Something that a lot of our lesson plans are missing is an understanding of the Van Hiele levels and how it plays into understanding geometry concepts. Often when our older students aren’t grasping what we are teaching, it is simply because they aren’t ready for it.
When they were younger, they didn’t truly understand the first levels of learning. And this is where the Van Hiele Levels come into play. What are the Van Hiele Levels? This theory originated in 1957 by husband and wife team Dina Van Hiele-Geldof and Pierre van Hiele from the Utrecht University in the Netherlands. It helps to describe how students learn geometry. The Van Hiele levels have helped shaped curricula throughout the world, including a large influence in the standards of geometry in the US (source). How do they work? Geometric reasoning starts as soon as we can start processing information and in early schooling. However, depending on the individual, the ages in each stage can vary, especially as they progress through school. Basically the level is dependent on the experiences that each student has, no matter what their age. In Learning Mathematics in Elementary & Middle Schools, Cathcart, et al ”In general, most elementary school students are at levels 0 or 1; some middle school students are at level 2. State standards are written to begin the transition from levels 0 and 1 to level 2 as early as 5th grade “Students identify, describe, draw and classify properties of, and relationships between, plane and solid geometric figures.” (5th grade, standard 2 under Geometry and Measurement) This emphasis on relationships is magnified in the 6th and 7th grade standards.” (source)
Level 0: Visualization
They can recognize shapes by their whole appearance, but not its exact properties. For example, students will think of a shape in terms of what it “looks like.” A rectangle is a door or a triangle is a clown’s hat. And the student may not be able to recognize the shape if it’s rotated to a different standing point. Level 1: Analysis (Description) Students start to learn and identify parts of figures as well as see figures in a class of shapes. They can describe a shape’s properties and are able to understand that shapes in a group have the same properties as well. A student in this level will know that parallelograms have opposite sides that are parallel and will be able to group them accordingly. Level 2: Informal Deduction / Abstraction A student in this level will start to recognize the relationship between properties of shapes. They will also be able to participate and understand informal deductive discussions about the shapes and their different characteristics. Level 3: Formal Deduction At this level students are able of more complex geometric concepts. They can think about properties are related, as well as relationships between axioms, theorems, postulates and definitions. According to John Van Del Walle, students should be able to “work with abstract statements about geometric properties and make conclusions more on logic than intuition.” Level 4: Rigor Finally, students will reach the last level of learning geometric reasoning. Even in the absence of concrete examples, they should be able to compare geometric results in different axiomatic systems. Basically, they will see geometry in the abstract. Mostly, this is the level of college mathematic majors and how they think about geometry. Some students may seamlessly pass through these stages, while others may be get a little left behind. And in the meantime, of course the curriculum keeps going, so without proper attention to the missing links or tutoring they won’t ever be able to full catch up with the lessons. You can dial in your student’s Van Hiele level understanding by including some extra activities in your classroom. Make sure to check out these ideas from NRICH.ORG.
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(and an Intro to the Theory that is a More Accurate Representation of How to Teach)
What’s the problem with learning styles?
You may already be balking at the thought that everything that was taught about learning styles could possibly be wrong. But that’s exactly what the case may be. We turn to cognitive psychologist, Dr. Josh Cuevas, Ph.D of Educational Psychology at the University of North George for some answers and much needed research.
“Five years ago a team of highly respected cognitive psychologists (Pashler, McDaniel, Rohrer, & Bjork, 2009) published what should have been a bombshell in a rational world. They identified the type of evidence necessary to confirm the learning styles hypothesis and then went about searching for studies that could provide that sort of evidence, ultimately finding none. None.”
He later continues that “What Pashler et al. (2009) found was that there was virtually no research at all to support the existence of learning styles or their impact on student learning. A handful of other researchers have recently examined the literature and have come to similar conclusions.” (source).
Why learning styles do not work
One of the main reasons is simple: input overload. Our brains have a certain encoding process. Studies have long determined, with high amounts of certainty, that our brains have two hemispheres, the left which is responsible for language functions and the right that is mostly used for spatial reasoning and visuospatial processing. And that is exactly the part of our cognition where the myth of learning styles lies.
When you tailor a lesson or even a tutoring session to a student who is thought to learn by language better than auditory stimulation, they can get overloaded. Our synapses can only hold so much information. The brain is easily inundated with too much information in one hemisphere and therefore “dumps” important information into temporary or even unnecessary compartments of memory. The area that stores that particular type of input will overflow before it can convert it into long-term memory. Therefore, students retain far less information than they would if the lesson was balanced. That means no matter what way a person learns best, if any one given area of the brain is overstimulated, information is lost. Even if someone thrives on language, when they’re bombarded with words and powerpoints with even more words as text, their language conduits are overloaded. As Dr. Cuevas states, “Think about what it would be like if your spouse were to talk to you about dinner while two kids explained their encounter with the neighbor’s puppy as you’re trying to read this. Not so good for processing.” What is Dual Coding, and Why Is It So Important?
When you can access both hemispheres at the same time while learning there is no overload. It’s a shared experience in the brain.
When we can activate both the right (artsy) hemisphere of the brain and the left (logical) side of the brain at the same time, the two hemispheres communicate across the corpus callosum. Further insight from Dr. Cuevas states, “These results, with all participants performing better in the visual condition and worse in the auditory condition, are exactly what dual coding does predict. When the participants were provided with stimuli that required them to use imagery and activate the visuo-spatial areas of the right cerebral hemisphere, in addition to using the left, they remembered more of what they were exposed to. The pictures they created in their heads to go along with the word helped them to remember more information than those who just focused on the words and the sound of them.” In essence, Dual Coding Theory tells us that graphic input and linguistic input are stored in two completely different areas of the brain. The two sets of information are processed there in short term memory. However, we can increase the chances of that information being retained (converted to long-term memory) by building connections between the two. When we integrate images and text (like in a visual note taking strategy), we help students build a stronger understanding of each concept AND a stronger understanding of the relationships between the terms and ideas! Visual Triggers: Examples of Graphic Input Combined with Text
When I create visual analogies for a doodle note lesson, the goal is to help students understand and retain concepts. I call these "visual memory triggers," because they help students to recall and differentiate between ideas.
The doodle note strategy allows students to interact with their lesson notes using both hemispheres of their brains. Kids can color, draw, doodle, highlight, and embellish the page to get the most of the visual input and interact through embedded student tasks.
For the commutative property, I teach students to remember the word "commute" and place one letter per window of the bus. They remember that was the one for the property that moves variables "back and forth."
For surface area vs. volume, I use a paintbrush and a pool. Students remember that the term "surface area" can be split into two words - one for the handle of the paintbrush and one for the bristles. They keep it straight from volume by knowing that was the one that covers the outside of the shape like painting. For a three-layer reading strategy, the visual analogy is a cake with layers. Students fill in what to do on each re-read of the text, and then they remember that this particular method requires reading in "layers."
There are so many ways to teach and so many ways to learn. And there is no way to know how to teach students across the board. No one thought, construct, or theory should be a defining factor. After learning more and more about the research behind cross-lateral exercises for the brain, I've become convinced that our students need to be activating the right hemisphere of the brain in math class. The proven benefits of communication between the two hemispheres of the brain include focus, learning, memory / retention, and even relaxation. We constantly need to strive for what’s best for our students.
So take a break from trying to meet all learning styles, and offer your students strategies like doodle notes, which fit the research behind visual learning and dual coding theory. I developed the doodle note teaching strategy to encourage left and right brain communication, blend visual and text input, and offer increased focus and retention of the lesson content.
Letting your students learn with this balance of visual and linguistic information will benefit ALL of them in the long run, despite any learning preferences.
Learn more about out visual note taking and Dual Coding Theory, then dive in deeper at doodlenotes.org
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I hope that your students enjoy these, and that you can relax knowing that they are each on their own perfect learning track, not wasting time while you are out! (Even if you aren't absent, you can always use these for a quiet work day!)
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