Top-Down Versus Bottom-Up Learners

I am probably giving away my age here (I now understand why my mother told everyone she was only 29 for years), but when I was in school, there were simply good students and poor students. If you were lucky enough to be a good student, it meant that you were disciplined, respectful, and innately smart. If you were unfortunate enough to be a poor student, it meant that you were lazy, inattentive, and destined to a life of failure. Students listened to lectures and completed worksheets, and everyone was expected to do well in this setting. If you didn’t, it was your fault for not trying hard enough.                                                 Oli

While the concept of different learning styles was probably known among educators way back then, the use of alternate teaching techniques to accommodate these different learning modalities was rarely employed. I am willing to bet that many of those supposedly poor students were actually trying extremely hard to do well but couldn’t succeed because their individual learning styles did not correspond to the teaching methods used in traditional schools.

Both of my children had a couple of experienced and extremely talented, primary school teachers who first introduced me to the idea of different learning styles. I used to volunteer frequently at my boys’ school, and I had noticed that some of the kids responded quite differently to different projects. They would excel at a coloring exercise but struggle immensely with a listening activity. I was soon researching all I could about visual, auditory, and kinesthetic learners and started to understand why these students were performing so disparately on different assignments.

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When I began homeschooling my boys, I thought I was armed and ready with this newly acquired knowledge coupled with my suspicions of which type of learning style each of my children possessed. Has anyone else noticed, that as soon as you think you have this education thing all figured out, some new issue emerges, and you feel like you’re back at square one?

Well, it turns out there is a lot more to learning styles than just visual, auditory, and kinesthetic. There are numerous sub-types of each of these categories and any individual learner may possess a unique combination of any or all of the various styles. These personal learning preferences represent difficult enough issues to address when teaching, but there is also a fundamental, overriding framework through which students learn new concepts that must also be recognized to effectively instruct them. This framework is referred to as top-down and bottom-up learning.                                                           yves_guillou_double_arrow

Bottom-up learners tend to learn things best in small sequential steps that gradually build upon each other until you have a complete concept. These learners are comfortable mastering each incremental step without necessarily being aware of what the final product or process will be. A bottom-up learner will learn to nail two boards together, then learn how to connect groups of boards, then learn how to cut a hole in the boards, etc until they have built an entire house complete with windows, doors, and chimneys. They do not NEED to know beforehand that the skills they are learning will eventually be used to complete a home. I am unequivocally a bottom-up learner.

Top-down learners tend to learn things best when they can visualize the final concept or product and are then allowed to deduce the steps used to get to that final destination. These learners absolutely NEED to know what the final idea is before they learn any of the steps used to achieve that concept. A top-down learner must see the completed house before they can master nailing two boards together, then connecting groups of boards, and then cutting holes in the boards. Both Aristotle and Archimedes are one-hundred percent top-down learners.

“Great,” you say! You’re a homeschooling mom who knows that Aristotle is a top-down, auditory learner and that Archimedes is a top-down, visual-spatial (unbelievably visual-spatial), kinesthetic learner. You’re all set! You can now choose appropriate curriculum, experiments, and projects that will complement their learning styles. You can now demonstrate or explain complex concepts in terms they will easily comprehend. Well, sort of. The problem lies in the fact that I am a bottom-up learner, and I have an incredibly difficult time understanding the boys’ top-down perspective.

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Intellectually, I understand the concept of top-down learning, but when it comes to actually presenting a new topic in a true top-down fashion and structuring the delivery of information in a way that works for my sons, I am often completely at a loss as to how to do this effectively. I simply don’t see things in a top-down way.

My husband is also a top-down learner and tells me, as do the boys, that he just “sees” the answer to problems. In fact, he often cannot explain the steps one would take to find the answer; he just knows it.

Aristotle and Archimedes also have an extremely difficult time showing their work in part because they also just see the answer or because they have developed their own way of solving the problem. Aristotle has frequently amazed me with his explanations of how he adds two numbers together; he divides the first number by 3 and multiplies the answer by 10 and then subtracts 24 and then adds 13 or some other long set of calculations. I kid you not that these strange and, in my mind, excessively difficult and seemingly unnecessary, extra manipulations always gave him the correct answer to all his practice math problems. He had deduced his own method of solving equations because he “saw” that was the way to do it.

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Although this is an ongoing area of frustration for me, I have found that providing an overview of a topic and an actual real-world example of the concept has been helpful for my boys. I have also learned to trust that whatever technique they have developed to address problems is usually very effective, accurate, and reliable. I am doubtful that I will ever be able to truly comprehend how Aristotle and Archimedes process information, but it is something that I work on every single day in the hopes that I can teach them in a way that is understandable and workable for them!

It’s Okay for Homeschoolers to Ask for Outside Help

Aristotle despises math! Okay, the original Aristotle probably loved math, but my Aristotle quite literally hates it; a fact that has perplexed me from his earliest interactions with the topic. Math always struck me as a very logical, structured, rule-oriented subject, something that should appeal to my very rule-abiding, structure-loving child. While it is true that higher level mathematics can get quite abstract and confusing, basic arithmetic is very concrete and obeys a relatively small set of rules. It also involves a certain degree of rote memorization. Following rules and possessing a computer-like ability to memorize and organize information are two of Aristotle’s many remarkable skills. If he can remember the name, type, and move set of every Pokemon ever created, math should be a piece of cake, right? Unfortunately, not for Aristotle.

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I vividly remember sitting in the psychologist’s office watching Aristotle work through some pattern recognition tests when he was about four years old. I was a proud mother reveling in her child’s ability to accurately predict each pattern, and I was completely shocked and devastated when the psychologist revealed that, though Aristotle’s answers were correct, the speed with which he recognized the patterns was far, far below the average of typical children his age. Furthermore, his grasp of abstract concepts was virtually none existent.

Aristotle was fortunate enough to spend the first few years of his education in a very supportive and understanding public elementary school. He also enjoyed the attentions of some very experienced and talented teachers who were quick to identify some of his learning challenges with math and help me help him with his assignments. One thing we all noticed was that Aristotle could not complete addition and subtraction problems without assigning some sort of description to the numbers. The equation 2+3=? was too abstract for him to grasp, but if we said, “2 cats plus 3 cats equals how many cats,” he was able to complete the calculation. A number on its own meant nothing to him; it had to be attached to a physical object for him to understand it. In addition, his processing speed for math problems was abysmally slow.

Like the Aristotle of old and like many special needs students of today, Aristotle is very intelligent and has subsequently developed many of his own strategies to conquer the math tasks expected of him. Most of these strategies are something of a mystery to him (and utterly incomprehensible to me), but he is somehow able to correctly solve many math equations using his own unique numerical manipulations. He is able to perform all the basic math operations, he can execute the calculations required for many algebraic problems, and he can usually pass a math exam with excellent scores, but he has absolutely no understanding of what he is doing and cannot apply the concepts he has learned to a new, slightly different problem or an actual real-life situation.primary-kbruch-exercise-common

I spent countless hours trying to understand Aristotle’s learning styles (he’s a top-down, auditory type of student) and trying to figure out what specifically bothered him about this subject all in an effort to either purchase or customize an appropriate math curriculum for him, but it was to no avail. We struggled through math lessons using a myriad of very good programs, and we managed to slowly move forward, but never to the point of clear understanding or appropriate application of the various math concepts. The one bright spot in our math studies was Aristotle’s increasing ability to verbally express his confusion with mathematical ideas as he got older. He often stated that he simply could not trust numbers. He fundamentally couldn’t accept that two plus two is always four and instinctively felt that there was some strange magic controlling the value of the numbers. Clearly, not an easy obstacle to overcome.

We live in an area with relatively few homeschoolers and while there are some popular, extra-curricular, tutoring programs reasonably close by, I was hesitant to try them due to their high cost and their use of the same, standard, teaching techniques that had failed us previously. So, we were left to just keep experimenting with and adjusting our methods as best we could. It wasn’t until Aristotle took an algebra class at the local community college that a little spark of understanding was ignited, and it was all due to the efforts of a wonderful professor who knew how to speak math in Aristotle’s language.profesor_1

This professor understood all the ways students misunderstand math and was skilled in explaining things in a way struggling students could comprehend. Suddenly, concepts that had been sources of constant frustration were now manageable. Relationships between various, abstract, math concepts were now understandable to Aristotle. He started to gain some confidence in his ability to tackle increasingly complex equations and even faced advanced algebra with minimal trepidation. Mind you, he still personifies mathematics and thinks it’s a sneaky, evil construct bent on global annihilation, but he has mastered it enough to use it in his daily life and complete the math courses required to eventually transfer to a four-year college.

So, what was the lesson for this homeschooling mom in this long, complicated journey? The lesson was simply that sometimes homeschooling parents and students need outside help, and it’s okay to ask for said assistance. When we left the brick and mortar school behind, I incorrectly assumed that all traditional sources of educational support were no longer available to me. I believed that it was my sole responsibility to provide the perfect education to my children, and it was up to me to figure out how to do it successfully. Sure, I could search the internet, the library, or the words of other parents for tips and techniques, but relying on anyone else for day to day instruction seemed wrong and out of reach. In hindsight, it probably would have been much wiser to seek the help of a professional teacher or trained tutor early on to assist Aristotle than to try to teach myself how to work with his challenges. In the end, it has all worked out, but I have learned that I can’t always do it all and that sometimes getting help from others is the best way to provide that perfect education I so want for my children.

Spelling with Dyslexia and CAPD

Archimedes was a brave man. After all, he dunked the king’s crown in his bathtub, designed weapons to keep the vast roman army at bay, and reputedly ordered said army to pause prior to executing him so he could complete his final set of calculations. My Archimedes is also brave in his own small way. Each day he must face numerous tasks that most would consider easy but which are, in fact, extremely difficult given his numerous disabilities. He generally approaches each of these obstacles with a smile and quiet determination. There is, however, one thing that will strike terror into his heart like no other and crush any sense of achievement and fortitude he has managed to muster that day. No, not monsters under the bed, not broccoli, not politics, not even a trip to the dentist (though that is a close second). No, that unspeakable thing is – spelling.

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Spelling has been his archnemesis since early childhood, but there are several good reasons for this. My Archimedes has central auditory processing disorder and dyslexia. He also possesses a very, very strong visual-spatial learning style. Most people are reasonably familiar with dyslexia, a disorder in which the orientation of letters and numbers in words and equations appears inverted and transposed. Central auditory processing disorder or CAPD is a less well-known but equally frustrating condition. In CAPD the ears are fully capable of detecting all the volumes and pitches of normal hearing, but the brain routinely and inconsistently misinterprets the information it receives. My Archimedes cannot reliably hear all the sounds in the words we speak and is often confused as to what people are saying. You may declare, “The cat is soft and furry,” but he hears, “Ton cap is often hurry.”

Needless to say, sounding out words, recognizing common diagraphs, and spelling phonetically are incredibly difficult for anyone with this combination of disorders, and, unfortunately, most spelling curricula rely heavily on the aforementioned techniques. While there are a number of curriculums that focus on helping students with either dyslexia or CAPD, there are virtually none that address both issues simultaneously and effectively. Thus, we do what homeschoolers do and adapt existing programs to better fit our needs or even resort to creating entirely new ones. This method of customizing study materials has been incredibly successful in many of the subjects we have investigated, but I must admit, we are still struggling a lot with this spelling monster. I found great comfort in the list of famous authors (Agatha Christie), world leaders (Winston Churchill), businessmen (Charles Schwab), and entertainers (Walt Disney), just to name a few, that site director Carolyn K. identified in her article “Twice Exceptional = Exceptional Squared!” at Hoagie’s Gifted Education Page. There is hope for the spelling-challenged!

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One of the programs we tried early on was All About Spelling, a very comprehensive program designed to address spelling visually, auditorily, and kinesthetically. It is a beautifully composed, very thorough, and user-friendly program in my humble opinion. It’s use of color-coded spelling tiles was especially appealing to my hands-on, visual Archimedes, but because he has disabilities in two of the three pathways this curriculum utilizes, we weren’t as successful as we had hoped. Remember, it is extremely difficult to associate a letter or letter combination with a sound if the sound you hear is different each time and the letters change orientation in an inconsistent way – no fault of the program, just a reality of Archimedes’ learning style.

A couple of years ago during a late-night, stress-inducing search for help in this area, I stumbled upon a video presented by Dianne Craft, a veteran special education teacher, who seemed to really understand CAPD, dyslexia, and many other learning challenges. In the video, Ms. Craft demonstrates a technique of drawing a picture which represents the meaning of the word but also reflects the physical shape of the word. It also attaches a simple story to the picture to help give the student a way to remember the details of the drawing and thus the letters of the word. I thought the idea was brilliant, and dutifully began using the process with Archimedes. He liked the technique and initially responded quite well to it, but drawing and coloring are extremely difficult with his neuromuscular difficulties, dysgraphia, and OCD, and the frustration of completing each picture quickly overshadowed any progress he gained in remembering the spelling of the word. I soon learned that having Archimedes do the mental work of determining what image he would choose for the word and then having me do the actual work of drawing it for him to later color worked the best. The only real drawback to this system was that eventually he tired of the process and certain words (in fact, many words) were pretty difficult to depict easily. I recently saw that Ms. Craft has launched a very informative website we and online store, and I am seriously considering purchasing her Brain Integration Therapy book to see if some of her additional techniques might serve to deal with Archimedes’ multiple learning disabilities more effectively. Both Archimedes and Aristotle benefited tremendously from the many integrative therapies employed by their amazing occupational therapists, and I have high hopes that Ms. Craft’s recommendations will have a similar positive impact for us.

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There are times when homeschooling parents have to come up with completely new curriculum on their own. Each parent knows his or her own child’s skills and weaknesses and also knows how that child has responded to each program he or she has tried. I have often had to create my own programs using combinations of techniques and pieces of multiple curricula that I know my children respond to. Sometimes these things work spectacularly. Other times they fail equally spectacularly, but each time I learn a little bit more about how my children process information. And so, I am in the process of creating a spelling program for Archimedes that will play to his strengths and incorporate strategies that seem to work for him. I will be using the Dragon speech recognition software, keyboarding, patterning, and color-coding. When the details are done, and Archimedes and I have tested it out, I will share the method and let you know if it worked or not.

There are many great spelling resources on the market and on the internet, and though most do not exactly fit my Archimedes’ needs, they all have certain qualities that work very well for many students. The key is to identify those effective qualities and then modify the program to fit your individual child’s learning style. Sometimes you’ll have to take those qualities and use them to design something of your own making. This can be a difficult process, and it can be very frustrating to abandon a curriculum you’ve invested in financially and emotionally, but the rewards when your child finally conquers a difficult subject are indescribable. Please, feel free to share your successes and frustrations with the specialized materials you have had to develop for your own children in the comments! I would love to hear about them!

We’re Secular but Are Grateful for Christian Curricula

My husband and I both come from families with one religious parent and one not-so-religious parent. Our families also come from two, very different, fundamental religions. We are both fairly spiritual people, but we do not follow the specific doctrines of any particular religion, and, as such, we have chosen to provide a secular education to our two boys. We believe in teaching Aristotle and Archimedes about the histories, beliefs, and practices of as many of the world’s religions as possible while demonstrating the way to be kind and honorable people who are compassionate, giving, and accepting of all others regardless of their religion, race, or lifestyle.

For anyone just entering the homeschooling world, you will find your search for secular materials and curriculum to be a little daunting. Christian families were among the first to homeschool their children in modern times and have subsequently developed a significant proportion of the homeschool curricula currently available on the market. While it is relatively easy to purchase the student textbooks used in many public schools, it is sometimes extremely difficult to acquire the accompanying teacher’s manual. In addition, these books are targeted for large groups of students and are structured in a manner that frequently wasn’t working well for our children in the first place. The Christian curricula, on the other hand, are often written with a single child as student and a single parent as teacher in mind. Student texts, teacher manuals, and appropriate supplies are consistently packaged together for ease of use in the homeschool environment.

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I have found over the years that there are many really wonderful Christian programs that can easily be adapted to a secular curriculum or which provide excellent opportunities for discussion about religion and its influence on one’s interpretation of data and world events. These curricula are well-written and are easy to implement as they are intended to be used in a home setting with a limited number of students and with supplies that are readily available outside of brick and mortar classrooms.

One of the curricula that stands out for me is Apologia Educational Ministries’ Exploring Creation with Biology course that I used for Aristotle’s study of high school biology. The text is written by Dr. Jay L. Wile who has a very engaging writing style and a definite ability to explain complex concepts in a very down-to-earth way. He expressly states his firm belief in creation and frequently references God in his writing, but he does also work to present the evolutionist’s point of view throughout his text (arguably for the purpose of refuting it, but at least it is actually recognized). Aristotle responded well to the conversational style of the book, the pacing of the course work, and the clear explanations of topics that had previously been difficult for him to grasp. I responded well to the course’s ease of implementation, the convenient availability of all the materials, and my complete happiness in Aristotle’s success. This curriculum also benefits from the presence of many supplemental products such as videos and laboratory supplies which are widely available on the internet in both new and used condition and can serve to really enrich the student’s experience with the course.

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For some secular educators, the religious perspective of this program may be counter to their educational goals. However, I found that the creationist versus evolutionist commentary was a terrific platform for us to explore the creation beliefs of various religions and cultures. It also afforded us a concrete example of how two different ideologies can examine the same set of data (the fossil record, for example) and come to completely different conclusions. I felt this was an invaluable lesson for Aristotle as there will be many times in his life where he will have to carefully evaluate information before drawing any conclusions, all while being acutely aware of his own and others’ unique biases.

Another group of wonderfully composed Christian programs are the history curricula developed by Beautiful Feet Books. These programs utilize a detailed study guide, complete with discussion and essay questions, combined with a great variety of related works of literature. Students read age-appropriate biographies, historical fiction, personal accounts of daily life, reviews of art and architecture, and detailed descriptions and analysis of world events for whatever time period the study guide is addressing. Aristotle and Archimedes particularly liked the various biographies and found the general history texts by Genevieve Foster to be so much more interesting than standard textbooks.

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The creators of this curriculum, Russell and Rea Berg, are Christian and do incorporate religion into their study guides both through the use of authors with biblical worldviews and the use of essay questions that specifically refer to scripture. However, almost all of the literature used in this program (at least for the study guides we used) is not overtly Christian and includes descriptions and discussions of cultures and religions that are not based on Christianity. In addition, the list of discussion and essay questions provided with each lesson is extensive with only a couple of questions specifically related to biblical teachings or scripture, and these can easily be excluded from the secular student’s course work without compromising their complete understanding of the historical topic being studied.

These are not the only programs that have worked well within our secular academic plan, but they serve to demonstrate that religiously based curricula can often be adapted to non-religious studies and provide enormous benefits to homeschooling families. The time and frustration saved in modifying an already well-researched and well-written product as opposed to creating your own curriculum cannot be overlooked. To be sure, there are an equal number of Christian or other religiously-based programs that really don’t lend themselves to use in secular situations, but before you eliminate a particular curriculum from your syllabus, give it a thorough examination. You may find that you can easily modify it to fit your secular needs. Yes, we’re secular, but we are grateful for the many Christian curricula that have been a successful part of our homeschool.