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.

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.

Differentiation

When I first started teaching, it was all I could do to figure out what systems I wanted to use. Was I going to give homework every night or give one large packet on Monday and have it due Friday? How would we figure out who would get to take out the two playground balls each recess? How would I communicate with parents in my class, many of whom didn’t speak English?

I was overwhelmed with the possibilities and drove my students a bit batty with my constantly changing systems. I had been trained to look at each child as an individual and meet his/her specific needs. Yeah, it all sounded good but in the moment I was not thinking about how to meet the needs of each child in my classroom. A colleague told me it takes three years to get settled and I found that to be just about right.

By the end of my first three years, I was feeling settled within my classroom. I had systems that worked for my students, their parents and me. I was feeling confident and I was repeating some lessons, doing them better each time. It was then that I began to think about differentiation and how to meet the multiple and varied needs of all those little people sitting in front of me.

Whenever you feel ready to start differentiating in your classroom, I highly recommend reading, Strategies for Differentiating Instruction by Julia L. Roberts and Tracy F. Inman.

The first few chapters of this book provide a great explanation for why teachers should differentiate. The authors draw examples from every day life and make a compelling case for changing our teaching to meet each child’s needs.

The authors then offer some practical ways to differentiate. I particularly enjoyed their chapter on Venn Diagrams. This is a tool that most teachers already use. A little bit of tweaking can make it a tool that can challenge higher level thinkers while still including students who are at the beginning stages of learning a concept. All students can be involved in studying the same subject, but in a different way. Students can then learn from each other as they share their work. All students will be engaged in the work they are doing yet all will still feel part of the larger lesson.

I was also very glad to see their chapter on Bloom’s Taxonomy. Since national testing currently focuses on the first few levels of the taxonomy, teachers are often unfamiliar with how to design experiences that address the higher levels. Roberts and Inman offer many examples that will help teachers become more familiar with this tool.

Using Venn Diagrams is another way to engage all students in the same topic yet provide more depth and complexity for those who are ready for it. While employing differentiation, I have always worked to keep my students engaged in the same topics at the same time. I think it builds community because students have common ground to share. I recently visited a Montessori classroom and I asked about this sense of community. Since the model of Montessori is that all students work at their own pace, often on different topics, I wondered how the teachers built community. The teacher I spoke with said that even in their classrooms, the students come together a few times a day to engage in a group activity or experience. This builds community, trust, and energy in the classroom.

Of course, when one has different students engaging in different activities, the real question is assessment. How does one compare apples to oranges? Roberts and Inman see rubrics as the solution and they provide many samples in their book for teachers to use. One school I was at used narrative reports in place of report cards. This allowed the teacher to write about each child’s work, their strengths, and their challenges without needing to compare apples to apples. It is time consuming but maybe if we are differentiating to the fullest, then the students’ report cards should be differentiated as well.

Throughout the book the Roberts and Inman repeat that a teacher’s expectations should be continuous progress for all students. I would add “in all areas” to that as well. As a teacher I have always felt that “continuous progress” is a goal for me too. This book provides many ideas that will help teachers in their journey to continually improve their practice.