While it might seem obvious that living in a three-dimensional world would require a certain amount of innate spatial abilities, it is less obvious in how this spatial ability informs science and math learning. Current research in visuospatial ability does show that children who have an understanding of how shapes fit together, and can see an object from a perspective other than their own, also have a significant advantage when it comes to problem solving in science and mathematics. Even something as important for small children as learning the number line or stacking blocks can be improved by spatial understanding.
Piaget and Inhelder worked with young children to try and understand their development of spatial reasoning and they found that young children do have a limited concept of space. For a young child, all objects exist in a fixed location relative to their own position and it is very difficult to represent in their mind’s eye the same scene from a different position, often referred to as perspective taking. As a child grows older they begin to construct their own conceptual model of space representing our three-dimensional world as a Euclidean space (horizontal, vertical, and depth axis). Piaget and Inhelder used the “water level task” as a procedure to test children’s spatial ability. In this task, a child is shown a container half full of water. Then an image of an outline of the same container which has been “tipped” at various angles is given to the child who is then asked to draw in the line representing the water level in the tipped container. Their research showed a definite age progression in the completion of this spatial task. Before the age of nine, children typically cannot consistently produce the correct answer. But much to everyone’s surprise many older students, both high school and university students, have significant difficulty with this task. Since that time numerous studies have explored spatial reasoning with university level students and have found that only about half could correctly draw in the correct water level on a consistent basis.
I find these results regarding spatial learning fascinating. Piaget’s water level task is an event that everyone experiences multiple times a day in the real world, yet is difficult for a significant number of people to represent on paper. We certainly all have experiences representing this task, so wherein lies the difficulty? Clearly there are gaps in our understanding of space, perspective, and frame of reference that spatial learning could help address in the classroom. How do you think you would do on Piaget’s water level task? Why don’t you give it a try.
Leslie Love Stone joins Chris to describe how art, and mathematics come together in her Geometric Abstract style of painting. With an incredible collection of processes, and metaphors Leslie typically collects and layers information sets upon layers. Chris and Leslie spend some time describing a series she recently painted, “California National Parks ∩ Last of… Continue Reading
To sum up the 2017 NCTM annual conference in San Antonio, Texas takes only one word, AWESOME!! As I’ve shared before, I look forward to conferences. They provide opportunities for me to be laser focused on education, a time to reconnect and collaborate, an opportunity to be current, a time to meet other like-minded educators,… Continue Reading
How many times do you sit in your classroom looking over fluency tests or the latest reading assessment you gave your students? I have many memories of diving into these assessments with my grade level team. We would spend time looking at our student’s scores one child at a time. By the end of our… Continue Reading
At the AIMS Center, we work with children to learn how they do math, to learn what’s in their thinking process, and to verify the results of research. It may seem like the children are learning, or at least remembering what they are being taught. Standardized test scores, though, seem to paint a bleaker picture.… Continue Reading
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Allowing our students to talk to each other about mathematics is very important in today’s educational culture. Gone are the days when students sat in rows quietly working on repetitive worksheets. Instead, we want to hear what students are thinking. How are they processing information? What do they see as important? What solution pathways are… Continue Reading
Based on the vision of education contained with the writings of Paulo Freire and others; Dr. Joseph has studied within the field of Teaching With Social Justice. This is to say she has sought to create, within her classes, a socially just system for learning. This podcast, we discuss the three aspects of teaching with… Continue Reading
I’m in a Professional “happy place”. I am attending the National Council of Supervisors of Mathematics (NCSM) conference in San Antonio, TX. Where do I start, and how do I ingest and digest all of the great sessions that I have attended? Being an attendee, I try to stay focused on what I have come… Continue Reading
I always knew that April was the month for mathematics! At least… I thought I knew that. Just for kicks and giggles, I looked on the internet to see what other things are claiming April as their month and I found lots! This is just some of the ones I found: Public Schools Month School… Continue Reading