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Math mastery: Where do your students land?

On the broad spectrum of math mastery, where do your students land? In every math class, there are students who excel and students who fail. Students who join every discussion, and some whose voice is never heard. As teachers, we know our students and how they perform. Sometimes those trends can become definitions, though, and it’s important to step back and take an honest look at our students’ strengths and weaknesses. Where do your students land on the wide spectrum of math mastery?



Level One: Elemental


Students at the Elemental Level are brand new to a topic. They might be learning new vocabulary, like the first time they hear “perimeter”, “theorem”, or “quadratic”. They might be seeing new images, like the first time they see an Absolute Value graph. At this level, they don’t have a lot of prior knowledge to rely on. Students with learning challenges, especially dyscalculia, seem to be stuck in an Elemental Level in most math classes. Help your students write personalized class notes that speak to their needs-- a student with strong visual skills, or a student with dyslexia or dysgraphia, might need more worked examples and less text. A student with Non-Verbal Learning Disorder (NVLD) or dyscalculia might prefer to write out procedures in sentences, almost like they’re talking to their future selves. When you see a student make the same mistake over and over again, have them add a specific reminder to their notes.


Level Two: Beginning


Students at the Beginning Level have prior knowledge, like connecting adding to multiplying, or connecting linear graphs to scatterplots. They don’t feel confident yet and they might not answer questions in class. They work slowly and get a few questions right, but not all. There are many reasons why students get stuck in the Beginning Level. Today’s pacing charts move students through topics so quickly that many kids have trouble building a strong base in new topics. Students with dyscalculia appear to be in the Beginning Level of math topics for far too long, but with the right support, they can progress past this level very quickly. They can also move on to Emergent or Competent levels when they work forward-- in adding, multiplying, or one-step equations-- but remain in the Beginning Level for backward work-- subtracting, dividing, or using multiple inverse operations to solve equations.

Level Three: Emergent


Students at the Emergent Level are answering questions in class. They have a solid foundation in the topic but struggle with extension questions, backward work, or multiple steps. They aren’t ready for a test, but they are on their way. Students with dyscalculia seem to be in the Emergent Level during class or when completing homework, but slip back to the Beginning or Elemental Levels during quizzes and tests. This is because the parietal lobe of the brain dumps math information when people have dyscalculia, which is why having calculators, reference sheets, and notes are important for these students.

Level Four: Competent

Students in the Competent Level are asking questions in class. They have a solid understanding of the topic. They are passing quizzes and tests and feel confident in their work. This is the level we want our students to get to, and it is possible! In fact, it’s probably already happening. Every student is competent in some area. It could be a specific math topic, or it could be in their pattern recognition, or it could be in their unique way of turning math into art or music. This is especially true of students with dyscalculia, who tend to be very linear, and very creative, thinkers. Don’t fall into the trap of believing struggling students are only struggling. Look for their strengths, too.


Level Five: Masterful


Masterful Level students are ahead of the pack and might be a little bored in class. It can be hard to keep their attention and they can be off task. It can be helpful to keep a stack of mandalas, a deck of cards, or logic puzzles on hand to keep these students entertained.


Remember, all students will land on an Elemental Level and a Masterful Level on different topics. When you find a weak student’s Masterful Level, you recognize their strengths and increase their belief in themselves as learners. When you find a strong student’s Elemental Level and help them grow in that area, you help them accept that even great students are new learners sometimes, and that’s ok. Members of the All About Dyscalculia course can grab their free pdf download to reflect on their students.


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