Ask one or more of the following questions about a topic or content standard:
Why study…? So what?
What makes the study of…”universal”?
If the unit on …is a story, what’s the “moral of the story”?
What’s the “big idea” implied in the skill or process of…?
What larger concept, issue or problem underlies…?
What couldn’t we do if we didn’t understand…?
How is… used and applied to the large world?
What is a “real-world” insight about…?
What is the value of studying…?
For what kinds of important capacities will this content actually equip us?
Relative and suggestive pairs:
absorb and reflect
action and reaction
capital and labour
harmony and dissonance
idiom and language
important and urgent
meaning and syntax
nation and people
nature and nurture
constant and variable
continuity and change
factor and result
fate and freedom
light and shadow
like and unlike
literal and figurative
matter and energy
power and governance
sign and signified
structure and function
sum and difference
“Uncoverage is thus not merely a nice strategy or philosophy of education; using questions to frame the curriculum is not merely an aesthetic or ideological request on our part. One might say that not exploring key ideas in the content through genuine questioning and sustained inquiry is like leaving all courtroom claims and evidence unexamined, to be taken on faith. Such teaching leads to a hodgepodge of unprioritized ideas and facts that end up feeling like so many random opinions. There must be a deliberate interrogation of the content so that students can see the key understandings as the result of connections and inferences (as opposed to authoritative textbook or teacher claims to be taken on faith—as “facts” for memorization).”
Even though I haven’t finished watching this yet, I need to record my frustrations – as my son has told me to stop talking to the iPad! I feel saddened to think that in South Australia someone has spent a lot of time researching the dominant pedagogy used (in high schools), when most of us could have simply described the practices that we were exposed to, knowing that things haven’t changed that much. What makes me angry is that not only does this seem to me to be a complete waste of time, I am now worried that the rest of the video is going to tell me how to change this practice – which I have been arguing against for a long time. (And is the implication really that practices like these are also being used in the Early Years?)
Surely, as a system when you provide teachers with a curriculum – now a National one, and a description of good teaching practice (TfEL) and then expect teachers all over the state to use their professional experience and knowledge- which would range considerably, to create interesting, engaging programs, you are setting up a system for text book providers to reap the benefits. To then simply take the examples in the text book and re-fashion these lessons into more meaningful experiences for students seems to be to be an ineffective way to address the inadequacies of our system.
Perhaps we could do something more constructive and supportive of teaching and learning by looking to other states/ places in the world. In other states research has been focused on identifying student learning, observing common misconceptions and providing teachers with support structures to diagnose and act on these. Surely in South Australia we could support teachers more in order to improve the learning of students in our care, and I mean deep learning – not just superficial content.
Now I will see if I can watch the rest of the video.
Ahh… purpose identified…”achievable for teachers.”
Is this enough? Is this what our students deserve?
I think “transforming tasks” is a very slow way of getting change happening.
Chapter 4: The 6 Facets of Understanding
Different aspects of understanding:
Have self-knowledge – meta cognitive awareness.
Facet 1: Explanation
Look for good explanations by getting students to: support, justify, generalise, predict, verify, prove and substantiate.
Use assessments (e.g., performance tasks, projects, prompts and tests) that ask students to provide an explanation on their own, not simply recall; to link specific facts with larger ideas and justify connections; to show their work, not just give an answer; and to support their conclusions.
Facet 2: Interpretation
Students must have activities and assessments that ask them to interpret inherently ambiguous matters- far different than typical “right answer” testing.
Facet 3: Application
Real life, problem solving approaches are required to see if students can apply their learning. Performance based learning, authentic tasks.
Facet 4: Perspective
Instruction should provide explicit opportunity for students to see alternative theories and diverse points of view. Same important ideas from different perspectives.
Facet 5: Empathy
Look to have students stand in someone else’s shoes to come to a deeper level of understanding.
Facet 6: Self-knowledge
Encourage self reflection, identifying blind spots, seeking to question and explore.
The Chocolate block task
Ten volunteers are asked to choose which chair they will stand at, knowing that they will share the chocolate with the people who have chosen that chair. Before the last two come on ask audience which chair they would choose and why.
How much chocolate will each person get and how do you know?
Visual model – chocolate lifted in the air so that chocolate – chair the vinculum – people under the chair.
Follow up activities: act out or discuss
1. The case where chocolate is out of the packet and clearly already subdivided. Now using fraction as an operator notion e.g., 1/3 of 24 blocks or 1/5 of 20 blocks.
2. The case where there are more blocks of chocolate at a chair than people.
Three pizzas are shared evenly between seven girls, while one pizza is shared evenly between three boys. Who gets more pizza: a boy or a girl?
Practical hints for the classroom teacher:
1. Give a greater emphasis to the meaning of fractions than on procedures for manipulating them.
2. Develop a general rule for explaining the numerator and denominator of a fraction. In the fraction a/b, b is the name or size of the part (e.g., fifths have this name because 5 equal parts can fill a whole) and a is the number of parts of that name or size
3. Emphasise that fractions are numbers, making extensive use of number lines in representing fractions and decimals.
4. Take opportunities early to focus on improper fractions and equivalences.
5. Provide a variety of models to represent fractions. Student made ones will help them to understand the importance of congruency when comparing fractional parts.
6. Link fractions to key benchmarks, and encourage estimation. Innovative strategy – residual thinking (when comparing 5/6 and 7/8 students may conclude that the first fraction requires 1/6 more to make the whole (“the residual”), while the second requires only 1/8 to make the whole (a smaller piece of number), so 7/8 is larger. Students sharing strategies is an important teaching strategy to encourage.
7. Give emphasis to fractions as division. Students need lots of opportunities to partition objects in sharing and other contexts to help build this notion.
8. Link fractions, decimals and percentages wherever possible. Students will choose to convert it to decimals or percentages, in order to make sense of it. This flexibility is to be encouraged, as percentages particularly seem to make sense to many students intuitively.
9. Take the opportunity to interview several students one-to-one to gain awareness of their thinking and strategies.
10. Look for examples and activities which can engage students in thinking about fractions in particular and rational number ideas in general. E.g., Cuisenaire rods:
What fraction of brown rod is the red rod?
If the purple is 2/3, which rod is the whole?
If the brown rod is 4/3, which rod is one?
If the blue rod is 1 1/2, which rod is 2/3?
Your brilliant question for another group!
Understanding by Design 2nd Edition
Teaching for understanding! Not coverage! How many times have I had this argument with secondary maths teachers!
“…conventional teaching abets the three “pathologies of mislearning: we forget, we don’t understand that we misunderstood, and we are unable to use what we learned. I have dubbed these conditions amnesia, Fantasia, and inertia” (Shulman, 1999).
Three types of “uncoverage” in designing and teaching for understanding:
• Uncovering students’ potential misunderstandings (through focused questions, feedback, diagnostic assessment)
• Uncovering the question, issues, assumptions, and grey areas lurking underneath the black and white of surface accounts
• Uncovering the core ideas at the heart of understanding a subject, ideas that are not obvious – and perhaps are counterintuitive or baffling – to the novice
What should students come away understanding?
What will count as evidence of that understanding?
One reason for focus on evidence is that this can be impacted upon through explicit teaching, evidence being what students do, make, write and say. It is through improvements in what students do, make, say and write that can infer what they have improved in terms of knowledge and understanding.