A Day in the Life....of 4th Grade Math

This morning I had the pleasure of observing a fourth grade math class. Though we have two mixed 4th/5th classrooms, every morning the students regroup by grade for math, and this year Jeff and Kellyne are teaching 4th grade math.

The class began with the teachers taking the students to the basketball court, and organizing them into two groups to play a 10-minute long math version of Giants, Elves and Wizards. One group was Even and the other was Odd; the teachers would shout a computation problem (such as 4x3), and the group with the appropriate characteristic to the answer (in this case Even) would then chase the other group to a safety line, attempting to tag as many people as they could (tagged students then had to switch sides and become part of the other group). This 10 minute warm up combined mental calculations of addition, subtraction, and multiplication, and knowledge of odd and even, with a kinesthetic action (chasing or fleeing) that motivated students to attempt to speed up their computational speed.

Everyone then moved inside to the rug, where they found their notebooks and pencils, and worked on a series of warm-up problems displayed on the interactive whiteboard. The students had 10 minutes to work on their own, and then 10 minutes of whole-group sharing and discussion about the problem set, which included logic problems (Two men play five games of chess, and each wins an equal amount as the other. How is this possible?), greater/less than symbol application (155 > 99), and connected pairs of algebraic problems involving addition or subtraction with one variable (If 27 - X = 20, what is X? Next, what is X + 14?)

The class then continued a stations-based work period begun earlier in the week, for about 30 minutes. One station drew on Marcy Cook curriculum for creating dynamic triple-digit addition equations involving regrouping. Two stations drew on JUMP! Math curriculum for investigations into linear measurement and time telling. One station drew on Everyday Math curriculum for work with pan balancing (solving equations using various weights on either side of a balance scale); and the last station contained cuisenaire rods for students to use in working with the Show Me 1/2 fractions curriculum. In the last five minutes of class, students returned to the rug to preview the homework assignment, ask clarifying questions, and organize their materials.

There were many aspects of this period that artfully embodied the elementary division's approach to instruction. The introductory activity (on the basketball court) combined the use of prior knowledge with current skill development, while providing movement-based reinforcement using a high-motivation game format. The second phase of the class (on the rug) provided guided practice on current concepts and whole-group sharing of strategies for arriving at answers, balancing individual students' desires to work alone (some students wore noise-canceling headphones to help them concentrate) or in groups (some students engaged in spirited conversation while attempting to solve the problems). The third phase of class (five table workstations) allowed for student-directed choice about which concept and activity to practice, and also gathered students together to support their understanding of how the homework connected with the work they had been doing. Taken as a whole, the tripartite structure of the lesson provided adequate time in each phase for students to dive into the knowledge and skills presented, while factoring in student motivation and the constraints of their ability to maintain attention.

The Brain's "Air Traffic Controller"

Today Kate, Kim, Renee and I gathered in the conference room for a free lunchtime webinar on executive function ("EF") led by Dr. Bill Jenkins and sponsored by Scientific Learning, where he is Chief Scientific Officer (and also a Founder). Dr. Jenkins is a former associate professor at the Keck Center for Integrative Neuroscience at UCSF, and he keeps a very interesting blog on all things neuroscience. Pleasantly, he didn't try to sell or push the company's products, but instead remained focused on the nueroscience of executive function. 

Dr. Jenkins described EF as containing three distinct and inter-related components that function as the "air traffic controller" of the brain. Working memory allows us to do tasks such as hold and manipulate information for a short period of time, hold multiple step instruction without reminders, and make decisions in social interaction such as turn-taking. Inhibitory control allows us to master and filter thoughts and impulses, hold of distractions, and select and focus attention. Cognitive flexibility helps us switch gears, adjust to new demands and experiences, consider new perspectives and change our speech and actions based on context. To give an example of how all three parts work together, consider the situation in which working memory allows you to hold two rules in mind, cognitive flexibility allows you to select which rule to follow in the moment, and inhibitory control prevents the "off" rule from being followed.

The stand-out takeaways for me from the webinar included the importance of providing scaffolding for students (such as establishing routines, providing cues, and breaking large tasks into discrete units); that EF takes decades to fully develop; that EF skills aren't automatically developed and because children will not necessarily outgrow certain behaviors, explicit intervention might be needed; and that EF development underlies success both socially and academically. The webinar concluded with some suggestions for developing EF, including allowing children to select high-interest topics for some schoolwork, providing both quiet time and time for detailed, extensive work at school, and encouraging participation in both team sports and/or drama activities as ways to learn to manage complex sets of rules and behaviors, and thus develop EF.

Update: Check out this video on adolescent brains sent to me by Kim, in follow-up to this webinar.

Executive Function and Neurobiology

During lunch and recess today, a group of seven faculty and I gathered to watch a free webinar from ASCD called "Strengthening the Brain's Executive Functioning." Executive functioning includes important higher-order skills such as analyzing, prioritizing, decision making, delay of immediate gratification, judgment, tolerance, empathy, and organization, and occurs in the prefrontal cortex region of the brain. Neural networks in the PFC are the last part of the brain to mature, and are at their peak period of growth and formation between the ages of 9-16 (though the PFC is in a state of constant maturation from the age of about 5 to about 25). No wonder, then, that so many students in upper elementary, middle school and underclassmen in high school struggle to stay organized, track their materials, complete work and in general manage their responsibilities at school and home; there's a neurobiological reason for their poor decision making! One implication is for schools; it is important to promote the development of neuroplasticity, which leads to increased executive functioning, by providing activities and opportunities to build flexible perspectives, learn to interpret and apply information to new open-ended tasks, search for multiple ways to solve problems, and develop metacognition - which obviously can't be accomplished in a teach-to-the-test environment. Another implication is for parents - how you choose to allow your child to spend his/her free time has a direct impact on the ways in which the neurological wiring of the prefrontal cortex is progressing, and thus how your child's brain is literally being formed. As one teacher pointed out in our discussion afterwards, if a child is playing video games for hours on the weekend, those neural pathways are getting tremendous reinforcement while others are neglected. In turn, this shift towards more complex digital lives for children has implications for schools - for example, if those are the neural pathways that are strongest for a child, rather than saying "no screens in school," we need to intentionally use screens to introduce both skills and concepts that we wish children to master. This is a perspective echoed by some of the interviewees in Monday's AP article "iPads take a place next to crayons in kindergarten" (sent to me by a friend who is a preschool teacher - thanks Lars!), and supported by the evidence from this webinar.

The host of the webinar was Dr. Judy Willis. While you can find the handouts of the webinar available for download here, I recommend you check out her great website, which includes information about the intersection of neurobiology and education.