Written by Rocio Colina, President of 502 Down Syndrome
In Guatemala, we lack options of schools with inclusive education. There are only a few schools that are open to inclusion, even though education is a human right of every child, regardless of his or her capacities.
In some cases schools are willing to open to an inappropriate inclusion, such as “accepting” children but in a “special needs class”. A true inclusive learning environment is not a place where students with a disability learn in isolation from their peers. In other cases, they accept children and have them form part of the same class as other students, but only with a shadow teacher or by attending the class simply as listeners, only occupying a space, but without learning or without a code from the Ministry of Education, which means that the institution does not have an educational commitment towards the student. In other words, it doesn’t matter to the institution if the student with a disability learns or not, because there isn’t a commitment.
Real inclusion means regular schools welcome the child, permitting him or her to form part of the same class as regular children, with pairs of the same age, learning the same contents with pedagogical adjustments, based on an educational commitment. Inclusive education is about how we develop and design our schools, classrooms, programs and activities so that all students learn and participate together, in which the student has an educational curriculum that is adapted based to his or her needs.
Picture by Lauren Shear
For children with Down syndrome, it is especially important for them not to have a shadow teacher because the purpose is to make them independent for an adequate development. In some extreme rare cases they might need a shadow teacher only if a multidisciplinary team determines it would be better for the student.
In Guatemala, the Ministry of Education has already a special education department, enabling all students to attend regular schools with pedagogical adjustments. The majority of educational institutions in Guatemala ignore the fact that they can count on this department.
A lot of times, because of the lack of information, they perceive it as something complicated to implement, or they might think that it can get difficult to deal with the Ministry of Education, which might lead to cause fear to be open up for inclusion. Other times this openness is denied due to the absence of attitude, information or will.
It is significant for schools to inform themselves and prepare their teachers to initiate with a real inclusion in order to have a successful inclusion. An excellent teacher who is skilled for inclusion becomes an extraordinary teacher.
Parents need to also be informed, learn and empower themselves to help their children in this path, inclusion requires team work and the most valuable members are the parents. Parents need to focus on learning to help their children, and that means also to recognize things that need to be worked on and being persistent on these things without guilt.
It is also important to recognize that inclusion is a human right, not charity. A lot of associations are working towards inclusion, respect and equal opportunities. There are a lot of myths, preconceptions, or lack of information that make this task harder. These associations work to create awareness, and educate about equality, including avoiding name calling and labeling people with Down Syndrome or disabilities. When we use names to describe a person with Down syndrome or a disability, we are making them different and not part of, which makes inclusion more difficult.
Inclusion has to be a commitment between the parents, the teacher and the educational institution, that needs to put in the same effort to every student that becomes part of their school. In spite of that, the Ministry of Education of Guatemala already has a department that can help schools with inclusion.
Another problem in Guatemala is that there isn´t any educational degree for special education, or some of other therapeutic degree, leading to the lack of professionals that may manage or follow up on the work of inclusion. We need to have these university degrees and start to, not only have inclusion, but a social culture of inclusion.
Inclusion does not only benefit students with disabilities, but also regular students, because they develop to more humane individuals, with a higher degree of tolerance, solidarity and respect for others. With the rejection of children with disabilities in regular schools we are teaching our future generations to refuse to include people that make an effort to success who want to learn to form part of a society and be productive; we teach them instead to be competitive rather than humanistic.
Author Bio: Cristin Howard runs Smart Parent Advice, a site that provides parenting advice for moms and dads. Cristin writes about all of the different ups and downs of parenting, provides solutions to common challenges, and reviews products that parents need to purchase.
It can be challenging to help your child learn a second language. So here’s a list of great reasons why it’s worthwhile. If you find your enthusiasm for language learning flagging, you can review this list to recover your motivation. We’ve identified the benefits your child will experience, right now, as well as in the future.
Improved Ability to Focus
A study done at the Cornell Language Acquisition Lab showed that children who learn a second language are better able to focus. Even in the face of distractions, children who have a second language can block them out and keep their attention on a single thing.
This ability to focus is believed to be because learning a second language exercises the part of the brain responsible for selective cognitive processes. In other words, because they have learned to choose a language selectively, then can apply this selectivity to other aspects of their lives.
Faster Learning With More Fluency
While children are young, their brains are hardwired for language learning. The older they get, the harder it is to pick up new languages. So the earlier you start them learning a second language, the more quickly they will pick it up. This is in part because they have less to learn while they’re young. They can focus on the vocabulary that they need. The older they get, the more they have to learn to get started.
Ultimately they are likely to reach a higher level of fluency than if they started to learn that language later. Starting with a small vocabulary makes it easier to get comfortable with the building blocks of a language.
Better Problem Solving Skills
Children who hear and speak two languages are getting much more cognitive exercise. There is much more processing going on inside their head. This extra work has benefits beyond the ability to speak a second language.
A study looking at preschoolers showed that even at that young age, they were experiencing benefits. The bilingual children were able to sort objects into groups based on shape more accurately. They could do this even when it meant matching against color: Eg, a round green shape into a blue bin.
Kids who speak a second language end up having a broader vocabulary in their first language. They discover that there are lots more words to know, and some begin to ‘collect’ them. Having a wide vocabulary in any language is an early indicator of academic success.
Higher Academic Performance
As we’ve noted, children who speak two or more languages have advantages in processing information. This is what lets them focus on one thing while ignoring distractions. Studies have shown that this applies to spoken language as well. So bilingual children can focus on verbal information, even when there is background noise.
It’s thought that this is responsible for an improvement in their academic performance. After all, it’s a lot easier to learn in class if you can tune out other kids chatting so you can listen to the teacher.
The language that we speak can shape the way that we think about the world. Language is a tool that we use to describe everything around us. Each language does this in a slightly different way. So the more languages your child speaks, the more views they have on the world.
When a child is used to looking at the same things from slightly different viewpoints in their day to day life, it fosters creativity. They automatically look for more than one solution, more than one answer. This creativity can have all sorts of benefits as they grow older, especially when it comes time to find a job and perform in the world of work.
Can Protect Against Dementia
This one is a benefit that you’re probably not going to be around to witness. But, bilingual people have significantly lower rates of dementia and Alzheimers. The act of speaking more than one language is a great mental exercise. So you’re giving your child tools for success and health at all stages of their life by helping them to learn a second language while they’re still young.
There are plenty of reasons to persist and help your child pick up a second language while their brain is programmed to do so.
The long contended phrase goes that “Music makes you smarter.” Is this true to some degree? Is it true at all? It’s more easy to believe this about some types of music more than other types of music. This is evidenced by the popularity of playing certain classical music for children before they are even born. The image of headphones on a pregnant mother’s stomach comes to mind. Does music really make you smarter? What does research say?
In a live Facebook event we went deeper into these questions. You can watch the 30 minutes talk below or read about the topic.
So, does music make you smarter? What do we mean by that? While some studies have reported that you can achieve a higher test score while listening to Mozart, more current research says “believing listening to music raises test scores and IQ is an oversimplification of what music does for your brain” (Musacchia & Khalil, 2020).
Music has been shown to do several things for your brain. Music, especially actively participating in and making music:
Increases your neuroplasticity,
Creates more active neurological pathways,
Interweaves sensory input,
Makes a stronger bridge between the right and left hemispheres of your brain (Musacchia & Khalil, 2020).
Let’s break each of those things down a little with examples.
Neuroplasticity is your brain’s ability to change, adapt, learn, and grow. The more neuroplasticity your brain has, that’s like saying the better it is at “going with the flow”. Your brain has more resources and tools to use for the things you experience, both in every day events and traumatic events. Benefits of neuroplasticity include, “enhanced memory abilities, a wide range of enhanced cognitive abilities, and more effective learning (Ackerman, 2020).” For those that experience a stroke or other traumatic brain injury, having greater neuroplasticity means your brain is able to compensate and reroute functions away from the damaged part of the brain. You’re able to relearn abilities lost in the damaged part of the brain. According to Harvard Medical School, patients with speech problems are “capable of singing words that they cannot speak (Harvard Health Letter, 2007).” I’d say that’s pretty amazing!
Because music uses so many parts of your brain simultaneously, you’re training multiple parts of your brain to work together in an organized and sensible way. It’s like doing a full-body workout versus focusing on one part of your body. If I’m someone who is a couch potato, certainly doing some hammer curls and push-ups every day will help. But, it’s like all the cardio exercise videos that are really serious; not only do they have you lifting weights with your arms, but you’re also in a plank position or balancing on one foot, or moving your legs at the same time. Sometimes you wonder if the video is really trying to help you, or give you a heart attack with how hard you’re working. With music, you’re hearing things, having to pay attention to timing, rhythm, creating the right words and pitch, and also using your sense of touch and sense of where you exist in the world all at the same time. It’s a major brain workout, making all the parts of your brain work together for multi-faceted sensory input with more neurons firing simultaneously. Music is never a passive activity.
In a very real and literal sense it has been found that every part of the brain is bigger and more developed in those who participate in creating music (Musacchia & Khalil, 2020). Studies done on children who actively participate in music have found that even by the age of 7 the corpus callosum, also known as the “information superhighway” connecting the right and left side of the brain was 25% larger than the average child who did not participate in music (Miller, 2008).
Picture from kidzmusic.com
What are the benefits of a larger corpus callosum? In certain instances we like thinking of ourselves as either right brained or left brained. That if we’re artistic and completely disorganized and terrible at spelling and math, well, “we’re just right-brained.” It’s a nice spin on it. “That’s just the way I’m wired.” Right? If we’re always correcting others’ grammar, a bookworm, and have trouble drawing stick figures well, “I’m just left brained. I just am not artsy.” Really, because music connects the right and left hemispheres of the brain, it means we can use both sides of our brain equally well.
A personal experience from my life: In about 6th grade every student at our school was given an aptitude test. This was supposed to help us plan which elective courses we could take in high school before we graduated. I had chosen band as my first elective in 6th grade and was greatly enjoying it and made many friends in band. We all were eager to take our test and get some guidance because there seemed to be a lot of choices for which classes to take. Did I want to take more physical education classes, some computer technology classes with programming? Maybe some hands on classes with wood or metal working? Should I focus on reading more, more art classes, animal or plant sciences, languages? The aptitude tests were supposed to measure what you’d be most successful at, and along those lines, they gave you a print out with a little graphic, showing you if you were more right-brained than left brained, and by how much.
If you received your aptitude test and it said you were very dominantly right brained they might not have suggested you do some of the elective courses to learn what accountants do, for instance. Doesn’t mean you couldn’t do that, but it’d probably be much harder for you. Well, so we all took the test, and in a few weeks got our print-outs back that would tell us which side of our brains were used more and it also was supposed to suggest three classes we’d be good at, with a sentence or two about why. Of course, we’re teenagers, so the first thing we all want to do is compare ourselves to everyone else and then probably just take whatever classes it said our friends were good at, because we just wanted to be with our friends anyway.
Well, we all brought our tests out at the end of band class, and we were all so terribly disappointed. All of us looked at the image of the brain, with the line going down the middle, and for all of us, the “dot” that marked which part of our brains we used most, fell exactly on the middle line of our brain. For suggested classes all of our tests simply said something like, “No clear aptitudes emerged from this test. You should choose classes from your own interests. You have no clear strengths or weaknesses.” What a downer of a test. We all felt like it was saying, “You’re boring and completely normal and there’s nothing special about you.” But really, when you look at that, that we all had the ability to use both sides of our brain equally, it was a bit like a golden ticket. It was essentially saying, you’re going to be pretty successful at anything you try. You don’t have anything holding you back that’s going to make anything inherently difficult for you.
So, how can we have music work for us in education, outside of band and orchestra classes? At Trinus educators establish structured learning spaces and routines that become safe environments for students to learn and grow. These routines include music in several ways. Students are immersed in a language rich English setting full of stories, narratives offering a more advanced approach to language acquisition and ownership.
At Trinus, educators are constantly singing. Each day begins with a series of songs and movements that are age appropriate and directly relate to what we’re learning in class. Music sets the tone of the classroom, and creates an inviting atmosphere. Singing helps children really arrive and creates that sense of a safe environment. This looks different depending on the age of the child, but singing very effectively and immediately creates a feeling of reverence, excitement, awe, quiet, focus, or energy in the classroom.
Singing and music and movement as a class is a regular part of the routine for each class at Trinus. Singing as a class greatly improves and builds memory. This is easily evidenced by thinking back on your own schooling and things you know because of songs. I can still repeat mathematical equations in songs from 8th grade. I don’t even know what the equation is and haven’t used it since 8th grade, but I still know the song.
Singing and movement as a class also builds social and emotional awareness and expressiveness. You learn things like blending your voice with others, being aware of and listening to others while simultaneously speaking yourself. You have to share space and coordinate the song and movement with those around you. This is not an easy thing to do, even for professional musicians.
When you sing and move together in the classroom you are also working on impulse control, or the ability to stop and start together, on a cue. This is very important to develop, especially in young children, and a very good way to do it that is less abrasive than telling the toddler, “It’s time to pick up your toys now.” But, you’re working the same skills and the same parts of the brain when a child stops singing with their class as when you tell them it’s time to pick up your toys, and they listen and do so. Studies have also shown that students who play music together are more likely to interact positively with those they play music with (Musacchia & Khalil, 2020). The class that plays music together stays together!
Singing has also been shown to improve our ability to hear (Musacchia & Khalil, 2020). The more finely tuned ears are then better able to pick up the nuances of speech better. Better hearing leads not only to better speech but also better reading. Students who engage in music have been shown to be better, more advanced readers and have better reading comprehension (Musacchia & Khalil, 2020). The benefits to reading and speech with musical participation have been shown to be true both in a person’s native language, as well as a foreign language. When you participate in music activities you don’t just get better at reading or speaking one language, you get better at all languages (Hausen, Torppa, Salmela, Vainio, & Särkämö, 2013).
By combining singing and movement in the classroom you activate the whole brain and have a whole physical, emotional, social, cognitive, and interactive experience. At Trinus students connect and live what they learn in order to gain meaning. Experiencing learning through movement and music is a key way to do this. Music is much more than a way to entertain. Neuroscience has shown that music activates many parts of the brain simultaneously. When we engage in music in the classroom we’re helping our brains grow in ways that will benefit us and our students for the rest of their lives.
Ackerman, C. E. (2020, September 01). What is Neuroplasticity? A Psychologist Explains [ 14 Exercises]. Retrieved September 22, 2020, from https://positivepsychology.com/neuroplasticity/#:~:text=7 Benefits Neuroplasticity Has on the Brain,-Building on the&text=Recovery from brain events like,pick up the slack);
Hausen, M., Torppa, R., Salmela, V. R., Vainio, M., & Särkämö, T. (2013, September 02). Music and speech prosody: A common rhythm. Retrieved from https://www.frontiersin.org/articles/10.3389/fpsyg.2013.00566/full
Children get bored easily, and keeping them entertained can be hard work. Great games for kids can spike up a birthday party with friends. In a family setting, they can also create special moments and fantastic memories for years to come.
Regardless of your child’s age, you should find the perfect games that your little one will love. Some of them can be homemade, while others can be found in most children’s stores.
Our dear old-school games can sometimes be much more fun than the newest ones on the block. This is, of course, if you don’t tell your kid they’re vintage.
What we love about these games is that they’re accessible to anyone, anytime. You don’t need to purchase any equipment or supplies. Here are our favorite ones.
The Telephone Game
This game is suitable for kids of all ages and will generally provoke lots of laughter. You will need at least several kiddos or family members to play this game—the more, the better. Place them sitting down, forming a straight line.
The first child whispers a word to his or her neighbor’s ear, who then repeats the word to the next person sitting beside them. The whisper continues until it reaches the last child, who then says what they’ve heard. For more of a challenge, pass-on a sentence instead of a word!
To play this game, you’ll only need chairs—one less than the number of kids playing. If five little ones are participating, only set up four chairs. Position them in a circle, with the backs towards the center.
Let them walk, run, or dance around the chairs to music. At your signal, when you pause the music, they’ll have to rush and sit on one. One child will remain standing and will be removed from the game.
Remove one chair and repeat until you have a winner!
Physical activity is crucial for any child, and at all ages. If you’d like your little one to get some exercise while playing, there are plenty of excellent options.
Hide And Seek
“Hide and seek” is a classic and never disappoints. It can be done both indoors and outdoors and is a popular game for all children. Plus, it can be played with any number of kids or adults you have at home.
The only element this game requires is good hiding spots!
Indoor Obstacle Course
This game should also get your child moving. It consists of placing objects on the floor and around the house to create an obstacle course. Parents then create rules around each item.
For instance, children would have to crawl under a chair, balance along a piece of tape on the floor, then use a hula hoop. Kids who reach the finish line with all obstacles completed the right way get a point. The game can last as long as your kiddos’ endurance!
You’ll find scavenger hunts to purchase that are ready-to-play, but you can also make your own. Kids have a list of items to find in various rooms of the house or garden. The one who finds them all first wins the game.
These types of games require some thinking and independence. While they’re best suited for older kids, young ones can team-up to take part.
Organized sports can be a blast as well. Soccer, basketball, baseball, and softball are all great team sports. Then there are individual sports like tennis. These sports can teach kids about teamwork and competition too.
Memory games are fantastic activities to work children’s brain function and learn to store information. Most of them can also introduce new vocabulary.
You’ll find many card games featuring popular illustrations such as Disney characters or superheroes. If you’re looking for a more educational memory game, some of them display animals, birds, or plants.
You could also make some DIY cards at home by printing the same pictures twice. Your child may be thrilled to play with a custom dinosaur or truck memory game. Some parents even use photos of family members.
This game can be played anywhere, anytime on the fly. Not only does it test a child’s memory, but young toddlers should be able to learn new words. You could create the game with fruit, toiletries, or even regular home objects.
Start by placing a number of items on a tray. The longer you talk about each object—colors, shape, purpose—the easier it is for the child to find the missing object.
Let your child observe each of them for a minute. Then ask them to cover or close their eyes and remove one of them. Your kiddo will have to guess which one is missing.
To increase the challenge, start adding more objects. You could even remove more than one object at a time.
Great games for kids also include those that’ll make your child think and build strategies.
Connect 4 is another classic game that withstood time and fashion waves. It’s also a game that can easily pass from one generation to the next.
The concept of this game is simple. It comes with a vertical grill and red and yellow disks. The winner is the one who can place four discs of the same color in a row, either vertically, horizontally, or diagonally without being blocked by the opponent.
This teaches your child how to create a strategy. Your kid will also have to watch the opponent’s game, planning for the next move.
Although Battleship can be played by all kids, it’s very popular among the boys. Your child places ships of various sizes on a grid—showcasing numbers horizontally and letters vertically.
Players need to call a boat by guessing its exact position—such as A7. They’ll then have to figure out the length of each ship to sink it entirely. It’s a fantastic strategy game that also allows kids to practice tactics, numbers, and letters.
Puzzles are a great game to get your little one thinking. They enhance hand-eye coordination and fine motor skills for the youngest ones. It can also teach patience and logic.
There are different types of puzzles designed for all ages. Models aimed at young toddlers are typically made of wood and come with knobs for little hands to grab.
Toddlers can also try out two-piece puzzles before pushing the challenge to more complicated models. Puzzles can easily turn into a hobby that continues into adulthood.
Other activities are fantastic to develop our kiddos’ creativity, imagination, and artistic side. They generally make excellent family games, bringing laughter and building bonds.
Who hasn’t played Pictionary at one point in their life? This game can also be made at home by creating cards from which kids pick. The goal is to draw the word well enough for the rest of the players to guess it.
This game may uncover real talents and little artists!
If your child isn’t about drawing, what about acting? This game consists of describing a word only with movements, without speaking, and in a set amount of time.
It’s a good method to get your child to think outside of the box. It also encourages self-expression and is engaging even for older kids—and adults.
You’ll find charade games ready-to-play. Other parents print pictures and fold them up before placing them in a bucket for kids to choose from. Either way, it should bring entertainment for everyone!
If you’re looking for games to play on vacation or to create quality family time, there are a few worth considering.
Monopoly is one that can’t be ignored, although young kids may need to be teamed up with someone older. While my favorite remains the classic model, it now comes in “Avenger,” “Lion King,” or even “Star Wars” versions.
This is another popular game that can be played in a family setting with up to four players. The characters need to find the fastest route through the labyrinth to reach the final line.
If you’re looking for a great game for kids, there are plenty to choose from. Some can be created using objects at home, while others are popular games available to purchase in-store or online. Either way, they create fantastic memories, whether playing with friends or family.
These games are generally educational and should keep your kiddo away from electronic devices. What better ways to combine learning and fun?
Article written by The Waldorf School of Philadelfia
“In these secret places, children develop and control environments of their own and enjoy freedom from the rules of the adult world.”
Educational and environmental psychologists, along with educators in the field, have taken a keen interest in fort building. It’s a constant presence in early and middle childhood, the creation of secret places, often in plain site, and the experts agree that den, fort or secret space creation offers a host of cognitive and psychological benefits for the developing child.
The most comprehensive review of this research comes from architect, Maria Kylin, at the Swedish University of Agricultural Sciences. She identifies the three prominent scholars as Roger Hart, David Sobel, and Mark Powell, and compiles their research, along with dozens of other studies, that contribute to the comprehensive picture that is child-led fort building.
The creation of something new is not accomplished by the intellect but by the play instinct acting from inner necessity – Carl Jung
Maria notes this theme of “control” as well, saying, “The common factor in the experience of the den as a social and a secret place is the sense of control that children feel they have, both over the den as a physical space and over the other children who share the den.”
But it extends beyond a simple need to control their personal world. Montessori Teacher and Education Administer, Mark Powell, found that social control was also key since order and control extended into social hierarchy and culture among children. He notes that, during and after fort building, rules were established and managed among the children to a point where he felt fort building was an excellent training ground for social competence.
In the realm beyond control and social culture, The Islington Play Association in the UK outlines even more perceived benefits of fort play in the guide for “playworkers” titled: Children’s Places of Secrecy and Play: A Playworker’s Guide to Dens and Forts. They speak to the privacy and solitude fort play grants children and notes how essential alone time is for a child’s imaginative play and development of an “internal quiet voice.”
But mostly, they discuss the importance of forts in terms of a child-created space, custom-made to suit the child’s specific needs. “When children build new spaces for play, they create a new world to experience, and that experience creates a new world – one that runs according to different material and social rules. What this means is that play gives children the opportunity to change their world to suit them. When children construct their own play environments, they naturally create ones that are most responsive to their needs, both at the moment and in terms of their long-term development. The benefits to the children are clear – stronger senses of self and community, belief in one’s own abilities to construct, adapt and demolish, the chance to identify and satisfy one’s own social, material and spatial needs.”
Forts at School
Waldorf early childhood programs nurture and protect the young child’s sense of wonder and imagination
Our role, as educators, is to respect these sacred places children build and to create environments that encourage their creation. Early childhood classroom design, in Waldorf Education, gives children space and materials to build these special places that help them learn in developmentally appropriate ways. Our classroom’s large free spaces are ideal for building and linens, scarves, blocks, along with empty mobile and modular shelving along with other elements often lead young ones to create these spaces indoors.
Out on the open playgrounds, older and younger children alike have plenty of space and material to make these spaces. And, most importantly of all, they are given the time needed at recess to create and cultivate these spaces together.
Forts at Home
Parents can encourage fort building at home as well. The New York Times asked prominent architects for their advice on how to best help children make special places inside their homes in their article, Lessons in the Art of Pillow Fort Construction. As a prime example of the pro tips offered, Dallas architect, Bob Borson, says, “Use sheets for the roof, since they’re lighter than blankets. Couches are a great anchor. And umbrellas are great for super fast fort construction. Just throw a sheet or blanket over the top of a big golf umbrella — or two, if you have them — and you’re all set.”
For the visual learners, check out this page at Pinterest, which offers examples of the best of the best from a simple cardboard box or sheet on a string to elaborate couch and outdoor creations for the children at home and in all of us.
Discover Waldorf Education
For fort building in action visit a Waldorf early childhood classroom. Discover the mixed-age Pre-K and Kindergarten program serving children ages 3-5 years of age at the Waldorf School of Philadelphia. Children work together in mixed-age groups in our pre-academic, play-based program that provides the strong foundation needed for the academic work of the grades program.
The home-like environment of a Waldorf early childhood classroom is carefully prepared for the developmental needs of the young child. Warm, nurturing, inviting and intentionally filled with beautiful, natural elements including pieces of wood, seashells, beeswax for modeling and handcrafted dolls and toys to encourage children to create, imagine and wonder. Their day breathes with a natural rhythm and nurtures them with folk tales, puppetry, and community.
Taught by Waldorf teachers specifically trained in early childhood education, Waldorf early childhood programs nurture and protect the young child’s sense of wonder and imagination. Children learn how to cut fruit for sharing, roll dough for baking fresh bread, and how to finger-knit with organic plant-dyed yarns, a practice that develops fine motor skills and teaches them how to recognize mathematical patterns.