Maths - Where do our problems lie?
Our next round is at Granville East and we hope to deepen our understanding about how to teach and lead so that our students can think like mathematicians.
Our blog is started by Nicki from GEPS. She writes:
According to Di Siemon, Number is routinely identified by teachers as the most difficult aspect of school mathematics to teach and learn....and differences in performance are almost entirely due to difficulties with larger whole numbers and related concepts such as multiplicative thinking. Do you agree? What makes you say that?
In a recent report, “The Problem with Finding the Main Idea” by the John Hopkins Institute for Educational Policy the authors argue that in recent years curriculum has been overlooked as a pillar for school improvement. And I tend to agree. We have been caught up in reforms to make learning and thinking visible, to embed formative assessment, to ensure effective feedback and enable student self-regulation among others. Our priority has been “how” we’re teaching (the critically important pedagogy). We have neglected the “what” of learning and teaching (the curriculum).
And maybe this is because because the “what”, the curriculum in our schools, has become so all-encompassing, with strings of outcomes so long it would take a lifetime to master them, that leadership and change in the curriculum in our schools has become too hard.
In the hard-hitting video, as the first of Global Ed Talks, Dylan Wiliam makes statements that challenge our thinking about what’s important for our students and our curriculum. A major point (made in the first half of the video) is that to enable our students to be successful we must pay greater attention to recognising the role of knowledge in the curriculum. He says,
Mehta and Fine in the “What, Where and How of Deeper Learning In American Secondary Schools” suggests that deeper learning comes from the intersection of mastery, identity and creativity. In planning for deeper learning then, we need to consider both the cognitive and affective, the short-term and the long-term, and the individual and the social.
Be that as it may, Wiliam’s concern with an emphasis on generic skills mirrors the concern of Australia’s Chief Scientist, Alan Finkel. He speaks of a confusion about what we mean by 21st century education, “I say students should be work capable – and people hear ‘we need more generic skills like collaboration, instead of content knowledge like chemistry’”. He argues we need to teach students concepts, fact and principles – and that content needs to genuinely challenge students.
Finkel refers to the IBM concept of a “T-shaped worker” where the vertical line of the T stands for deep expertise in a discipline – this is what you need to acquire first. Once you have that you can branch out along the horizontal bar and use that expertise flexibly, creatively and collaboratively.
A recent study showed that this knowledge is critically important ( “The Problem with Finding the Main Idea”) It found that finding the main idea is not a skill that can be taught in isolation. Good readers can only find the main idea when they know how to decode and have the content knowledge to understand the text they’re reading. How important is it then, in developing proficient readers, to ensure that all students are exposed to quality texts, and all students are exposed to knowledge across the learning areas in the Arts, in Science, History & Geography?
In the article, “Knowledge & Practice: The Real Keys to Critical Thinking”, Daniel Willingham reinforces Dylan Wiliam’s points. His three main ideas:
Our students need to learn to think like mathematicians, scientists and historians. Amongst other skills, in mathematics our students need to reason, in history they need to examine historical events from different perspectives, in science they need to observe carefully and collect data. How frequently does “disciplinary thinking” occur in your classrooms? And if the answer is “not often”, how do we change this?
But disciplinary thinking is not enough, students need to develop the key ideas and understandings of the discipline. What knowledge and what understandings? We can’t cover everything! Wynne Harlem tells us we need to identify the nature of progressions from small to big ideas as an essential guide to what students should be learning. For example, in maths we need to focus on the big ideas to develop conceptual understanding. Dianne Siemon is showing us how to do this for the Number strand in the early years.
As leaders, how do we ensure our school’s curriculum enacted in our classrooms covers a broad range of content for all students? Ensures that students develop discipinary thinking? And focuses on big ideas and not on trivia?
Obviously, professional learning of our teachers is critical. My equally important answer is in our assessment. We need to put in place structures that ensure when we assess students all these three aspects are at the heart. “What gets measured, gets done”.
To sum up, here’s a twitter post from Tom Hills. “I think there are 3 debates all doing a merry dance.
Which of these is your greatest dilemma in leading curriculum in your school? And how have you, or could you, start to address your dilemma?