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A student learns additions and subtractions with counting cubes.

Fostering Conceptual Understanding in Tessa International School’s Math Curriculum

October 16, 2024/in Curriculum, Teaching and Learning /by Tessa School

We are living in an era of extraordinarily rapid change, where technological advances and global events unfold at an exponential pace every day. Amidst these transformations, we see incredible opportunities for growth and progress in our teaching-and-learning approach, aligned with our mission to prepare students as future leaders who are always ready to move forward.

This is where conceptual understanding comes in. Instead of relying on rote memorization, conceptual understanding engages our students in meaningful Math learning experiences built around consistent concepts, helping them build solid knowledge with deeper comprehension.

Students at Tessa International School actively learn with encouragement from our Math Teacher.

Conceptual understanding helps students learn more flexibly and retain knowledge better.

What Conceptual Understanding Is

Conceptual understanding refers to the process of organizing and connecting seemingly isolated facts in a meaningful way throughout the learning process. This ability to arrange, structure, and integrate knowledge builds cognitive competence, facilitating appropriate retrieval and application across various contexts and disciplines.

In the field of Math, conceptual understanding involves comprehending mathematical concepts, operations, and relationships. When students grasp a math concept, they perceive their knowledge as part of a larger, connected whole, rather than as isolated facts or single approaches. Consequently, conceptual understanding often leads to students finding that there is less to learn, as they can identify underlying similarities in superficially different situations.

Examples of Conceptual Understanding in Math

According to Adding It Up: Helping Students Learn Math (National Academies Press, 2001), in addition to fluently verbalizing relationships among concepts, another significant indicator of conceptual understanding is the ability to represent Math situations differently and recognizing how they can be useful for different purposes.

Take adding and subtracting fractions as an example. Students demonstrate conceptual understanding when they are able to use real-life examples, visual models (such as number bars), and the common denominator method to arrive at the same answer. Using different representations shows how students progress from understanding part-to-whole concepts to applying algorithmic steps, which also can support them to draw connections with integration in calculus at higher levels in the future.

The degree of conceptual understanding is related to the richness and extent of the connections students have made.

Math Education at Tessa

At Tessa International School, we believe Math is more than just memorizing formulas. We ensure our students truly understand the “why” behind every concept and how it applies to their interactions with the world through an integrated curriculum of IB PYP Math and Singapore Math.

IB PYP Math

Concept-driven learning is at the heart of the International Baccalaureate Primary Years Programme (IB PYP), and Math, rather than being seen as a series of equations and theorems to be memorized, is viewed as a way of thinking that helps learners make sense of the world.

In this philosophy, the development of conceptual understanding can start much earlier than we might imagine, as IB PYP emphasizes the importance of the realistic, relevant conditions in which students live. Students acquire knowledge and skills by abstracting from their real-life experiences into symbolic notations and validating their understanding through problem-solving, where conceptual understanding shines.

Singapore Math

To fulfill the above idea that Math is a way of thinking, we implement the Singapore Math approach from Preschool to Primary School at Tessa, which is known for its intentional sequencing of concepts. This approach purposefully and efficiently organizes the Math terrain for students, breaking down complex concepts into simpler parts to build a strong foundation for advanced study.

One of the key features of Singapore Math methodology is the Concrete-Pictorial-Abstract (CPA) progression, based on the work of American psychologist Jerome Bruner. The three-step learning method introduces Math concepts in a tangible way and progresses through increasing levels of abstraction. As the name suggests, students gradually gain a deeper understanding of a concept at hand through three modes of representations:

Physical objects (Concrete),
Visual diagrams (Pictorial),
Math symbols and numbers (Abstract).

A core principle of this method is that learning is not linear but should be revisited and built upon, with a strong sense of connectivity and increasing complexity. While the Singapore Math approach refers to this as a strategy of mental Math, the CPA method indicates the reasoning, arranging, and communicating of understanding at a conceptual level.

There are multiple reasons why we love Math – we admire its intrinsic logic and beauty, and we value the passions and curiosity it inspires. More importantly, learning Math not only helps our students become more academically successful problem solvers, but its insistence on conceptual depth also develops a sense of resourcefulness and confidence, preparing them to excel in more complicated adventures, both within and beyond the classroom.

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Why Early Bilingual Education Boosts Brain Function and Development

April 5, 2023/in Bilingualism, Language Learning, Teaching and Learning /by Jamie Kreps

There has been an immense amount of discussion and research done on bilingualism in recent years. As scholars and educators dive deeper into the effects of studying multiple languages, more and more evidence is found to support international language learning.

Over the past two decades, researchers have focused specifically on the cognitive benefits gained by children who are introduced to bilingualism at an early age. Specifically, they have measured the ways in which children learn and react to various aspects of their education and found astounding results for multilingual children.

According to NPR.org, these results show benefits so great, they will be utilized and carried throughout your child’s entire life. It is a lifetime of learning in a way that is unparalleled to any other learning approach available.

Bilingual Education Benefits

While the benefits of bilingual education are exponential, there are several benefits that are so great, they should be considered priority in terms of learning. Among these benefits are invaluable skill mastery of things like problem solving, concentration and focus on any given task, and the ability to think critically and choose words with purpose and meaning.

“Researchers found that young adults proficient in two languages performed better on attention tests and had better concentration than those who spoke only one language,” according to LiveScience.com.

Problem Solving Skills

For starters, children who are introduced to a second language, are essentially challenging their brains to sort out multiple information and channel appropriate times to use each piece. By doing this, it is similar to solving riddles or puzzles – it forces the brain to consider information as a whole (call it “big picture thinking”) and sort out conflicting data. In terms of language learning, the child must sort out each language and decipher which language is appropriate to use at different times.

“Bilingual people often perform better on tasks that require conflict management… (because they possess) the ability to ignore competing perceptual information and focus on the relevant aspects,” explains the US National Library of Medicine.

Mastering Focus

Another benefit of bilingual education is the inadvertent mastery of focus and concentration. Since bilingual children must constantly think before speaking in order to ensure they choose the correct language to adequately communicate, they are naturally training their minds to reach mastery levels of focus and control.

“Because both of a bilingual person’s language systems are always active and competing, that person uses these control mechanisms every time she or he speaks or listens. This constant practice strengthens the control mechanisms and changes the associated brain regions,” the National Library of Medicine explains.

Critical Thinking

This level of concentration and focus that children with bilingual education will master, is what leads to an impressive critical thinking development. Essentially, by training their minds to pause before speaking and focus on what they wish to say, bilingual students learn the basis for a lifetime of critical thinking skills.

“Bilingual children as young as age 3 have demonstrated a head start on tests of perspective-taking and theory of mind – both of which are fundamental social and emotional skills,” reports NPR.org.

Overall, children who participate in bilingual education programs are proving to be more adept at communication in general, as well as having a greater cognitive ability and focus than their monolingual counterparts. Research continues to pour in on the benefits of bilingualism in early childhood education, but the results already reported have shown exponential plusses to international language learning.

Learn more about a bilingual education at Tessa International School here.

The Effects of Early Educational Bilingualism on Cognitive Development

March 2, 2020/in Bilingualism /by Jamie Kreps

When it comes to the topic of bilingualism in early childhood education, many parents often find themselves questioning when – and if – to introduce a second language to their children. The question being, whether or not the additional language studies would serve to benefit or inhibit their child’s cognitive developmental process. For some, the subject may be less of a choice and more of a necessity or way of life (think homes with bilingual family members already), but for many, the decision can bring many questions as far as how bilingualism will affect the cognitive development of their little one.

With decades of research devoted to studying these effects, scholars and researchers have been focused on the correlation between multiple language learning and developmental processes for quite some time now. In fact, many of these studies may seem a bit contradictory to others, making the outcomes somewhat confusing and raising even more questions for concerned parents. The truth is, however, as with all studies, new findings are possible every day and are revised to reflect the most recent and relevant information based on the latest comprehensive research. In other words, the more it’s studied, the clearer the picture becomes. So, what does this mean in terms of the effects of bilingualism on cognitive development?

Bilingualism and Cognitive Development

The number one concern for most parents considering a bilingual educational tract for their child is whether or not introducing a second language at a young age will cause confusion during a critical language learning time. Since understanding communication skills is critical to the successful development of virtually all other cognitive learning processes throughout their lives, it’s easy to grasp the basis for parental concerns for something that could potentially inhibit language mastery. The question becomes then, are these concerns for cognitive delays warranted, or are they part of some outdated research findings?

In order to answer that question, we must first take a look at the full picture. That is, we need to understand that there have been multiple studies done on the topic over the years, which inevitably leads to different findings. The key is to examine the most recent and comprehensive studies available in order to ensure you’re not looking at older information that has since been rendered essentially irrelevant. It’s also important to consider all contributing factors involved with the success rates of bilingual children such as parental involvement and cultural influences on the overall cognitive development process.

Previous Studies and Findings

Many of the earliest studies are what are behind the apprehension of today’s parents who are considering bilingualism for their children. Studies from decades past had showed a potentially slower learning rate for children who were learning two languages simultaneously – a rate which they attributed to the “confusion” of studying dual communication processes. It was believed that children were showing signs of inhibited learning because they were using both languages simultaneously – or “mixing up” the language of choice.

What these previous studies failed to do, however, was take into consideration the familial and socio-economic factors that helped determine a child’s overall understanding of communication. They also didn’t fully grasp the degree of focus and ability these children were exhibiting by simultaneously mastering the concepts of not just communication, but compartmentalization and empathy as well. Essentially, in the earliest studies, what was once viewed as confusion has later become better understood as a heightened sense of cognitive development and overall communication mastery by young children.

Recent Studies and Findings

In contradiction to earlier research, the latest studies today have shown immense cognitive development benefits in bilingual children. Not only has the theory of confusion been discredited, but researchers have found that children who are introduced to a second (or third) language during early childhood educational stages have a much higher level of overall learning comprehension as well as a more developed sense of values and problem-solving abilities than their monolingual counterparts.

“Research has shown that, contrary to what many people once believed, bilingualism does not trigger confusion, has no inherent negative impact on children’s development and even has some socio-cognitive advantages,” explains the Encyclopedia on Early Childhood Development (EECD). These advantages come in the form of a more developed level of intellectual focus, higher overall test scores, greater problem-solving skills, a heightened understanding of non-verbal context, and more flexible cognitive abilities in general. In other words, recent studies have shown that bilingualism, when introduced in early childhood, not only has no negative associations with cognitive development, but also comes with a large number of invaluable benefits instead.

Overall Benefits to Developmental Process

Since the brain function of a child learning dual languages requires that child to not only communicate, but correctly choose which language to communicate with, it forces bilingual children to fine-tune their ability to focus and concentrate. It also requires a sense of compartmentalization – a skill which will be crucial in later development. Essentially, young children who study multiple languages are getting a more well-rounded cognitive development than single language children because they are inherently learning multiple lessons at once.

“…Bilingual children show some advantages in understanding the beliefs of others and the communication needs of their conversational partners, picking out the important variables to solve a problem and entertaining two possible interpretations of the same stimulus at once,” writes the EECD.

It is important to remember, however, that these findings are largely dependent upon the outside factors involved in your child’s bilingual learning process. In order for your child to be truly bilingual (and not just a second language learner), requires a great deal of immersion studying and being surrounded by both languages – not just in the classroom. In order for young children to gain the greatest benefits from studying multiple languages, their learning process must be continued at home and on a regular basis, as well as during in-class studies.

Will Technology Ruin Your Child’s Development?

January 15, 2019/in Parenting, Technology /by Jamie Kreps

Whether it’s screen time or surfing the web, the majority of parents today have questioned the effects of technology on their children. Many have been left feeling rather confused with the immense amount of data on both sides of the debate. Is the internet going to melt the brains of our kiddos by destroying their ability to focus? Or is it going to open up endless possibilities and prepare them for an ultra-successful future?

Since technology led by the internet age is still, in essence, in its own childhood phase, we have limited resources for determining the full effect on developing minds. We don’t have the ability to examine historical patterns nor do we know how fast things will continue to expand. Nevertheless, there is plenty of data out there to help parents make a fully-educated decision.

The fact is, technology is empirically unavoidable today. There are technological devices and influences in virtually every aspect of our lives, and our children are no exception. Technology influences extend much further than video games and cell phones anymore. In fact, many classrooms are well-equipped with laptops, tablets, whiteboards and other devices to supplement their learning experience.

So how do we determine if these devices are helping – or hurting – the development of our children? According to the US National Library of Medicine’s National Institution of Health (NIH), technology has offered us a wide array of both productive and counter-productive outcomes in terms of the effects on developing minds.

In layman’s terms? Technology is both good and bad for our kids and basically, it’s up to us to weed them out. Before you get discouraged, there are methods that will help you sift through the digital drudge, as well as research to back up which methods are helpful and which ones are – well – not so much.

Technology Brain Food

As the NIH explains, if you think of technology’s effects on your child’s development in terms of “nutrition”, it can help you to gain a better perspective on how to sort it out. We know our children need well-balanced daily meals in order to grow physically healthy and strong, right? You wouldn’t feed your kiddos junk food and sweets every day and expect them to be fit as a fiddle. By the same token, technology is full of “nutritious” and “junk food” influences that will affect your child’s cognitive development.

The Junk Food

“Technology conditions the brain to pay attention to information very differently than reading,” says Dr. Jim Taylor, psychologist and professor at the University of San Francisco. According to his article in Psychology Today, the key to weeding out the “junk food” technology lies in monitoring methods that do not require a deep focus. What does this mean? In comparison with reading, surfing the internet for research is basically giving developing minds too much information too fast. In other words, it keeps kids from focusing on one specific concept. Doing so causes an undeveloped sense of understanding children could otherwise grasp from concentrating on a book.

Anything requiring little to no thought to complete (internet surfing, non-educational video games and television programs, etc.) will have a negative impact on the way brain connections are made. In fact, according to Taylor, influences such as the internet will adversely affect the way our children learn. These mediums bypass the need to focus and leave children “only able to focus fleetingly.”

The Vitamins and Minerals

On the flip side, there are many ways in which technology mediums have a profoundly positive impact on developing minds. These ways, which we’ll call the “vitamins and minerals” of technology, have the ability to improve overall development.

Perhaps the most important aspect to consider is to keep in mind that their futures will be filled with technology. This generation is one that will be engulfed in technology in pretty much every aspect of life, so including it from the beginning is giving them the tools they’ll need for a future filled with technological advancements. Think of digital learning tools as preparing your kids for their digital-filled futures.

According to the NIH, content is the most important thing to consider when filtering the vitamins from the junk food. Content, more than the type of device, is the key to finding what your children will benefit from the most. Ensuring whatever outlet they use (tablets, laptops, mobile phones, and yes, even video games), is used wisely, is the key to keeping their cognitive development healthy. Using nourishing content such as educational games, read-along programs, and digital media like interactive whiteboards to promote a learning experience is the difference between a nutritional digital experience and a junk food one.

Can Bullying Affect a Child’s Development?

December 14, 2018/in Parenting /by mtesalona

By: Jamie Kreps

It probably comes as no surprise, but bullying has been linked to an enormous amount of developmental issues in children – both in those who have been bullied and those who have bullied others. In fact, according to the National Institute of Child Health and Human Development (NICHD), bullying has a lifelong impact on the social and emotional development of children that puts them at risk for everything from severe mental health issues to stunted professional growth later in life.

According to the NICHD, children who are involved in bullying experiences (on either side of the situation) are at an increased risk of developing issues such as:

Depression and anxiety
Low self-esteem and personal drive
Trouble focusing and falling grades
Behavioral problems
Social and relationship issues
Substance abuse later in life
Self-harming behaviors

Bullying can also affect other children who witness the acts – even if they aren’t directly involved – by leaving them feeling insecure in their environments and fearing they could be next. The long-term effects of bullying go well beyond the initial instances and the people at the center of it and can often stay with a person for the remainder of their life. Since bullying can essentially destroy a child’s self-esteem, it can manifest itself in ways that will jeopardize future opportunities for years to come.

How It Manifests

As explained by ViolencePreventionWorks.org, “Nearly one in five students in an average classroom is experiencing bullying in some way,” but the effects are not limited to those involved directly. While it may seem obvious that those who are bullied have a higher risk of developing developmental issues, what’s less obvious is that bullying also affects the on-lookers.

Bullying brings negative affects to everyone who witnesses the act by way of creating what feels like an unsafe environment. It can make children feel as though they are helpless, planting a deep seed of insecurity and disdain for their classroom (and classmates) as a whole. Bullying also makes kids feel as though they can’t be protected by those they trust (teachers, aides, parents, etc.) which can lead to withdrawal and a failure to thrive.

Often, it is this withdrawal that is the first and most obvious sign that bullying is taking place, apart from actually seeing the incident in person. Over time, if bullying continues, those who witness it will likely begin to show other signs such as attention issues, fear of participating in normal activities, and acting out or other behavioral problems such as vandalism or destroying toys or objects.

The Long-Term Effects of Bullying

The effects of bullying are so debilitating, in fact, that researchers have linked it to a lower rate of success and quality of life decades later. According to Psychology Today, the low self-esteem and attention issues of youths who had been bullied translated to lower incomes and a greater risk for becoming involved in criminal acts as adults.

Research showed that individuals who had been “involved in bullying had poorer educational attainment and less income than adults who had not been involved in bullying,” the Psychology Today report explained. Not only do children involved in bullying suffer from mental and behavioral issues throughout childhood, but the research shows it deeply affects their cognitive and emotional development in ways that long outlast the actual incident.

How to Stop It

Thankfully, bullying prevention has been put in the spotlight in recent years and has gained momentum in educational facilities across the country. Many schools and childcare providers now implement some variation of an anti-bullying policy, which has had a major impact on developing minds everywhere.

Most anti-bullying policies include tips such as keeping a watchful eye, utilizing activities that encourage kids to speak up about their experiences, and keeping an open line of communication with youngsters to ensure they are comfortable with sharing any unwanted behaviors by others.

If you’re in need of some tips on implementing an anti-bullying policy in your facility, check out the US Department of Health and Human Services website, StopBullying.gov for more information.