Part 2: The Science Behind the Method
The method of education used in the Knowledge level of education is extremely important, as it sets the physical and emotional tone for the student’s learning – many times, for the rest of their lives.
It is at this foundational level that the use of neuroscience-backed, whole-fact, right brain approach, like that used in the Math Lessons for a Living Education series, is more effective than the left brain, “bits-and-pieces,” traditional approach. According to Dr. Jill Bolte Taylor, neuroanatomist, author, speaker, and national spokesperson for the Harvard Brain Tissue Resource Center, our right hemisphere develops first, while the left hemisphere does not come completely “on-line” for a number of years. Because the brain and its functions are so extremely crucial to the early learning process, I would like to take a few moments to touch on some of the data that research has uncovered in recent years.
Dr. Bolte explained it this way in her TED talk, which she gave in 2008 at the TED Talk Conference: Our right hemisphere functions like a parallel processor. It’s all about this present moment…Right here, right now. The right hemisphere thinks in pictures, learns kinesthetically through movement of our body, and through sensory information, which streams into it simultaneously. The right hemisphere then makes a huge collage of all that sensory input, connecting us to our surroundings and to each other. [This is whole-fact, whole-picture, right-brain thinking.]
Our left hemisphere functions like a serial processor. It thinks linearly and methodically. Our left hemisphere is all about the past, and it’s all about the future. It does not process or relate to the here and now. The left hemisphere is designed to take the collage of all the present moment, which was created by the right hemisphere and pick out details and more details about those details. Then it categorizes and organizes all of that information, associates it with everything we have learned in the past and looks to the future at all of our possibilities. The left hemisphere thinks in language. It’s the hemisphere that creates the internal chatter that connects my internal world to my external world. It’s the part of us that separates us from others.
Because the hemispheres process things differently, they think about different things, care about different things, and have different “personalities.” They do communicate with one another through the corpus callosum, which is made up of some three hundred million axonal fibers (which are actually electrical pulses, not physical fibers), but other than that the two hemispheres are completely separate. [TED Talk Conference – 2008]
In young children, whose right hemispheres are more developed than their left, learning takes the form of playing. As they play and interact with their world, their right hemisphere is busy taking it in, making a huge collage of whole-picture information from the sensory input, and building synapsis, in preparation for the left hemisphere to come completely “on-line” so it can break it down, determine details, and organize and categorize the information for future use. During these formative years, the right hemisphere is busy being in the moment and has little interest in anything else.
Now that we understand a little about how our physical brain hemispheres function, let me move into the interaction between how our physical brain and our emotional mind work together in the learning process.
This is where science and relationship merge. Dr. Jo Boaler is an education author and professor of Mathematics Education at the Stanford Graduate School of Education. In her excellent book, Mathematical Mindsets, she talks about the negative mindset that many people have towards math in particular.
Throughout the first chapter of her book, she “says that the current secular viewpoint of learning has created a severe and crippling dichotomy in the world of education, especially where the teaching and learning of math is concerned. She challenges the practice of approaching students as “math minded” or “non-math minded.” She writes that mindset has far more to do with the ability to learn math than natural “math-ability.” The Bible says it this way in Proverbs 23:7: For as [a person] thinks in his heart, so is he.
This is a clear example of how the “academic and non-academic” categorizing of students is mostly a consequence of not understanding how the human brain actually works. Because of the focus on standardized test scores, many teachers and students approach the study of mathematics with fear and trembling.
These negative messages come from the left hemisphere that is taking in and categorizing the (faulty and negative) information from the right hemisphere and building a monumental file of “I’m bad at math” brain chatter. We are literally training our minds and our children’s minds to be bad at something we can all learn to do.
Dr. Boaler says this: Students also receive and absorb many indirect messages about mathematics through many aspects of math teaching, such as the questions they work on in math class, the feedback they get, the ways they are grouped, and other aspects of mathematics teaching… This is the bad-brain math approach that is so prevalent in our culture’s educational model, and science does not support it.
In the last ten to fifteen years, research scientists have used technology to access the inside story of what happens in a brain during the learning process. Their biggest discovery…the plasticity of the brain. Dr. Boaler says this about it: It used to be believed that the brains people were born with could not really be changed, but this idea has now been resoundingly disproved. Study after study has shown the incredible capacity of brains to grow and change within a really short period…When we learn a new idea, an electric current fires in our brains, crossing synapses and connecting different areas of the brain. These are the sensory information collages made by the right hemisphere and broken down into details, categorized, and filed by the left hemisphere.
Remember, the right hemisphere is the part of the brain that brings in the world around us. When that information speaks truth to the child, approaching them like the whole person that they are, it is taken by the left hemisphere and categorized and filed, eventually becoming positive “brain chatter.” The Apostle Paul, under the influence of the Holy Spirit put it this way in Romans 12:2, “Do not conform to the pattern of this world, but be transformed by the renewing of your mind. Then you will be able to test and approve what God’s will is—His good, pleasing and perfect will.” [NLT]
Let us move into the Comprehension Level, the next level in the Cognitive Realm. The Comprehension Level is the largest level of learning because it includes both comprehension and application. In this level, students begin to think through given information in “concrete” terms related to immediate context.” (page 48, para 1)
This is the first step in the left hemisphere’s work, as it begins to sort through and draw details out of the right-brain collage of information. The more natural, fluid, full-picture, and whole-fact the information was taken in by the right hemisphere, the clearer, more detailed, and complete the information collage is and the easier it is for the left-hemisphere to do its job of categorizing, organizing, and making connections.
An example of this level of learning would be the student putting a concept in their own words, beginning to interpret observations and draw personal conclusions. This level is crucial to all other subsequent levels of learning as it is the personalizing and connecting-to level.
In the Math Lessons for a Living Education curriculum series, this level of learning is engaged through the oral narration process and the show-and-tell presentations.
Oral narration requires the student’s left hemisphere to pick out details, organize them and draw conclusions about them. This is why oral narration is so much work for young students. Understanding and comprehending requires complete engagement at the brain level. Because the MLFLE student has had concepts and information presented to them in a whole-fact, in-context, complete manner, the left hemisphere has a complete picture with which to work.
The next level of the Cognitive Learning domain is Application. This level works hand in hand with the previous level, Comprehension, yet follows it in sequence. Where Comprehension is like recognizing someone you have met in their usual context, Application is like recognizing them out of context. Application is the ability to correctly use a principle or concept in a new situation that is not related or rehearsed.
After the principle or concept is taken in through the right hemisphere and made into a collage (or part of a collage), then sent over to the left hemisphere, where it is interacted with and some of the main details organized and personally connected with in its original context, the left hemisphere takes it and compares it to past or possible future contexts to see if it fits anywhere. This is quite a fascinating process, and one that is still being studied, but we do know that as the brain studies the information, connects to it, categorizes and files it, the elements and connections of the concepts becomes more permanent in the student’s memory.
In Dr. Newton’s model, this process is indicated by the circular arrow which spirals down deeper and deeper towards the heart. The knowledge is making its way towards wisdom. Dr. Newton explains, In this way it is easy to see how learning could move from a simple cognitive domain to ‘doing.’ As we will see in every category, the deeper we get in the journey towards the heart, the more integrated learning becomes. [Pg 48, 2nd para] The more integrated learning becomes, the more divergent* the student’s thinking capability becomes.
*divergent refers to the ability to think creatively – this takes acute critical thinking and creative thinking working together.
In Math Lessons for a Living Education, application is seen throughout the course in various ways. Because the curriculum is strong in the previous (yet simultaneous) levels, Knowledge and Comprehension, Application is a natural extension of the process. For example: the child is taught the concept through stories which show the whole concept/principle in context. Next, the child is walked through the steps of learning how to do the concept themselves in a hands-on fashion, which reinforces the story – the Knowledge taking-in stage completed by the right hemisphere.
After some work with these concepts through continued hands-on and simple written practice, the student moves into the Comprehension level by working out an oral narration presentation, still using their hands-on element of manipulatives. Next, the student is encouraged to move what they are learning into a more unrehearsed setting, Application. The MLFLE student does this by doing a project that takes the content/principles they have been learning in their story and book-work and moving it into another area of life in the form of sewing, cooking, measuring, and creating something tangible and unrehearsed. These activities set the stage and help the child prepare for using these concepts in real life in ways that will become a permanent part of who they are. The knowledge has made yet another spiral down through the levels of mind, emotions, and will, reaching deeper into the heart of the student.
Next in the Cognitive learning journey are the Analysis, Synthesis, and Evaluation levels. Like the levels before them, these three work together almost inseparably. They are slightly different than the Knowledge (take-in) level, and the Comprehension and Application levels; while those three levels are actual steps taken in the learning process, the Analysis, Synthesis, and Evaluation levels are more like tools used once the student gains the ability to comprehend and apply. We can think of them as tools of trade for the deeper levels of learning. It is through using them that the student moves the knowledge down into their hearts where it becomes wisdom. These three tools are left hemisphere functions.
Analysis is the constant studying and identifying parts and connections in order to organize the materials being taken into the mind. Analysis focuses on the way the parts of the material are broken down and also on the organization of their relationships. Initial Analysis involves three subcategories: Identifying the various elements in the learning experience, identifying the relationships, interactions, and connections between the elements [think cause and effect type analysis] and recognizing the organizing principles, which hold the parts together. Analysis is crucial in discovering major principles and why they work. There is a final organizing identification that “completes the picture through action.”
In the Math Lessons for a Living Education curriculum series, the use of analysis is seen in the way the student is encouraged to study the relationship between concepts presented. For example, multiplication and division are taught almost simultaneously because these concepts are closely related to one another. By taking in the information in a whole-concept, in-context right hemisphere fashion, the student is seeing the whole picture together: multiplication and division are not to abstract, distantly related concept-cousins; they are mirror-image twins that are always together no matter where you find them. This approach to teaching math concepts naturally walks the student through each of the tree subcategories of the Analysis level.
It is important to note that each individual human processes through the levels of
learning at their own God-made speed. It is absolutely imperative that students be encouraged to work through the analysis stage (and all of the other stages) at their speed, not a speed dictated by an arbitrary grade level or standardized test. This is where the principle of Skill Level Math verses Grade Level Math is most crucial, as it is in learning to use these tools that will enable all of us to rework our thinking concerning the learning process.
Unfortunately, I have witnessed many children being convinced that they are “bad at math” because their teacher or curriculum demands that they move too quickly (or slowly) through these levels of thinking and learning. This is how we need to facilitate an education that fits the child.
Next in our journey towards the heart and the ultimate goal of wisdom, are the Synthesis and Evaluation “levels.” Again, these are more like tools than levels, and they are used, in many ways, simultaneously with the Analysis. Synthesis is really the opposite function of Analysis. Where Analysis studies the parts of the whole and the relationship between them and whole, Synthesis focuses on the putting together of elements and parts so as to form a whole. This is where the student applies a unique element of creativity in pulling together what has been learned in the production the original application of the facts, concepts, principles, and understanding learned up to that point. Like Application, Synthesis is a left hemisphere function.
This stage could be considered a culmination of learning up to this point and it involves sequencing what has been learned in a unique way to reflect the nature of both the subject material and the learner. On Dr. Newton’s model, this stage is the next to last spiraling circle indicating the journey of knowledge down to the heart of the student.
Evaluation is the last circle in the journey to the heart of the student. This level is also where the Cognitive, Emotional, and Dispositional domains meet on Dr. Newton’s model. Evaluation is the making of judgments about the value, for some purpose, of ideas, solutions, methods, materials, etc.
By this stage, the informational knowledge that the right hemisphere took in to create a big, colorful collage, has been broken down into multiple levels of detail, each studied closely, connections made, organized and reorganized, filed and added onto, made into new and different material, applied to situations rehearsed and non-rehearsed, and sifted through to find the most important part to be turned into wisdom…knowledge lived. Thus is the journey of knowledge to wisdom.
Go to the next page to read Part 3: The Elements of the Charlotte Mason Method Used in the Method