A very smart person a long time ago is supposed to have said that knowledge is a belief tied down by understanding. 

As an elementary school student, I believed that 5 is a prime number. I believed this because it was my understanding that all odd numbers are prime numbers. If I got this question in a test, I would get this question right. But because my correct answer was based on this misunderstanding, it is not true that I knew 5 is a prime number – I just got lucky!

If I was asked if 9 is a prime number I would also answer yes based on my misunderstanding that all odd numbers are prime numbers. I definitely didn’t know that 9 is a prime number – because it isn’t!

My belief that all odd numbers were prime numbers was strengthened by the fact that, when quizzed on prime numbers by my teachers, I always got more than half of the questions right (half the questions would be even numbers) and more than half right when more odd numbers than not happened to be prime numbers.

The more quizzes I did, the more questions I got right. I would remember more of those weird odd numbers like 27 and 35 which were marked wrong when I marked them as prime. My belief developed into ‘all odd numbers are prime numbers unless my teacher tells me otherwise.’ But even if I got really lucky and answered all the questions in a quiz correctly, I couldn’t say that I knew if any number was really a prime number.

Fortunately, while we were dividing our odd numbered class into equal groups, a teacher observed that, despite quiz scores that would suggest otherwise, I did not know what a prime number was. She took my beliefs about prime numbers seriously and helped me understand the properties of a prime number. Now I know that 5 is a prime number but 9 is not. I now know what a prime number is because my beliefs about prime numbers are now based on correct understanding.

My prime number story popped into my mind this week during a meeting about standardized MAP testing. We plan to resume MAP testing in February. These tests will provide us with useful information about our students in Math and English Language Arts that we can use to further develop our students’ knowledge and skills in these core curriculum areas. However, in isolation, these multiple choice tests are not necessarily suited to identifying the understanding or misunderstanding that a student has based their answers on. 

A student with a clear understanding of prime numbers might incorrectly answer a question through carelessness while a student like me might answer that same question correctly based on a misunderstanding or memory. This is not to say that MAP testing data is not valuable or reliable – it is both of these things if it is analyzed in light of the understandings and misunderstandings of students which are visible to teachers through classroom observations and assessments. MAP testing provides an independent set of data that teachers can combine with classroom data to learn more about a student’s understandings and misunderstandings.

A school that takes seriously the understandings and misunderstandings of students is far more likely to develop knowledgeable students who will be able to apply and adapt that knowledge to the future. The learning process should therefore be designed to make student understandings and misunderstandings visible so that teachers can develop or correct them to create student knowledge. 

Starting with our Reggio Emelia-inspired Early Elementary classrooms and continuing through to graduation, our ISY interdisciplinary curriculum framework is designed to allow teachers to make student understandings and misunderstandings visible. 

A safe, compassionate learning environment is vital and students are given the opportunity to freely share what they believe about a topic. Teachers are able to use these beliefs to guide student learning in such a way that student understandings or misunderstandings about a topic will be uncovered. And once they are uncovered, teachers can use them to help students develop key knowledge that will stay with them beyond a MAP test and well into the future. 

Susan Sauvé Meyer. Ancient Philosophy: Plato & His Predecessors [MOOC]. Coursera. https://www.coursera.org/learn/plato

Gardner, Howard. Unschooled Mind: How Children Think and How Schools Should Teach. Basic Books, 2011.

Internet Issues

Offline Learning Activities

Every Friday, your child’s homeroom teacher will email you a PDF of offline learning activities that your child will be able to do if they lose access to the internet. 

Please only use these plans if your child is unable to access the internet. If you have the internet, your child will be able to attend online classes as usual. 

To make sure the offline learning activities stay connected to what is happening in class, our teachers will review and, if necessary, update the offline learning activities each week. Please download the PDF document attached to the email as soon as you receive it on Friday. The email will also have a link to this instructional video:

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