Regarding expressions and equations: if they are going to be
asked to write both, then what they need to know is the
difference between the two. I just had to look it up because I
had no clue. Now rethinking the TA, I think maybe they should
not have to define but give you an example of an expression and
an example of an equation and then be able to tell you the
difference. Whether they can actually define the two, I'm not
sure, although it may be essential. Now that I know what these
are since I just looked them up, I think these would be harder
for the kids just as you learned in the preassessment than the
questions they got right. BUT i don't think there is an actual
dependent sequence. They don't have to know how to define
before solving but they will have to know eventually. So, what
you had is a TA with a non dependent sequence and you know
exactly what they didn't know.

Whoever said teaching was easy? Now I'll be thinking about
equations and espressions half the night like I did those crazy
triangles.

On 10/27/09, Jan wrote:
> 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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