The Importance of Math in Elementary School

This week's article summary is Kindergarten Math is Often Too Basic, which bemoans the math curriculum in most schools.

As you read the article, note how different Trinity is in terms of what we teach in math, how we teach it, and what we expect of our students.

Even though we are not a standardized-test-drive school, our annual ERB results indicate strong student foundation in math skills and concepts.

Our overarching philosophy of teaching math is that conceptual understanding leads to automaticity and fluency, which is the opposite of most other schools that believe that skill and repetition will lead to conceptual understanding.

Activities like Number Talks, subitizing, and asking students to solve math problems in multiple ways help them see that math is fluid and multi-dimensional.

Thanks to the oversight and coordination of Jill and Kerry, Trinity’s math program from Early Learners through sixth grade enables our students to understand math at a deeper level.

With this strong foundation, they are truly set up to thrive in math after they leave Trinity!

Joe 

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Kindergarten may be math’s most important year — it lays the groundwork for understanding the relationship between number and quantity and helps develop number sense, and how numbers relate to each other.

But too often teachers spend that crucial year reinforcing basic information students may already know. Many kindergarteners learn early on how to count and recognize basic shapes — two areas that make up the majority of kindergarten math content. Though basic math content is crucial for students who begin school with little math knowledge, a growing body of research argues more comprehensive kindergarten math instruction that moves beyond counting could help more students become successful in math later on.

For a variety of reasons, kindergarten often misses the mark: math takes a backseat to literacy, teachers are often unprepared to teach it, and appropriate curriculum, if it exists at all, can be scattershot, overly repetitive — or both.

Deep thought is important, even in the earliest grades. Kindergarten math proficiency is especially predictive of future academic success. Students’ number competence in kindergarten — which includes the ability to understand number quantities, their relationships to each other, and the ability to join and separate sets of numbers, like 4 and 2 making 6 — presage mathematical achievement in later grades, with greater number competence leading to higher math achievement.

But the math content commonly found in kindergarten — such as counting the days on a calendar — is often embedded within a curriculum in which the teaching of mathematics is secondary to other learning goals. Learning experiences in which mathematics is a supplementary activity rather than the primary focus are less effective in building student math skills than if math is the main goal.

Breaking numbers apart and putting them back together and understanding how numbers relate to each other does more to help develop kindergarteners’ mathematical thinking than counting alone. Students should move from using concrete objects to model problems, to using representations of those objects and then to numbers in the abstract — like understanding that the number 3 is a symbol for three objects.

One reason for redundancy in kindergarten math may be that classrooms lack cohesive materials that progress students through skills in an orderly way. Only  36 percent of elementary schools use high-quality instructional materials.

Some worry that increasing time spent on academic subjects like math, and pushing kindergarten students beyond the basics of numbers and counting, will be viewed as unpleasant “work” that takes away from play-based learning and is just not appropriate for 5- and 6-year-olds, some of whom are still learning how to hold a pencil. Kindergarteners can be taught more advanced content and are ready to learn it. But it should be taught using practices shown to work for young children, including small group work, hands-on work with objects such as blocks that illustrate math concepts, and learning through play.

Mathematician John Mighton, the founder of the curriculum JUMP Math, said it’s a mistake to believe that evidence-based instructional practices must be laborious and dull to be effective. He has called on adults to think more like children to make more engaging math lessons.

“Children love repetition, exploring small variations on a theme and incrementally harder challenges much more than adults do,” he wrote — all practices supported by evidence to increase learning.

Simple lessons, when done well, can teach complex ideas and get children excited.

“People say kids don’t have the attention,” to learn more advanced concepts, he said, but he strongly believes that children have more math ability than adults give them credit for. Getting students working together, successfully tackling a series of challenges that build on each other, can create a kind of collective effervescence — a feeling of mutual energy and harmony that occurs when people work toward a common goal.

 

6 Ways to Capture Students' Attention

This week's article summary is 6 Ways to Capture Students' Attention.

During pre-planning, I talked about how students need to know they’re safe and cared for in the classroom. That’s why over the first few weeks of school teachers devote much time to setting class norms and routines. Once students become familiar with these practices, they can focus on school work and learning.

The challenge for teachers is that while there’s comfort for all of us in routine and predictability, our brains need periodic jump starts to maintain attention.

So, teachers have the seemingly contradictory challenge to be predictable on the one hand and unexpected on the other.

Just as we all find the sweet spot intersection of cherish/prepare and nurture/challenge, teachers must do the same for routine/novelty.

The article below provides some helpful hints to maintain and stimulate student attention within an organized, predictable, well-run classroom.

Most of us have utilized most or all of these techniques. Still, the article is a reminder that even though we have set up a classroom for learning with our patterns and routines, we need to ensure that we keep student on their toes so their focus and attention remain alert.

Joe

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The brain evolved to promote survival. 

Every second, millions of bits of sensory information from the receptors of the eyes, ears, internal organs, skin, and muscles make their way to the brain’s attention entry gate, but only about 1 percent of it enters consciousness. 

In the wild, an organism is well-served by an attention system that gives priority to things that are unexpected, changing, and different from the usual: Any perceived source of danger is prioritized. However, in the absence of threat, attention is directed to any changes in an animal’s or human’s environment. 

Although survival in the wild isn’t much of a priority for most humans today, our brains still attend to perceived threat and change. If students feel physically and psychologically unsafe in a school or a classroom, they’re less likely to focus their attention on the lesson. In the absence of perceived threat, our brains are particularly receptive to what’s new, curious, or unexpected. 

In school, the students’ brains are always attending… just not always on the topics we’re teaching! When students aren’t attentive to a lesson or a textbook, their brain isn’t giving priority entry to the teacher’s voice or words on the page, but to other more interesting or distracting sights, feelings, and thoughts.

In order to capitalize on the brain’s selectivity, here are six practical and proven attention-getters you can use at the start of a new unit or lesson.

SURPRISE STUDENTS: Since the brain is attracted to novelty, do something unusual or unexpected to arouse curiosity and open the brain’s attention filter. Examples: Wear something unique, bring in an unusual object, or play a song when students enter the room to promote curiosity, hence focus. Tell students that there’s a link between your clothes, the object, or the words in the song and something in the lesson. Invite them to guess what it is.

PRESENT ODD FACTS, ANOMALIES, OR DISCREPANT EVENTS: The brain is fundamentally a pattern-making organ. Constructing patterns enables humans to make sense of the world. However, when an established or expected pattern is broken, the brain is immediately aroused. Example: A science teacher blows up a balloon, then slowly pierces one end with a sharpened wooden cooking skewer. To the amazement of students, the teacher pushes the skewer through the opposite side of the balloon without bursting it.

INVITE STUDENTS’ PREDICTIONS: The ability to make sound predictions is fundamental to survival, and the brain rewards successful prediction through its release of dopamine, a pleasure-inducing chemical. Teachers can provide opportunities for students to make predictions about the relationship of the curious sensory input or other novelty to the lesson. When this happens, students will seek information to help them make correct predictions and remain attentive as their brains seek to find out if their predictions are correct. Examples: In a science lesson for first graders, ask children to predict which objects will float and which will sink in a tub of water.

POSE A PROVOCATIVE (HOOK) QUESTION: A stimulating question can be an “itch” in students’ brains that they’ll want to scratch. Can what you eat prevent zits? Is aging a disease? What superpower would you want? The best hook questions are open-ended. They’re meant to stimulate thinking and discussion and to open the door to further exploration. Give students a reasonable amount of quiet thinking time before they answer. Have them do a quick write about their thoughts and/or engage in a think-pair-share with another student. After this personal engagement, learners are likely to be more attentive to your teaching on the related topic.

CITE A CURRENT EVENT OR ISSUE RELEVANT TO STUDENTS: Students often have opinions about current events or controversial issues in their school, town, state, etc., and these can be used to spark engagement. Example: For a unit on persuasive writing, a middle school teacher shows a newspaper article about a school board proposal in another district that would require students to wear uniforms. Students then discuss the pros and cons, state their position, and even switch sides to try to better understand different perspectives and develop rebuttals, all as an opening to the unit on persuasion.

USE HUMOR: Humor is a guaranteed dopamine booster and can serve as a great attention hook. Example: A sixth-grade mathematics teacher begins a unit on ratio and proportion by presenting funny caricatures of celebrities. She asks students to describe why the pictures are funny, and they note that various physical features (e.g., eyes, nose, ears, head) of the characters are greatly exaggerated. Then, the teacher shows da Vinci’s Vitruvian Man to illustrate idealized proportions of the human body. 

HOOK AND HOLD ATTENTION: We recommend that you rotate your attention-getting techniques to avoid being predictable. The intent of using the techniques described above is to hook student attention, but the intent isn’t simply to gain immediate attention for the moment. The longer-term goal is to hold that attention over time. There are numerous ways to capitalize on initial attention by employing active-learning strategies, including the use of authentic tasks and projects, inquiry-oriented instruction, cooperative learning, Socratic seminars, simulations and role-plays, and design thinking (e.g., using makerspaces, where students can create tangible products), and allowing students appropriate “voice and choice” options in assignments and performance tasks.