Pat Gere education, learning, teaching

Using the Hand to Optimize the Mind

Concrete materials instead of screens, worksheets or textbooks

Concrete, well-made, open-ended materials that require manipulation have so much more to offer education than textbooks, worksheets, screens or apps, especially in a world with AI. And the younger the student the more imperative their use.

Here’s an example:

This material is called the Golden Beads. It has unit or one beads, ten bars, hundred squares and thousand cubes, and cards to go with each hierarchy. If you have an elementary-aged child, you’ve probably seen drawings of these on worksheets or in a textbook, but we should provide the material instead of the illustration. Here’s why:

Photo by P Gere

A concrete material-

  • Requires movement both large – getting the materials to a mat on the floor where you are going to work, and small – manipulating and organizing the components. (As modern humans we’re often enjoined to move more and so should our children.)
  • Combines not only the visual and auditory senses (seeing something and being told the name) but also the physical sense of dimension – how small, large, long, flat, etc.) and the baric sense (the sense of weight)
  • Provides the opportunity for working together – cooperating, negotiating, delegating, and sharing information
  • Is reusable rather than consumable
  • Is shared – requiring taking turns, as well as care and a return to its place so that others may use it (Think beyond the classroom to the reinforcement of ‘Reduce. Reuse. Recycle.’)
  • Flexible – can be used for multiple lessons – learning hierarchies and relationships, adding, subtracting, multiplying and dividing, borrowing and carrying
  • Obvious – students can see the material on a shelf and be reminded that they can work with it
  • Open-ended – students can create their own problems to work on. Young elementary students particularly enjoy ‘big’ things, the bigger the better. They can set themselves as large a problem as they want and have the immense satisfaction of solving it ‘Myself!’ At an age when repetition is not highly sought, doing huge problems provides the repetition necessary for consolidation of a concept without requiring an overseer.
  • Exploratory – “What happens if each of the three of us take out a quantity of beads without showing the others? Can we figure out who took out the largest number? How much did we take out altogether? How much did we leave on the shelf? How much does our class have when all the material is back in its place?”
  • Incremental – One concept leads to another. Learning to count and exchange categories/hierarchies to find how much you have in total before learning to add, learning to add the same addends leading to the concept of multiplication
  • Flexible – the speed with which new concepts are introduced can be easily adapted to each student as well as adapting the size or complexity of the problems tackled
  • Observable – the teacher can observe students using the material and, without interfering in any way, ascertain whether the concept has been mastered or not, and whether additional instruction is warranted – continuous assessment without tests
  • Independent – once a lesson has been given on how to use the beads for a certain task – say adding several quantities of beads together, students can work independently 
  • More likely to create flow or focused engagement – since an adult is not needed and students are having their needs for independence, movement, socializing and success met as they work, they are more likely to achieve the stage of focused engagement/flow where learning is the most efficient and effort results in renewed energy and feelings of worth and joy.

Why don’t we use concrete materials?

Why don’t we gift our students with multi-sensory, movement-required and thought-required materials that have such open-ended possibilities? It is true that successful use of materials requires a learning environment conducive to student engagement and opportunities for choice. Shouldn’t we be guiding students in making good choices as a life skill? Shouldn’t we be giving students ‘flow’ experiences so that they know the deep joy of engaged activity as an alternative to the addictive, short-lived high of being entertained, even if the entertainment is educational. Shouldn’t we be encouraging the ability to work together?

In addition to a learning environment that provides for using concrete materials, the materials have to be carefully designed in order to be optimally productive. A material should Isolate a concept but be open-ended. The only difference in these beads is how they are arranged – as single, ‘one’ or ‘unit’ beads, in a bar of ten, a square of a hundred or the cube of the thousand. There are no distractions such as cute pictures of animals, flowers or cars, only the beads. The material should be durable and beautiful and be of a size that best fits the students who will use it. Originally these beads were made of glass. Now almost all are plastic but hopefully plastic that has enough weight to give the physical sensation of the difference between the hierarchies. Practical – It isn’t practical to have hundreds and thousands made with beads, so after the concept is introduced most of the hundreds and thousands are wooden representations of the squares and cubes. The material should also be part of a continuum – before the Golden Beads a child would use a number of materials to be introduced to and consolidate the quantities and numerals 1 to 10.  After the Golden Beads the learner could use a material that represents the hierarchies with stamps that are the same size but are different colours to represent the different hierarchies, gradually moving the student from the concrete to the abstract. It’s important to see each material as related to what comes before and after, as well as to other disciplines.

A well-designed material is ageless. When I was taking my Montessori teacher training for 3- to 6-year-olds, we were working with the Trinomial Cube in the stairwell of Victoria College in Toronto. The Trinomial Cube is a physical representation of (x + y + z)3 that is introduced sensorially to children around the age of four as a 3-dimensional puzzle solved by matching colours and shapes. In Elementary classrooms it is used to explore cubing trinomials through assigning numerical values to the variables, and then to explore cubing and finding cube roots – an introduction to algebra. A gentleman passed us going down the stairs, then paused and returned to our landing. Was this what he thought it was? A physical representation of a trinomial? This math prof immediately plopped down on the floor beside us, fascinated.

alisonsmontessori.com
Photo by P Gere

What were your favourite manipulatives as a youth? Lego, puzzles, building sets, an Easy-Bake oven, carpentry tools, games like ‘Hungry Hippo’ that you had to build first? Chances are they involved movement, possibilities, creation, action and result.

We shouldn’t confine learning to paper and pencil or to the ubiquitous screen. We limit what we and our students can achieve by doing so. Instead, here’s to exploration and learning that engages the hand as a powerful tool of the mind. Here’s to an advantage we have over AI.

Pat Gere education, learning, teaching

The last week of school and grading gets a failing grade

Assigned work and grading detracts from life-long learning.

It’s the second last Wednesday of the school year. My Grade 8 granddaughter is musing that tomorrow is the last day her teacher will accept assignments. “What about any work we do in the last week. How does it count?” Such a pertinent question! 

“How does it count?” When schooling is about doing what you’re told to do, in the way you’re told to do it, in order to be told how well you have done, in order to get a grade, it fails even if students get ‘A’s.

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Learning for the sake of learning; learning how to learn and discern, being engaged, being curious. These are the attributes humans need to thrive in today’s world. A thirst to learn, discern and act. A wonderment and a belief that we have a role to play in this world of ours.

Our curriculum-centred, teacher-directed, graded schooling does not encourage these attributes; in fact, it squashes them.

Several years ago, the parent of a second grade student named Meg engaged me, the principal of an independent K – 8 school, in a quick conversation on the sidewalk after morning drop-off and before rushing onto her job.  “I thought this school didn’t assign homework.”

She was correct. Our school did not assign students homework except if a student had a special need where a small amount of repetition at home would help, such as practicing math facts for 5 minutes in the car on the way to school. We did assign parents ‘homework’. We asked parents to read daily with their children. We asked them to spend time with their children doing something together that they both enjoyed like going for a bike ride, or something that needed doing like making a meal. Driving to an activity or watching a screen didn’t count!

Why was she asking? Meg’s mom explained that the previous night she had found a book about animals, a pencil and some papers where Meg had made notes – in Meg’s bed, where she had obviously fallen asleep while working. Why hadn’t she been told that Meg had an assignment due? She and her husband would have been happy to help her complete the work. I said I’d look into it for her.

Image AI generated

Well, it turns out there was no assignment, there was no homework. Meg had become interested in marsupials and had decided to do a project. School ended for the day but Meg wasn’t done so she took the book and her notes home. Meg didn’t ask her teacher; she just assumed that her exploration, her work, could continue at home. Why not?  Meg wanted to know more and didn’t see the need of waiting for school. This was her learning. Meg believed it could take place anywhere, whenever she had time, even in bed before falling asleep.

Schooling would do a much better job of educating youth if the system supported this type of learning – student-driven, curiosity-driven, I-can’t-wait-to-find-out driven!

Superintendents, principals, teachers, and most parents expect work to be assigned and assessed. As a result, the last weeks of school are often filled with entertainment designed to keep students quiet as teachers need time to receive work, mark it, write up report cards and have those reviewed. This is a systemic problem, the system encourages completion of assignments for the sake of getting a good mark rather than encouraging learning for learning’s sake.

But how will we know how well students are doing if we don’t grade? How about keeping track of mastery? This is what we did in Meg’s school. We didn’t give grades. We did keep careful weekly records of what each student had been introduced to, was working on and had mastered. This was essential for us because our teaching was individualized even though we had classes of 25 to 30 students. It all worked because we relied on students’ natural desire to be challenged and we tailored our interactions to their interests, abilities and needs. We could say what a student could do well, what they were working on and what they were just being introduced to in any week of the year. We had no need to give them a grade to be able to discuss who they were as a learner and where they were on that journey.

Think about it. We don’t give toddlers marks for learning to walk or talk. We support each toddler where they are with encouragement, support and joint celebration of their accomplishments. We don’t compare or grade them and yet they all become accomplished walkers and talkers unless there is some disability and even then they are driven to achieve these skills in whatever way we can help make possible.

A non-graded schooling model based on students initiating their learning for inherent joy and accomplishment would lead to a much different learning culture than the one that is most common now. The last weeks of school would have as much learning value as all the other weeks of school. And, as Meg demonstrated, learning would more likely continue outside of school, in the evenings, on weekends, and even over the summer break.

Instead of learning only in and for school, youth should be groomed to learn for life. Then our education system would be much more likely to meet today’s ever changing needs. A thirst to learn, discern and act – here are some Canadian, Indigenous and international programs that are stepping into this possibility and some organizations and individuals who are encouraging it.

Pat Gere education, teaching

Student Angst: The Disconnect Between Classrooms and Student Needs  

(As I was preparing to post this article, the CBC published Jessica Wong’s article Teacher shortages persisted this school year. What’s being done to fill the gap for the next? The CBC article is broad ranging, as it should be, but clearly indicates that student angst plays a major role in teacher shortages.)

As the principal of a large preschool through Grade 8 independent school, I did not often have students brought to my office for disciplinary reasons. Our school worked diligently to meet the individual needs of our students at each stage of their development. With careful observation, freedom for teachers to choose appropriate responses, and joint problem solving, there were few disciplinary problems. But one boy, Paul, new to our school, was acting out in his preschool class of 3- to 6-year-olds. He was 4 ½ years of age but big for his age and easily mistaken for a 6-year-old. He was being aggressive towards the adults and just couldn’t settle to any activity. He was challenging and rough on the playground as well. His teacher, the other adults, his parents and I had talked about him and tried a number of different approaches and agreed that if he was having a particularly difficult time, he could be brought to my office and ‘hang out’ with me. He could work/play at a table in my office or come with me as I did my daily ‘walk-about’ the school and then return to his classroom when he was ready. This worked on several occasions but it so happened that one day, when his teacher brought him to my office, he stood just outside my door but wouldn’t come in. After some discussion with him, I finally said, “Just step in for a moment.” Well, that’s exactly what he did. He stepped over the threshold, paused and immediately stepped back outside. I had to laugh, and so did he. I stepped out and invited him to walk with me to see what we could see around the school. He came with me and eventually I dropped him back at his class.

Illustration AI generated

This was a turning point – for me! When Paul, stepped into and then immediately back out of my office, a light bulb went on. Paul was in the wrong class! By age and academically he should be with the 3- to 6-year-olds, the preschool group, but when I thought about it, he had many characteristics of an early elementary child. He was physically large for his age and well-coordinated. Outside he loved to play organized sports, not be in small, less organized groups that younger children prefer. And, as he demonstrated at my office door, he had the mindset of an elementary child with the play on words. Now his academic skills were not high and there were many things, including being able to read, that he couldn’t do as well as an elementary student but we could manage that whichever class he was in. So, after explaining this to his parents and then to Paul, ‘We think you’ll be happier in an elementary class. Would you like to give a try?” we moved him to a lower elementary class of 6- to 9-year-olds, Grades 1, 2 and 3.

And that was almost the end of Paul’s visits to me. His elementary teacher had conferred with his previous teacher and brought materials that he might need into her class and put them on the shelves for anyone to use, including Paul. Elementary children being pack animals who love to play and work together in groups, welcomed Paul into their midst.  With bigger kids to work and play with all day long, Paul was in his glory and deeply content. His new friends helped him when he needed their assistance. He worked hard to try to catch up and keep up. Now he only visited me in my office to show me a project he and his new friends wanted to share.

What happened? Paul had reached the developmental stage of an elementary child early and he needed learning and play environments that matched his advanced development even though he wasn’t academically ready. His developmental needs trumped his academic abilities and once his needs were met, his misbehaviour disappeared and he used his energies to become one of the gang in every sense, including academically.

Perhaps the most striking example of this disconnect in education today is seen with adolescents. The apathy, anger, disrespect and violence evident in high school is the tip of the iceberg. The underlying truth is that high schools do not meet young people’s needs and now more than ever that matters. Without the discipline and expected respect of previous generations, high school students are acting out, as they have done in earlier times, but with greater frequency and at a more disturbing level.

All humans are born with drives to strive, explore, move, order, learn patterns, socialize and communicate. We use these extensively as we are growing up to become an adult adapted to the times we live in. These drives are with us throughout our lives but at different periods in our development these and other drives are more prominent.

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The preschool child must move. Sitting still for any length of time is difficult if not impossible. These children are refining their motor skills. They use their senses and movement to absorb what is around them. They learn through their activity. They love to repeat things over and over. Their sense of order is very strong and they are attentive to detail, to small things. All these tendencies support their absorption of the culture surrounding them, language being an obvious example. At this stage they have literal understanding – everything they experience is real. While they enjoy the company of other children the focus is on themselves and their own increasing capabilities. This is the age of “I can do it myself.”

Around age six, about the same time as physical changes occur like losing their baby teeth, there are changes in what interests and motivates children. The elementary-aged child no longer likes to repeat – “I’ve already done that.” Details are much less important to them, but they love large things and the want to understand how everything is organized. They are able to imagine entire worlds. This is the age of dinosaurs and space, past civilizations and impressive human accomplishments. They still need to move and create. Their interest in organization also shows up in socialization – not just the groups they now always want to be with and in, but what’s fair and what isn’t and what you do about this. Elementary-aged children generally are busy refining themselves and figuring out where and how to fit in rather than changing exponentially.

Adolescence, however, is a time of great transition and uncertainty. We all remember, none of us escaped. Our bodies changing, our emotions on edge. Where do we belong? Where are we going? Who are we supposed to be – and will anyone like us when we get there? 

Photo by Photo By: Kaboompics.com on Pexels.com

Much of the adolescent angst we see in high schools is a result of, or at least magnified by, the conditions high school places on youth. Ask an adolescent about their experience in school on any particular day and the most likely response will be about some extracurricular activity – a sport , a band or a drama, art or debate club. You have to press to find out what they are doing academically because academics have little to do with what they are biologically programmed for – who they are becoming and where they fit.

Adolescents need authentic experiences that introduce them to and prepare them for the real world. They crave authentic challenges, not sitting in a classroom walled off from the world they are driven to be part of. They crave making their own decisions, testing themselves. Generally, the closest they can come in school to an authentic challenge is the extracurricular activities where they have some agency.

Adolescents also need a mentor, someone, other than a parent, who is there for them. If a high school student belongs to a team or a club, that mentor is often the coach or teacher in charge. Sometimes the mentor is a subject teacher. But every adolescent should have someone who walks beside them through high school. Not a different person every year or for each subject but a true mentor for the entirety of the high school years. Ideally, small (<15), consistent mentor groups would meet regularly, at least weekly, so that an adolescent with a concern, or who the school is concerned about, has someone who they know and trust, and someone who knows them, to turn to with the challenges that inevitably accompany adolescence.

What if high school was organized around adolescents’ natural drive for maturity and agency in the adult world? It would be an entirely different high school. What if school at each developmental level used the characteristics of that age to advantage? What might we discover about the power of youth if we used their schooling to work with and for them rather than against their very natures? Here’s a peek.

Pat Gere education, learning, teaching

Valedictorian Censured – The Damaging Mismatch of High School Goals

The challenges of schooling in today’s world were front and centre at an Ottawa high school’s graduation ceremony. This time of year is filled with graduations, one of the few rites of passage we have in Western secular society, a time for graduates to celebrate their accomplishments and experiences, a time for schools to celebrate what they’ve been able to develop and pass on. In this high school though, the principal censured the valedictorian for her interpretation of what that experience included.

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The valedictorian included this statement in her remarks: “As a commitment to truth and reconciliation, I must acknowledge colonial and genocidal atrocities today, including the massacre of more than 17,000 Palestinian children in Gaza.”  The valedictorian said she felt this reflected her experience in school, the lived reality of many of her fellow graduates. She felt that she had connected the situation to the values of the school board and what she had learned throughout her four years at the school.

The principal felt that her statement caused harm and was uncomfortable enough with the situation to send out an email to parents stating that the speech “intentionally took focus away from the purpose of the event, celebrating the achievement of our graduating class.”

Hopefully the principal and the student have resolved the situation in a manner helpful to everyone.

For me, this unfortunate incident represents the challenge of schooling today. When we look at education as the successful completion of courses which represent specific bits of information and academic skills, we can miss the overall purpose – that of preparing young people for the world. This is a world they already live in, in spite of our attempts to protect them. When the school’s primary purpose is to transmit knowledge or skill, it is all too easy to lose sight of this more important goal.

We live in a complex world. Youth live in this complex world for which they will soon have responsibility. It’s a lot to ask of schools, to take on this complexity. Hey, it’s a lot to ask of youth, of everyone, but do we really have a choice? Taking a more comprehensive view that includes this complexity would change the way we school. High school adolescents are developmentally ready to be engaged in life. They need supports, yes, but they learn best by doing, by working on real problems that have significance for them. We could encourage youth to explore areas of interest, areas of importance to them, areas that make a real difference in the world now, and support them to do so; then figure out how these explorations meet or could incorporate the curriculum goals. (AI anyone?) Let’s celebrate this drive and use it instead of relegating it to the shadows.

Our schooling system is outmoded and focused on too limited a scope. The movement for change has started. Here are some examples. Let’s help everyone – the students, teachers, administrators and our world by embracing this change.

Pat Gere education, learning, teaching

The Benefits of Multi-Age Classrooms in Education

In my grandchildren’s public school, they’ve chosen to have combined Junior/Senior classes, each class having both 4- and 5-year-olds. Oh, to see this idea extended so that schools would have combined Grade 1 to 3 classes, Grade 4 to 6 classes and Grade 7 and 8 classes!

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While children change as they develop, it is widely agreed that within these three-year age ranges, children have similar physical, emotional, social and intellectual characteristics and needs. (3-year-olds also have the characteristics of the 4- and 5-year-olds, and, in developmental terms, Junior High should encompass 12- to 14-year-olds, Grades 7, 8 and 9). We can efficiently provide for the physical, emotional, social and intellectual needs within one class even with a three-year age range, if we choose that age-range to coincide with natural human development.

Let’s put aside the challenges of covering three grades of curriculum for the moment, and look at the advantages of multi-age classrooms.

Having students in a class for three years allows for a community to develop and to be passed on each year as only a third of the class graduates and is replaced by younger students. Two-thirds of a class remains to hold its mores and rituals. No need to start fresh each year. New students learn what is acceptable through observation, participation and role modeling.

In a three-age classroom there is a wider continuum of achievement. Where you fall in comparison with your age mates is not nearly so visible. Everyone is on a continuum, improving from where they are. Students can still tell you who best to go to for assistance with spelling or math or a computer glitch, and it’s not always an older student. There is more diversity and therefore more opportunity to be valued for being who you are and for what you are achieving. There is also more opportunity to move comfortably at your own pace through the curriculum so you aren’t left behind or ‘passed’ into a grade for which you’re not ready

In this multi-grade community, the teacher is not the only one who can help or direct. More experienced students can offer assistance if you’re having trouble, and may even give instruction. Everyone has more opportunity to offer and accept help, to get better at helping, and to reap the reward of having value. The old adage that one of the best ways to learn is to teach can be used to advantage.

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In a three-year class there is a continuum of community experience. You enter a new community in your first year and find your way. As a second-year, you are grounded in knowing you belong. As a third-year you are experienced and a leader but you also begin looking at the next transition. A three-year class gives students a variety of experiences in what community is, how to join one, how to maintain one, and how to welcome others in.

From the teacher’s perspective – imagine having a learning community that grows more stable each year because it doesn’t need to be created anew. As well, you know two-thirds of your students and their parents from day one and they know you. You can hit the ground running, adding weeks to the time you can devote to academic learning. You have only one-third the number of students to get to know, and more time and focus to be able to do that as the returning students are old hands who don’t need as much attention and, in fact, can assist the new ones in settling in. Having a very diverse class of abilities and needs means that you can offer students the opportunity to hone their skills and knowledge by assisting less advanced students, and provide less advanced students with one-on-one assistance all while celebrating the ability we have to be of assistance to one another.

Three-grade classrooms have enormous advantages in the academic realm as well if curriculum and instruction can be managed. How though? It isn’t using a system designed for a single grade and it’s not hiding behind a screen. For younger students, concrete, hands-on materials that teach as they are used can be arrayed around the classroom for students to choose and work with independently. (Why concrete and not screen-based? So many reasons including being able to clearly observe what a student is doing, using the hands to manipulate and explore as humans have always done to learn rather than just listening and seeing, and ease of sharing with others.) For older students concrete materials become less prevalent as project-based learning and independent, self-directed studying increases. In these classes, a teacher provides instruction in how to use the material or approach the project, observes carefully as students engage, and then offers support to the students who need it when they need it.

Photo by P Gere

Some students are naturally curious and adventurous; they are easily directed and need only a little assistance. Other students may find it difficult to become engaged in an activity or need one-on-one assistance to gain confidence. The teacher is available since most of the class is working independently, and often it is helpful to both students if one helps another. In this type of class, the students become very independent. They know how the class is supposed to operate and will assist one another or a substitute teacher to make it so.

You may think this style of delivering curriculum would be a risky experiment to undertake with students whose learning will be irrevocably impacted if it isn’t successful. Fortunately, this system has been used and proven successful in high integrity Montessori education.

A word about the word – ‘Montessori’. There is no legal control over the use of the label Montessori. Anyone can call their program Montessori even if it bears no resemblance to the work of Dr. Maria Montessori. (This is one reason you may hear opposing concerns about Montessori – “Montessori is too rigid.” “Montessori doesn’t have enough structure.”) Accrediting organizations help with discernment.

High integrity Montessori programmes exist throughout the world, growing in number and influence in public systems but Montessori is not the only possibility for three-age classes. Other programs also leverage multi-year classes as do some Canadian public schools at the younger levels, as evidenced by my grandchildren’s kindergarten class.

The Killarney Public School program in Calgary has multi-grade classes as do the many Montessori public schools in the US. The Element High School in Ottawa, a non-profit but not public school, has multi-grade classes and the SparkNC programmes in North Carolina also have less emphasis of same age classes.

Mixed-age learning environments put the focus on students’ full development. Students can explore their place as valued individuals within a community while they cover curriculum: a two-for-one advantage, developing academically and socially at the same time.