In the previous Friday Bulletin we discussed Visual Mathematics, and the point was made that a compelling example of the visual nature of mathematical activity in the brain comes from a new study on the ways that the brain uses representations of fingers, well beyond the time and age that people use their fingers to count. The different studies on the brain’s use of finger representations give fascinating insights into human learning and clear implications for our mathematics classrooms.

We “see” a representation of fingers in our brains when we calculate. In 2015, researchers studied one specific region of our brain that is dedicated to the perception and representation of fingers, known as the somatosensory finger area of the brain. Remarkably brain researchers know that we “see” a representation of our fingers in our brains, even when we do not use fingers in a calculation. The researchers found that when 8-13 year-olds were given complex subtraction problems, the somatosensory finger area lit up, even though the students did not use their fingers. The researchers also found that this finger representation area was involved to a greater extent with more complex problems that involved higher numbers and more manipulation. In 2013, a different set of researchers found that even university students’ somatosensory knowledge of fingers predicts their calculation scores. They also found that finger perceptions in Grade 1 predict performance on number comparison and estimation in Grade 2. Researchers assess whether children have a good awareness of their fingers by touching the finger of a student – without the student seeing which finger is touched – and asking them which finger is being touched.

6-year old’s finger representation was a better predictor of future mathematics success than their scores on tests of cognitive processing. Evidence from both behavioral and neuroscience studies shows that when people receive training on ways to perceive and represent their own fingers, they develop better representations of their fingers, which leads to higher mathematics achievement. Researchers found that when 6-year old’s improved the quality of their finger representation they improved in arithmetic knowledge, particularly subitizing, counting and number ordering. Remarkably the 6-year old’s finger representation was a better predictor of future mathematics success than their scores on tests of cognitive processing.

One of the recommendations of the neuroscientists conducting these important studies is that schools focus on finger discrimination. The researchers not only point out the importance of number counting on fingers, for brain development and future mathematics success, they advocate that schools help students’ discriminate between their fingers. This seems particularly significant, given that schools pay no attention to finger discrimination now and no published curriculum that we know of encourages this kind of mathematical work. Instead, many teachers have been led to believe that finger use is babyish or to be moved on from, as quickly as possible.

There is debate among neuroscientists about the precise mechanisms by which finger knowledge improves mathematics achievement, but clear agreement on one thing, development of finger representations is critically important. A leading brain researcher in this area, states that if students are not learning about numbers through thinking about their fingers, numbers “will never have a normal representation in the brain”. Despite the clear evidence on the importance of finger use, dangerous instructions to ban finger use are communicated to teachers and parents. Telling students not to use their fingers to count or represent quantities is akin to halting their mathematical development. Fingers are probably our most useful visual aid, critical to mathematical understanding, and brain development, that endures well into adulthood. The need for and importance of finger perception could even be a part of the reason that pianists, and other musicians, often display higher mathematical understanding. The neuroscientists recommend that fingers be regarded as the link between numbers and their symbolic representation, and an external support for learning arithmetic problems.

Since no US curriculum materials that we know of include activities for helping students develop finger discrimination, the folks at YouCubed have developed a range of activities for use in classroom and homes, that can be accessed in the appendix below and at https://www.youcubed.org/category/visual-math/, to help this development in children and prompt further ideas and work in this area. Importantly teachers should celebrate and encourage finger use among younger learners and enable learners of any age to strengthen this brain capacity through finger counting and use. This does not mean that learners should keep counting on fingers as they move through school, it means that anyone who needs to advance their perception and knowledge of their fingers and count on their fingers should do so, at any age, as it is critical for their brain development. It is important to remove the stigma from counting on fingers and to see this activity as inherently important and valuable.

LCAP GOAL 3: STUDENT SUPPORT: Principles of Effective Empathy Education?

Empathy is at the core of everything that makes a school caring, a teacher responsive, and a society civilized. Moreover, students with high levels of empathy display more classroom engagement, higher academic achievement, and better communication skills. In today’s interconnected world, empathy gives students the edge they need to lead meaningful, productive lives. Effective empathy education requires seven core principles guided by strong, empathetic school leaders: 1) Ongoing: Educating for empathy is not a one-time lesson, but a continual focus. 2) Woven-In: Empathy competencies are integrated into content and interactions, not tacked on. 3) Meaningful: Instruction is authentic, touches the heart and mind, and stretches “me” into “we.” 4) Internalized: The goal is for students to adopt empathy competencies as lifelong habits. 5) Student-Centered: Students’ needs, not curriculum, drive the lessons and experiences. 6) Respectful Relationships: Empathy breeds in a culture of respect and caring. 7) Empathetic Leadership: Empathy is modeled, expected, and core to a principal’s vision, purpose, style, and interactions. Above all, empathy makes our students better people. It is what will help them live one essential truth: We are all humans who share the same fears and concerns, and we all deserve to be treated with dignity.

1). Teachers: Please remember to be outside on the yard for the 10 minutes of Yard Duty you share with your Grade-level Team. Sometimes we are short Pupil Supervisors, and we are counting on your presence out on the yard to keep our students safe. Thanks.

2). Teachers: Please make sure to pick up your students on time from the cafeteria after lunch.

3). Please make sure we close and lock all entrances to the school after we enter to ensure the safety of everyone on campus.