Last Thursday, September the 29th, members of the Soledad Rotary Club came to Rose Ferrero to distribute school supplies to all our first-grade students. Rotary Club members included Randy Bangs, (our school district’s Superintendent), Ivan Ibarra Mora (Rotary President and Vice President of our School Board), Joey Sanchez, Joseph Sanchez, Lorena Gonzalez, Flavio Diaz, and Elizabeth Ortiz. Also present was SUSD School Board President, Javier Galvan. All first-grade students were excited to receive these tools and supplies they can use in the classroom, and all of us here at Rose Ferrero want to thank the Soledad Rotary Club for these generous gifts to our students.

Unfortunately, there has been a common belief in education that visual mathematics is for lower-level work, and for struggling or younger students, and that students should only work visually as a prelude to more advanced or abstract mathematics. In other words, … words and mathematical symbols are for serious professionals – whereas pictures and diagrams are for the lay public and children. This idea is an example of a damaging myth in education, and there is now compelling brain evidence to help dispel the myth. It is important that visual mathematics be integrated into curriculum materials and teaching ideas across grades K-12. The provision of ways to see, understand, and extend mathematical ideas has been underdeveloped or missed in most curriculum and standards in the US, that continue to present mathematics as an almost entirely numerical and abstract subject. Yet when students learn through visual approaches, mathematics changes for them, and they are given access to deep and new understandings. The brain evidence we know of today helps us understand the impact of visualizing and seeing, to all levels of mathematics, and suggests an urgent need for change in the ways mathematics is offered to learners.

Good mathematics teachers typically use visuals, manipulatives, and motion to enhance students’ understanding of mathematical concepts. But for millions of students in US mathematics classes, mathematics is presented as an almost entirely numeric and symbolic subject, with a multitude of missed opportunities to develop visual understandings. Students who display a preference for visual thinking are often labeled as having special educational needs in schools, and many young children hide their counting on fingers, as they have been led to believe that finger counting is babyish or just wrong. Yet, there is stunning new evidence from the science of the brain, showing the necessity and importance of visual thinking – and, interestingly, finger representations - to all levels of mathematics.

In recent years, scientists have developed a more nuanced understanding of the ways our brains work when we study and learn mathematics. Our brains are made up of ‘distributed networks’, and when we handle knowledge, different areas of the brain light up and communicate with each other. When we work on mathematics, in particular, brain activity is distributed between many different networks, which include two visual pathways: the ventral and dorsal visual pathways. Neuroimaging has shown that even when people work on a number calculation, such as 12 x 25, with symbolic digits (12 and 25) our mathematical thinking is grounded in visual processing.

A widely distributed brain network underpins the mental processing of mathematics knowledge. The area of the brain shown in green, which is part of the dorsal visual pathway, has reliably been shown to be involved when both children and adults work on mathematics tasks. This area of the brain particularly comes into play when students consider visual or spatial representations of quantity, such as a number line. A number line representation of number quantity has been shown in cognitive studies to be particularly important for the development of numerical knowledge and a precursor of children’s academic success. Researchers even found that after four 15-minute sessions of playing a game with a number line, differences in knowledge between students from low-income backgrounds and those from middle-income backgrounds were eliminated. The researchers in the study highlighted the importance of students learning numerical knowledge through linear representations and visuals. This is just one of many studies that show that visual mathematics problems help students and raise achievement. The brain research sheds light on this, as it is showing that the dorsal visual pathway is the core brain region for representing the knowledge of quantity.

Another recent study showed that as children get older, they develop part of the ventral visual pathway (shown in orange in the figure above), and the brain becomes more sensitive and specialized in representing visual number forms. The study also showed an important and increased interaction between the two visual pathways. This indicates that as children learn and develop, the brain becomes more interactive, connecting the visual processing of symbolic number forms, such as the number 10, with visuo-spatial knowledge of quantity, such as an array of dots or another visual representation. Different areas of the brain are involved when we think mathematically, including the frontal networks shown in red and purple, the medial temporal lobe and, importantly, the hippocampus – the horseshoe shaped area in red. The important point to keep in mind is that the neurobiological basis of mathematics cognition involves complicated and dynamic communication between the brain systems for memory, control and detection and the visual processing regions of the brain. A compelling and rather surprising 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.

1). Teachers: Let’s take to heart that in our math classrooms, students experience math in the same way they’ll experience it in the real world: in groups, making mistakes, explaining their thinking, and in a way that makes sense to them.

2). Teachers: When you are out (absent), please make sure to add your YARD DUTY or AFTER SCHOOL DUTY to your sub plans

3). 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.