Tuesday, 24 October 2017
Written by Rona Reid, Instructional Coach
ReLeah Lent’s workshop on Interdisciplinary Literacy, on Sept 29, 2017, focused on "disciplinary tools that deepen student involvement and understanding in all subject areas. As students begin to use literacy the way experts do, they read and write about content, solve problems, ask questions, make decisions, discuss topics, and develop knowledge in a way that truly sticks.”
ReLeah explained that each disciple has its own unique approach to literacy; this post will focus on take-aways for teaching mathematical literacy.
What does literacy look like for Mathematicians? According to ReLeah Lent, “Mathematical literacy involves patterns, relationships and examples of understanding through visuals and abstract representations. Math is a discipline based on developing understanding through the act of solving problems, and the text often utilizes organization, language, and syntax that differ substantially from text in other disciplines.”
When Mathematicians read, they:
• use the information they are reading as pieces of a puzzle to be solved
• make meaning out of mathematical symbols and abstract ideas
• act as investigators looking for patterns and relationships
• seek to understand what the problem is asking them to do, rather than reading only for information
• ask questions as they read
• make notes of misconceptions or confusion
• read for accuracy and clear mathematical reasoning
• scrutinize ways that math is reported in the media or in real-world applications
• apply previously learned mathematical concepts
• look for what is missing
• think about how vocabulary may be used differently in math contexts
When Mathematicians write, they:
• explain, justify, describe, estimate or analyze
• use representations
• seek precision
• utilize real-world situations
• communicate ideas clearly
• Draw conclusions
Examples of how students can write in Mathematics:
• "When students celebrate Pi Day (March 14th), they write piku instead of haiku. Haiku is written in 5-7-5, but a piku is written 3-1-4.”
• Students create a “how to book” for quadratic equations, teaching each other using all five methods. Students then write a reflection on which method they prefer to use when solving, and include disciplinary vocabulary and real-world examples.
• When learning about parabolas, ask students to find/bring in examples of the curve in everyday life and then write a justification about why it is/isn’t a parabola.
• Create infographics
• Write student Mathematics blogs
"Collaboration in mathematics means that students have opportunities to hear and consider the thinking of their peers as they develop skills necessary for transferring their learning to other mathematical areas."
Prompts to spark math discussion/collaboration:
◦ What does the problem say? What does the problem mean? How would the answer be different if _______ in the problem were changed to _______?
◦ In what others ways could this problem be solved?
◦ How does the approach for solving an open-ended math problem differ from that of solving a closed problem?
◦ What patterns do you see in the three problems assigned to your group?
◦ How would you create a chart or other visual to demonstrate your thinking about the problem?
◦ How would the mathematical understanding needed to solve this problem be used in real-world situations?
◦ How is this problem different from or similar to others we’ve solved in class?
◦ Work with your group to explain why…
◦ Show the rest of the class what this concept looks like, perhaps through a graph, chart, or model.
◦ Convince another group that your approach to this problem is best.
Last idea: Math teachers can encourage students to read Math related texts by posting a sign like this on their classroom door highlighting what you just read, what you’re currently reading, and what you want to read:
but recommend Math related texts like:
Wednesday, 4 October 2017
Without designing more complex tasks, our students will not go deeper with their learning…
Written by Shanda Dupras, Instructional Coach
Dr. Douglas Fisher: Visible Learning for Literacy on August 16, 2017
“A critical difference between experienced and expert teachers lies in their ability to move students from surface to deep learning.” (Fisher, September 2017)
What is the Definition of Rigor?
This was Dr. Fisher’s question he posed to a hundred plus educators as he circled the room during his presentation. It is interesting, to watch teachers avoid making conversation within their table groups…I wondered if Siri knew the answer? Dr. Fisher broke the silence by explaining that “Rigor is the careful balance between Difficulty vs. Complexity.” We often confuse the two terms and use them interchangeably, when in fact they are two entirely different entities. Difficulty can be defined as the amount of effort that is required for a student to complete a task. Complexity is the level of thinking, the number of steps, or the abstractness of the task. (Fisher, 2017)
What Makes a Task Challenging?
Making students do a lot more work, does not drastically impact students’ learning…we know that when students are engaged in deeper thinking, students learn more. We were introduced to the “Difficulty and Complexity Quadrants.” It was noted that each quadrant that includes low difficulty and/or low complexity is not unimportant. When teachers are designing their lessons, they should know the level of difficulty and complexity they are requiring of their students. This can guide them in how to differentiate for their students as well as give effective formative feedback.
We want our students to end up in the Fluency Quadrant… this is our ultimate goal. (Fisher, 2016)
Change Complexity of the Task:
Simply assigning hard text to read will not ensure that students learn at high levels…students will not get any better. As educators, we will fail to move our students into deeper literacy learning. We must armour our students with the tools to allow and prepare them for the opportunities to go to battle beyond surface learning. We want our students to reach that FLUENCY quadrant!
Dr. Fisher offered four types of teaching that would prepare students:
· Concept Mapping
· Discussion & Questioning
· Metacognitive Strategies (including feedback to the learner)
· Reciprocal teaching
Focusing on just 1 of the 4 tools mentioned: Concept Mapping Effective size: 0.60
Concept Mapping is widely used throughout classrooms…but how do we ensure that is effective, engaging as well as being complex (level of thinking)?
Timing is everything…
· Concept Mapping is effective when it is used as a planning tool for something else. If students are just filling out a concept map and filing it in their binders, never to be seen again, it is no longer effective.
· The power of the concept map is the cognitive work that it prompts (the complexity!)
· Students lay out what they know…this becomes their planning for writing, research, investigation or presentation.
· Making Thinking Visible: Teachers and students are able to see the evidence/deeper level of thought and connections as more information is added to the maps. Do use the same concept map throughout learning task…add to it. Watch the thinking evolve!
· Using guiding questions as prompts for student’s thinking in their maps can also be powerful.
Example of a ‘Word Concept Map’ used during a popular book study: ‘The Giver.’
(Visible Learning For Literacy, Fisher, Hattie, Frey, 2016)
“In order for students to deepen their knowledge,
they need to have their learning made visible to them.” (Fisher, 2017)