from 2005 so for years now the school districts have been cutting back and cutting back and for some, there is nothing left to cut. Some districts like Palo Alto and Burlingame raise a lot of money from their community education funds. I surmise that they must be planning to reroute some of this money to cover the budget shortfall and thus continue with class-size reduction and many of their other programs like PE, music, and library. My friend in Palo Alto was asked to give $700 this year to the community education fund. In San Bruno we were asked to give $100. That leaves the communities with very different amounts of money to use in situations like this.

The schools are owed $11.2 billion dollars in outstanding Prop 98 balances from 2005-2006 to 2008-2009. The Governor would like to continue to ignore the repayment schedule for this money by deferring the first year obligation until 2012-2013. This will actually require a change in existing law and this is where parents and teachers need to come in. We need to let our legislators know that we do not support changing the law. This is the worst economic time for our schools in a long time. Schools have kept up their end of the bargain with the Governor and it is now time for him to pay up.

Ms. Burns closed her session by saying that people involved in education are often fair and accommodating. This, however, is not getting us very far on the political scene. She said we should have “righteous indignation” about the fact that our schools have not been paid. She gave a valuable lesson about how to get one’s voice heard and advocate for our schools. I want to share her information with all parents in the area so that we can effectively let the legislators know how we feel about this subject and hopefully make the voice of education louder so that when it comes down to a vote, schools get their due. Please come to a workshop Thursday, April 8 at 6:30 PM at the Franco Real Estate Group Offices at San Bruno Towne Center, 1230-A El Camino Real, San Bruno. We need to come together and work to close the gap.

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For up to date information on education issues, visit http://www.lao.ca.gov/laoapp/main.aspx Click on “subject areas” and then click on K-12 education. This website is maintained by the legislative analyst’s office and is meant and is meant to help lawmakers stay up to date on current issues. The general public can use it to stay informed as well.