In her #CMCS15 session, Jennifer Wilson (@jwilson828) asks:
How might we leverage technology to build procedural fluency from conceptual understanding? What if we encourage sketching to show connections?
What if we explore right triangle trigonometry and equations of circles through the lens of the Slow Math Movement? Will we learn more deeply, identify patterns, and make connections?
How might we promote and facilitate deep practice?
This is not ordinary practice. This is something else: a highly targeted, error-focused process. Something is growing, being built. (Coyle, 4 pag.)
What if we S…L…O…W… down?
How might we leverage technology to take deliberate, individualized dynamic actions? What will we notice and observe? Can weWill we What happens when we will take time to note what we are noticing and track our thinking?
What is lost by the time we save being efficient, by telling? How might we ask rather than tell?
#SlowMath Movement = #DeepPractice + #AskDontTell
What if we offer more opportunities to deepen understanding by investigation, inquiry, and deep practice?
A colleague messaged me privately concerning the “positivity trip” I’m on in my posts. While I don’t care for the word used, I’ll quote the question.
There you go again, Jill. I’m gonna ask one more time. Aren’t you concerned about positivity and wussification of our students?
That’s not what I’m writing, talking, and thinking about. I want to be better – intentional – about offering specific, actionable feedback. The more I use and practice with I like…because…, I wonder…, and What if…the more favorable the responses are.
I also wonder if we have a “no news is good news” attitude when marking papers. If we did a little data mining on the most recent set of graded papers or feedback comments, would we see descriptive positive comments? Or, it is habit to mark what is wrong or needs improvement? Do learners look at the whole of the assessment, or do they look for marks and comments? What is the positivity ratio of what they find?
Constantly scanning the world for the negative comes with a great cost. It undercuts our creativity, raises our stress levels, and lowers our motivation and ability to accomplish goals. (Achor, 91 pag.)
So, I’m curious… Is there anything wussifying <ick!> about the following feedback?
Example 1: Algebra I – I can evaluate an expression involving exponents that are integers.
I like that you showed your work and thinking, because I can see that you do understand negative exponents. Questions 9 and 12 show that you have a solid understanding when asked to evaluate a negative exponent.
I like that your work in Question 10 is clear enough to show that you correctly evaluated the negative exponent. I wondered if you had trouble with fractions until I read your work in Questions 11 and 12. Nice corrections, by the way. I like that you can see what you thought initially and what you now think, because it will help you when you review.
I wonder if you understand Question 11 even now. What if we meet for a few minutes to discuss your understanding of complex fractions and why a number raised to the zero power equals one?
Example 2: Leading Learners to Level Up formative assessment
I like that Level 4 challenges learners to convert between different forms of a linear equation, because this will help with symbolic manipulation that is so important in 9th grade physics.
I wonder if the language will confuse learners. As you can see from my work, I did not answer the question as you intended. I read intercept form and used the slope-intercept form. What if we ask for the equation written in two-intercept form? I wonder if the additional language will offer learners clarity.
Example 3: New Ask, Don’t Tell Art of Questioning document for Algebra II.
<Sam> What do you think?
I like it, because it is clear why each form has advantages, and that knowing all 3 forms is helpful. I like it, because it is easy, using the slider bar, to navigate between the three forms.
I like that it is easy to see that the value of a is constant no matter the form. I wonder how learners identify patterns in forms of hypotheses and then check. I wonder if they will struggle with writing their hypotheses in words.
I wonder why the manipulatable points are so large. I wonder why the user-added font is larger than the font of scale and values of the graphing window.
I like that the value of a changes in fraction increments and that the functions are displayed with fraction coefficients rather than
decimals. I wonder if learners will notice and document the pattern of the fractional coefficients when moving an x-intercept.
I like that a double root is possible. I wonder if learners will adjust the window to have the y-intercept in the graphing view. I wonder if learners will know to adjust and reset the viewing window.
What if the axis of symmetry is added to the graph? I wonder if it would help or distract.
What if the background of the graphing window is graph paper? Would it help the visual process to be able to count?
<Sam> Thanks for the feedback. Incorporated a few changes.. Font size is what it is.
I like the addition of the words: vertex form, factored form, standard form, because it provides clarity. I wonder – I think – that it will offer learners language to document patterns and hypotheses in words.
What if we practice taking the time to offer positive, descriptive, and growth-oriented feedback? How might we change outlook, efficacy, and attitude? How might we learn to spot patterns of possibility?