Well, you did it perfectly! The fact that they knew some steps
and not others is not unusual. Sometimes the question is
worded differently....for example they didnt know what a
mathematical expression was because they didn't have the
vocabulary. I love the "Wow!" They were thinking, that's for
sure.

Teaching them and then excusing them as you did when they got
it is right. What you might have done is give the
preassessment a couple of days ahead of time. Then you will
see what you have and can make plans for those who finish.
You can plan both how you will organize for instruction and
what you will give them for an assignment. In terms of
organization, you might find that you have only two kids who
don't have the step that everyone else has. You might pull
those two aside and teach that missing step the day before
you start the unit. Then you can start them all together.
But planning and organizing your instruction is best done
before so you need to give that preassessment several days
ahead. OOPS SORRY---JUST REREAD THAT YOU DID DO IT
AHEAD. Well, you got that part right, too!

Regarding the order of the task analysis. Some concepts have
steps that are sequential...that have a dependent sequence.
If they are, then they should be in order in the task
analysis. If there is no sequence....and in many concepts
there is not...then you just put them in any order using your
own best judgement as to what should come first.

My guess is that the task analysis is not in the wrong order
but that the first two steps using the word 'expression' was
vocabulary they weren't used to. Or, they have been taught
how to write a number sentence but never been given the
definitions. This is a concept without a dependent
sequence....they do not have to define an expression in order
to write an equation. So it didn't matter what sequence they
were in and, because they didn't get the first 3 questions but
got the last two doesn't mean your TA was in the wrong order.
it just means that there is no order and they know how to do
2 steps but not the others...and it doesn't matter where they
were placed on the TA.

It's late and I haven't thought this through, BUT, look at
your TA and see if all the steps are ESSENTIAL. Remember,
the critical attribute of TA is essentialness. It shows ONLY
the steps that they NEED to know, not the ones that are NICE
to know. So were your steps on defining ESSENTIAL? Do they
need to know how to do that in order to write an equation for
a word problem? If not, they should be removed from the TA.
It doesn't mean that you won't throw that information in the
lesson somewhere, that it isn't interesting information, but
if it's not essential, get rid of it. Essentialness is the
hardest thing in the world to determine. So many things are
nice to know but kids don't need to know them. And if they
don't need them to master a concept then they need to be out
because they will confuse the kids.

On 10/26/09, dc wrote:
> OK, so I gave my pre-assessment and analyzed it over the
> weekend. None of the 21 children were able to: 1)define
> an expression;
> 2)give an example of an expression (some of them
> wrote "Wow!" thinking that was a mathematical "expression"--
> CUTE!); 3) define a number sentence.
>
> A few kids were able to 4) write a number sentence and 5)
> read a word problem, then write the number sentence to go
> with it.
>
> So I was confused by that. None of the children knew the
> first three tasks, but some kids knew the last two steps.
> Does that mean that I didn't set up my task-analysis/pre-
> assessment correctly? Should it have been
> hierarchical/foundational in order? Should one skill be
> the pre-requisite of the next for a pre-assessment?
>
> So here's what I did today: I taught the definition of an
> expression and examples of expressions. This was my
> objective on the board: "I will define (tell the meaning
> of) a mathematical expression. I will write an example of
> a mathematical expression." After my lesson, I did a
> formative assessment on their white boards. Those students
> who mastered those steps were excused to have "free time"
> (which are academic centers in my classroom or computer
> time), while I continued to teach all the rest of the
> students who didn't get these first two objectives yet.
> Several more times I assessed and excused students as they
> mastered it. Soon I was able to get down to only 2-3 kids
> who still hadn't mastered it and so I called the kids all
> back to the group, making mental note of those two children
> for the future. This whole process took about 15-20
> minutes of teaching and assessing, but I was VERY SURE of
> who exactly had mastered it and who was still confused,
> which was nice for me.
>
> What I wasn't sure of was how to structure the "free time"
> of the students who had attained mastery. Help me here
> now. I just excused them for a few minutes with the
> instructions that I would be calling them back soon, so
> they knew it wasn't a long time that they would be
> excused. But I feel like their activity should have been
> congruent to the objective and working at a higher level on
> the Bloom's taxonomy as you said, Jan. I just wasn't ready
> for that yet. I'm still working on the lower levels myself
> (!) and could only handle one new learning for myself at a
> time today!
>
> I was pleased with the lesson, however, and the better
> knowledge of exactly who needed the lesson and who could
> move on. I'm just ready for more now. Can you help me
> with this next step?

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