Discussion in 'Editorials' started by Robert Heiny, Sep 21, 2012.
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I have addressed costs of learning previously in descriptions of NESI (New Era School Initiative) on Tablet PC Education Blog. I plan to elaborate notes of how using A Learners' View (ALV) on Classic Education at EduClassics.com allows refined calculations and management of individual costs of learning that can be aggregated in various ways to increase the rate and amount of learning promptly.
I'm curious how you would place time in your formula for determining cost. For example, a leaner does not have the immediate background to learn the biochemical process and must first learn other steps. This would add time - and skew the 'efficiency' idea because the cost would be higher.
You've stated the problem as if using a learners' view (ALV). That's good.
Costs of a lesson vary by the amount of time in seconds ($n) and/or in trial-and-errors ($TE, a learners' measure of time and effort) used to complete a lesson.
A lesson exists when a learner successfully completes the problem the instructor presented. From ALV, a Basic Lesson (BL) exists for 20 seconds with 0-3 Trial-and-errors among students instructed. A HydraLesson (HL) that teachers commonly present to fill a class period consists of multiple BL modules.
Each second of clock time costs $n and each trial-and-error (TE) by a learner costs $TE. The cost of a BL (CBL) to learn /a/ is the sum of $n + $TE (LC = $n + $TE).
Does this clarify the point enough to satisfy you for the moment?
Actually - this is the situation.
Learner A = has background to solve 2+2=
Learner B = never been exposed to symbols, therefore, learner needs to spend time on an "extra" task compared to Learner A.
From a learners' view, state in as few words and symbols as you can what one task you want completed in a 20 second lesson. Now describe the last step learner will complete before getting the result you want. Next show learner how to do that step.
Keep lessons to specific tasks. Combine 20 second lessons to fill your 50 minute class session.
Yes? Clearer now?
That doesn't reply to the scenario: two learners with different backgrounds. One learner sticks to the one task in your scenario. The second learner (less background) must do an additional task.
For example (very simple scenario):
Task: "Take out pen and paper."
Learner A: Takes out pen.
Learner B (no background): Does not recognize term pen, therefore, must learn symbol pen first.
Time for A is X seconds. Time for Learner B is Y seconds which includes background to learn symbol.
In other words, a simple task for Learner A is not simple for Learner B.
To your point, yes variations of response time exist. That means it can costs more for Learner B to learn the same thing as Learner A. Teachers can reduce these cost variations by adjusting instruction practices and lesson content.
Differences in time it takes for a learner to respond directly likely occurs when the lesson does not address behavior patters learners already use. Without getting into the weeds any further for now:
Skip over the language and other symbol stuff. Get behavior patterns of writing, drawing, speaking, silence, etc. you want to see, hear, etc., Say variations such as the following to the class, as with clapping exercise to get attention of a robust class of 9th graders; maybe use that as a warmup to the process instructor will use in this class session, then move promptly into instructing the second (20 second) lesson of the session, that is the first content lesson; alternatively, substitute the following for the hand-clapping:
"Repeat after me, 'This is a pen.' Choral response.
Say, "Take out your pen. Place it on your notebook (paper, whatever)."
Promptly, instructor moves on to first content step in lesson.
Monitor the slower responder. Sometimes a non-verbal prompt is used with that learner to do what others are doing.
Substitute the word pen with a diagram, picture, formula of the atom, molecule, or whatever is the lesson of the day.
Keep each lesson to 20 seconds. Chain them into fulfilling the HydraLesson for the class session.
Yes, it may take a few sessions for learners to adapt to short, fast moving, lessons. They will likely do so, if the instructor is consistent with offering clear instructons and sometimes cycling back to points learners appear to have missed.
A tip: instructing this way is a doing task, not a theoretical discussion task. Take theories and ideologies about education and learning and what-ifs to after school parties or dinners with other educators.
This was my point: how does time figure into a cost calculation?
We agree here. So - how does a teacher improve efficiency once they recognize there are time differences? Which you answered above.
Let me go back to my initial question, how does time figure into cost? How do you evaluate efficiency?
I'm getting to a major question that I have - some students "catch on quickly" while others "take intense focus and greater repetition" before the desired behavior is achieved. This is a major stumbling block for teachers. So - how do you help them overcome this challenge and focus on the expected outcomes? And I believe the answer is to monitor time.
<p>Good point! Yes, monitor time either as clock time or as blocks of trial-and-errors by learners.</p>
<p>Let me go back a moment. Learning, from the research that a learners' view represents, is the process of connecting dots. The teacher's job is to show-tell students where the dots are and how to connect them in order to solve the problem the teacher presents. Make those show-and-tells short and concise, offered, say, in 20 seconds for each two dots. (A 20-second-lesson is like a paragraph in writing.)</p>
<p>From ALV, teaching-learning is just forming behavior patterns that learners can use for the next problem.</p>
<p>To plan a HydraLesson, chain the dots together backwards, starting with connecting the last two dots.</p>
<p>So, in each minute of a class, offer three 20 second lessons, that's 150 of them in a 50 minute class period. It's no more complicated than that.</p>
<p>If one student takes more time to connect two dots, have that learner move on anyway with the rest of the class, review the steps every so often (that's a judgment call and a separate issue) so everyone can fill in the steps they missed.</p>
<p>Mechanically, it's that simple. Rubs occur when the instructor has not planned one or more 20 second lessons clearly enough for learners to follow along. Yes?</p>