At a glance, it seems like a school should be able to take all of the brightest kids, stick them in a class together, and simply move through the math curriculum at a faster pace. But, that doesn’t really work. To truly support the needs of our gifted and talented students within mathematics, we need to ensure that they’re starting at the right place, differentiating for the individual needs of the student, and providing an age-appropriate curriculum and learning environment.
Placement tests allow us to determine whether the students are ready for the starting point of a curriculum; we can use a placement test to determine which students have the necessary skills and knowledge to be able to learn the higher level material. Because many accelerated math programs actually skip part-of or all-of a grade-level of math, this means that students must often demonstrate math knowledge beyond what they’ve been taught in school. Most of these assessments only test to see whether the students know the pre-requisite knowledge; they don’t test to see if the child knows more. As a result, joining the standard accelerated math class may still be inappropriate for some students who are ready to start at an even higher level. One pitfall of this methodology is that gifted students that are not necessarily high achieving may lose out on these opportunities, necessitating a separate program for high ability students that aren’t ready for a higher starting point but do have the ability to move more quickly through the material and to look more deeply at concepts.
Routine pre- and post- assessments allow us to determine when students are ready to move on throughout the year; differentiation applies within the gifted and talented and accelerated math classroom too. Not every gifted and talented student is going to be ready to move through the curriculum at the same pace all the time. Some students will find certain topics easier while others will find them harder. Even within an accelerated math classroom, there’s still variability in the pace at which students learn, and an individual student’s pace may not remain the same for every new topic. This means that some students may need more (and different) activities to master a new topic, but they may be able to fly through others.
Kids that are very bright – the kids in the accelerated math and GATE programs have an insatiable appetite for challenge. If you give them something rote – more practice problems of the same thing to keep them occupied – they’re still going to be bored. It’s also very common to differentiate curriculum by simply giving gifted students bigger numbers, but it’s still more of the same. That isn’t motivating, and it isn’t challenging.
Gifted students need activities that provide them with the opportunity to discover something new, to satisfy their natural curiosity. Games, puzzles, and manipulatives allow for discovery and exploration, but as students move up each grade level, there tends to be fewer and fewer hands-on activities, games, and puzzles. Instead, this is often replaced by more worksheets and textbook pages. Because accelerated math students are studying higher levels of math at a younger age, they actually need a different curriculum to teach the same standards – one that recognizes that they’re still kids. I’ve designed puzzles, games, and other activities for this purpose.
Self-checking puzzles help kids see a process, to understand why each step of the process works, and to identify the connections between different concepts. The pieces of the puzzles walk them through a particular concept in the order that they’re presented, and when the puzzle is put together, they can literally see the whole picture.
Not only do the students love the self-checking puzzles, but the puzzles allow me to easily differentiate for each individual student’s needs. Although all of my students have qualified for our programs and have demonstrated a readiness for accelerated math, they’re each going to find certain concepts easier and other concepts harder. This means that some students are ready to move forward before their classmates, and some need to break down the concept into smaller pieces. I evaluate each student’s progress weekly based on five to ten “micro” standards or skills for each standard. I use this to determine what activities to give each individual student the following week. Each student can work on different puzzles, customized to their unique learning needs. They’re also easy to print and use at home if a child needs to work on a certain topic or wants to explore something new.
Cryptograms provide students with additional practice. Students are excited to reveal the hidden message. The hidden message provides instant feedback, acting as a self-checking mechanism, but it also doesn’t reveal any of the answers as some self-checking activities do. These are print-and-go activities that parents can send to school with their child as a push-in service when the school is unable to accommodate their child’s math needs. Teachers can use them as in class activities, stations, homework, or individualized assignments.
Not only do gifted students need a curriculum that moves faster, but the curriculum must also look at concepts more deeply. To do this, they need to have a higher level of fluency in the language of mathematics. They need to be able to translate the world around them into the language of math. There are very few people in the world that can do this. It’s this small population that can use their knowledge of mathematics to discover something new – to solve real world problems – and to be able to communicate those solutions with the rest of the population. Our gifted and talented students have this potential, but they need the relevant knowledge and skills, and they also need to have a very high level of fluency in the language of mathematics. I’ve designed my program with the understanding that our selection process is identifying those kids with the potential to be that person in the future.
The base of any language is vocabulary; math is no different. To communicate in the same language, we need to agree on the meaning of the terms. I begin teaching students the language of mathematics as early as second grade. I teach them to translate word problems into the language of mathematics – to rewrite the story as an equation. I build from there, providing students with vocabulary lessons that pair with the core math lessons. I’ve created math word lists and puzzles for each math standard that encourage students to think critically about math terminology. These are easy for parents to print out for kids to do at home or during school. They’re also easy for a teacher to use in the classroom to add a layer of complexity for gifted students.
I also introduce the concept of proofs in the elementary grades. Using their math vocabulary, students can explain exactly why they know their answer is correct. They’re able to check their own work, debate the merits of their work with their classmates, and use this knowledge to learn subsequent lessons.
By Algebra, I introduce the two-column proof, something that most people only associate with Geometry. If they know the terminology well enough, then they can explain why and how their math works. If they can’t, they know that they’re missing something.
By providing gifted math students with a challenging and engaging curriculum that caters to their unique needs, they’re more motivated and engaged, ready for the challenges of higher level mathematics, and equipped with the skills that they need to apply their math skills in unique ways.