Math Lesson from Phases of the Moon: Selecting Effective Activities and Manipulatives
Zone Proxima Approved
Bob Crelin's Moon Gazers' Wheel is a deep, accurate, profound interactive instructional model that supports embodied learning of the Earth-Moon-Sun system by adults and children. Moon Gazers' Wheel activities and application grows with the maturity and knowledge of the user.
Copyright 2009 by Bob Crelin, used with permission. http://www.BobCrelin.com
Fun + Hands-On ≠ Quality Instruction + Learning
Just because an activity is hands-on and “fun” doesn’t make it a correct or effective learning tool. Hands-on activities often seduce educators, whether dedicated homeschool parents or professionally trained teachers. However, instructional tasks should be evaluated before using them with learners. Unless the educational goal is rote learning, instructional activities that lack deep, meaningful connection to the to-be-learned topic should often be avoided. At best: activities lacking profound alignment to targeted learning content and goals can be a waste of time. At their worst, such activities can produce robust misconceptions, difficult or impossible to correct, that impede future learning. This topic is a central tenant of my professional expertise and outreach. It is important to share with homeschool communities.
An April 2023 Facebook post recommending an activity and manipulative for “phases of the Moon” caught my interest. I have instructional expertise with the topic, and I thought a brief case study might help you consider the importance of accuracy, alignment, and depth when selecting hands-on materials and activities. Using Moon phases as the to-be-learned, I briefly contrast three examples of hands-on activities/tools. As you can tell from the image and caption at the left, Bob Crelin's Moon Gazers' Wheel is an exemplar for quality interactive instructional manipulatives.
Example 1. Moon Phases Layered Wheel
The Moon Phases Layered Wheel offered by “The Art Kit” was recommended on FaceBook to “The Homeschool Quest Free And Affordable Resources & Printables” Community (https://www.facebook.com/groups/homeschoolfreeandaffordable/permalink/3165392587091661/). This Wheel presents an attractive task that may capture learners’ attention as they cut and paste. Cool! But, how much deep learning results from cutting and pasting together the Layered Wheel circles? What are Layered Wheel young people learning? Very little of the targeted learning is embedded into the structure of the activity. A look at The Art Kit Internet sites reveals use of the Layered Wheel format for other topics. So the structure of the Layered Wheel is independent of the targeted learning. According to the website, the FREE printables, subscription, and fee-based materials listed there were developed by a mom with an academic degree in digital media design. Again, she develops materials that are cool to look at! But where is the required behind-the-scenes subject-matter expertise informing activity development? The pedagogical expertise required for successful implementation? Layered Wheel learners practice cutting, may read a few sentences describing the lunar phase, and may sketch the phase. Granted, a learner might use the layered style of this wheel for drill and practice of labels and facts (such as the names, appearance, and description of a lunar phase). Is rote learning a satisfactory goal? Meaningful learning requires more than a mere assortment of independent facts.
Example 2. Bob Crelin’s Moon Gazers’ Wheel
Compare the Moon Phases Layered Wheel to Bob Crelin’s Moon Gazers’ Wheel.
The Earth-Moon-Sun system is conceptually challenging for the Earth-bound viewer. A viable mental model of Moon phases demands an understanding and convergence of multiple perspectives: the sun’s rays shining outward (the consistently lit side of the Moon), the position of the Moon in its monthly journey around the Earth (what portion of the lit surface Earth-located viewers can see), and the daily rotation of the viewer on Earth (time of day we Earth-bound see the lit portion of the Moon: apparent Moon rise, path, and setting). Mr. Crelin’s manipulative has integrated them all with the Earth-child at the core!
Crelin’s Wheel is a deep, profound model that accurately captures all of that complexity within an interactive instructional technology tool. Young users and adults can continue to use the Wheel as they progress from the simple appearance identification to profound, embodied abilities to predict and explain the location and characteristics of lunar phases.
Between 2007 and 2014, NASA and the National Science Foundation funded my research as I invented and developed Metaphorics: a theory for design, development, implementation, and evaluation of instructional technologies that cause and measure deep, meaning-filled learning (see http://math.zoneproxima.com/leadership). At that time, my domain content area was the origin and evolution of planetary bodies, with the Earth’s Moon as the exemplar. And that is when I met Crelin’s Wheel and used it with educators, parents, and young people across the country.
From this vantage, I am concerned that educators and parents develop awareness and the critical skills to evaluate the worth of the tools and tasks they select for their learners.
Bob Crelin captured the issue when he and I spoke in early April 2023. Tasks like this Layered Wheel, he said, “break the chain of understanding.” Bob knows the difference in Moon phase instructional tools and activities.
The Earth-Moon-Sun system is complex. It is the interplay of three different points of view in space and time. The Moon Gazers’ Wheel captures this complexity accurately, interactively, and profoundly. It supports hands-on observation and investigation. All that complexity successfully incorporates into the Moon Gazers’ Wheel. At $6.95, it’s a bargain. I have NO financial or other incentive for introducing you to the Moon Gazers’ Wheel, other than the pleasure in recognizing, using, and sharing a powerful learning tool. You can find Bob Crelin’s Moon Gazers’ Wheel at
Acorn Naturalists (https://www.acornnaturalists.com/moon-gazer.html)
Charlesbridge (https://www.charlesbridge.com/products/faces-of-the-moon-moon-gazers-wheel )
Nature's Workshop Plus! (price discounted to $5.95, https://www.workshopplus.com/products/moon-gazers-wheel?_pos=1&_sid=7c2186485&_ss=r)
In the years since 2009, I personally continue to benefit from embodied insights created through my use of the Moon Gazers’ Wheel. One can meditate on the Sun-Earth-Moon system using this tool.
In fact, today I used the Crelin Wheel to contemplate conditions (temperature, shadows, and light) during each of the Apollo lunar landings (see https://svs.gsfc.nasa.gov/4731). Crelin’s model is so accurate, I can map and comprehend why the conditions of NASA’s selected lunar day (phase) supported the location and timings at the landing sites. The sites and missions were just on the lit side of that current terminator. The terminator is the divide between the lunar light and dark (lunar day and night). I can match my estimates of each landing’s lunar phase with the actual Apollo event using Crelin’s labels marking the days of the lunar cycle.
Did you know that the Moon is the only object in the sky that allows Earth-bound gazers to view the history of the formation and evolution of the Solar System through the features preserved on its surface? Even binoculars will provide delightful views of lunar craters.
As I mentioned above, I learned about Crelin’s Wheel during my CyGaMEs project (http://selene.cet.edu). CyGaMEs was a $2.5 million NASA and National Science Foundation investment to construct a model for effective instructional game design, learning, and embedded assessment. The project content engaged and guided learners to discover and apply fundamental principles behind the origin and development of the Earth’s Moon and the Solar System. At the same time, the environment measured and reported learning. Theoretically, CyGaMEs applied cognitive science analogical reasoning theory to design learning environments that work the way the mind does. I became an expert in that and embodied cognition. And I recognize the astounding value of a $6.95 technology against my project’s cost.
Crelin’s tool can inform a profound, embodied understanding of the phases of the Moon within the Earth-Moon-Sun system. But this requires a user or mentor who understands how to employ the tool and can teach it to themselves or others.
Example 3. Oreo Cookies Phases of the Moon
A substantial number of educators use OREO cookies as the basis of an activity for student modeling of the phases of the Moon. I first searched online for the OREO activity in 2010. Now, as then, a simple search for the OREO cookie phases of the Moon activity displays an alarming number of posts by proud teachers and proud students sharing absolutely incorrect (and physically inexplicable, impossible) models for the Earth-Moon-Sun system. As you can see in Crelin's Wheel, an Earth-based viewer's Moon phase is the portion of the lunar surface visible from the Earth. Teachers and learners modeling without a viable knowledge base, often plot a visible lunar phase on the side of the Moon that faces away from the sun.
Consider the consequences when the learner’s OREO model is incorrect. At best, the OREO activity can be a waste of valuable instructional time. The worse consequence is very concrete and entrenched construction of faulty mental models.
As research shows, when such models are challenged by reality, people unwittingly tend to invent rationale to support them!
Learn a Math Lesson from Phases of the Moon
A faulty mental model for phases of the Moon may not be a deal breaker thwarting a child’s successful future. In contrast--robust, coherent, and viable Mathematics foundations are essential to academic success, lifelong fulfillment, and many careers pathways.
An embodied approach is the core of all Zone Proxima education, including its Math instruction for parents homeschooling pre-primary children.
Learn to be your child’s first math teacher. Zone Proxima Home School Math for parents and their children ages 4.5-6 is now accepting registrations.