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FAQ

Below are questions from teachers using Assessing Math Concepts in their classrooms along with the answer. If you are using Assessing Math Concepts and have a question, please let us know. Submit your question to info@mathperspectives.com. We will send you an email response as quickly as possible.

Select from the following subjects:

1) Re: Two Digit Addition and Subtraction
2) RE: Ten Frames
3) Re: Kindergarten Assessments
4) Re: Expectations for Hiding Assessment
5) Re: Follow up to Expectations for Hiding Assessment
6) Re: AMC Anywhere Hiding Question
7) Re: 2nd Grade Assessments
8) Strategies for Two-Digit Addition and Subtraction
9) AMC Anywhere Reports: What do the shapes mean?
10) Re: Assessing Math Concept: Concept 9 (Two-Digit Addition and Subtraction)
11) Two Digit Addition and Subtraction – Going back?

12) Re: Counting Objects
13) Re: Comments and Notes Section of AMC Anywhere
14) Re: Grouping Tens
15) Re: Using Assessment Information/Data
16) Re: Changing Numbers
17) Re: Ten Frames: Subtraction
18) Re: Grouping Tens
19) Re: Hiding Assessment
20) Re: Combination Trains
21) Re: Ten Frames Assessment
22) Re: AMC Counting Assessment
23) Re: AMC Anywhere Reports: What do the Shapes Mean?
24) Re: Students Passing the Tests
25) Re: Notes/Comments on Web Version of AMC

 

Question
Re: Two Digit Addition and Subtraction


I have had questions from multiple teachers and I am curious myself as to why students who touch the model, regardless of how they respond to the questions or the strategy used, score an "N". Can you explain to my why touching the model automatically warrants "Needs a Prerequisite"? I have provided an example below. The student knew the tens and ones that resulted from 33-14 and could put them together as a single number and their strategy was efficient (knows parts to break up tens). Please help me understand how to respond to this question. I appreciate your time. Smiley Face 

FAQ Image 1

Answer
from Kathy Richardson

I am so glad you let me know this is an issue for your teachers. 
Let me try to explain why touching or moving the model is so important. 
First of all, if the child touches/moves the model for one of the problems but not the other, they would get an "I". But if they need to touch it both times, it appears they are at a very basic level of needing the model to get answers. A child who knows parts should not need the model to figure anything out. I am wondering if the children who know a lot about numbers are using the model, not because they need it, but because they want to be sure they are right. Perhaps the teachers need to interrupt the children if they begin to move the model to ask them to see if they can do it without the model. If they know the parts and understand what is going on they shouldn't need the model. 
 
We are trying to move children to the place where they can work with symbolic problems. The models are supposed to help them understand what is going on when they add and subtract but not to be used as counters so they can go through the motions without thinking about what is happening. The concrete models should help children develop more and more efficient strategies as they learn to take numbers apart and as they recognize particular relationships among the numbers. The models need to be aids to thinking, not tools for getting answers or to demonstrate memorized procedures. Children should become less and less dependent on the use of the models for any particular concept, ultimately not needing the model at all. There are 4 stages of using models that children move through.

FAQ Image 2

Could you check back with some of the teachers to see if they think the children really know what is going on but like the security of using the models?  Or do they think the children are using the models without thinking much about what they are doing thus staying dependent on the model?
I would love to hear more about what they think is going on with the children.
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Question
RE: Ten Frames

Teachers have reported that when giving the 10 Frames assessment, children often have difficulty remembering the number they were asked to add to the existing stars.  I think it happens because of the question sequence. They break up the second addend then have to recall how many filled the 10 frame and how many extras.  I know this is all important, so I want to proceed carefully, but teachers want to know if it would be acceptable to write the second numeral on a white board if the child seems to need it.  What do you think?

Answer
from Kathy Richardson

I think having the number written down could influence the way children respond, so I wouldn't have them do that. This is hard for the children to remember because they aren't yet proficient breaking up numbers or thinking of ten as unit. If the child seems perplexed or is taking way too long, I would rather the teacher check in with them- saying, "Do you remember how many you added?"  Then, if they forgot, I would remind them by restating the problem. "You are adding 6 more to the 8" or whatever.  Oftentimes when you ask, you find that children do remember, but they are lost with all the parts and pieces, which is what we are trying to uncover. 

Remind your teachers that it is important to uncover what the children need even if we wish they could do better. 

Hope this helps. 
Kathy
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Question
Re: Kindergarten Assessments

We have a question about the Assessing Math Concepts assessments for Kindergarten.  Why, in Kindergarten, do we go from assessment two (Changing Numbers--to assessment four (Number Arrangements) and skip assessment three (More/Less Trains)?

Answer
from Kathy Richardson

Thanks for your question.

There are 4 Core Concepts that we are assessing within the Assessing Math Concepts series:
Within each concept (except for Counting), there are a series of assessments.
Changing Numbers (Assessment 2) is the first level for number relationships and Number Arrangements (Assessment 4) is the first level for Number Composition.
More/Less Trains (Assessment 3) is the second level for number relationships so it is actually harder for young children than Number Arrangements. 

Topic: Counting
1: Counting Objects

Topic: Number Relationships
2. Changing Numbers
3. More and Less Trains

Topic: Number Composition/Decomposition
4. Number Arrangements
5. Combination Trains
6. Hiding Assessment
7. Ten Frames

Topic: Place Value
8. Grouping Tens
9: Two Digit Addition and Subtraction

Kathy
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Question
Re: Expectations for Hiding Assessment

Some of our first grade teachers are tracking their students on the Hiding Assessment. They set goals for where they would like to see students in a month's time... and then choose activities from the Developing Number Concepts books to help guide student development.

At the end of four weeks, it is almost routine that they won't meet their goal, and will then wonder what they've done wrong, or which activities they should be doing instead, etc. I'm wondering if they
are just asking too much of their students. This is where I thought it would be useful to know what numbers a "typical" first grader is able to "know" combinations for at the A level, the P level, etc.


Answer
from Kathy Richardson

The results of the Hiding Assessment are often a shock to all who give it. First Graders typically know parts to 6 by the end of the year. A few may know parts of 7. Once children are Ready to Apply for 6 or 7, they can usually get Ps for the rest of the numbers.

Some children may learn parts of 10 before they know 7, 8 and 9.

I tried to allow for showing stages of growth by including minuses and pluses in addition to A, P, I and N.

If teachers feel they are not seeing progress, they may want to take notes while they are giving the assessment.

They may be able to see smaller steps of growth than is shown by recording only the instructional level. For example, a child may only know 4 and 1 at first and when reassessed know 1 and 4. Or they may just be more confident when figuring out a missing part.

Below are descriptions of the instructional levels in case they can also be of help to you.

6. Hiding Assessment
Part One

(A) Ready to Apply

Knows all quickly, no errors
Students are ready to apply if the know all the parts of numbers to 10 with automaticity with counters.

(P) Needs Practice
Students need practice if they know some parts, count on, or use relationships for parts they don't know.

(P+) Knows all but 1 quickly, no errors, no counting all (may count on or back or use relationships for one combination)

(P) Figures out two or more, may have one error, may not count all

(P-) May have one error, counts all for up to half of the combinations

(I) Needs Instruction
Children need instruction if they often make errors, or if they must "count on" or "count all" most of the time. May have two errors, counts all for more than half of the combinations

(N) Needs Prerequisite
Three or more errors or guesses.

Kathy
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Follow-up Questions to Reply
Re: Expectations for Hiding Assessment

Kathy,

One clarifying question: Our data reveals a great disparity between what the students can do with a model vs. what they can do without a model. Is that also typical? I am looking at one class, for example, in which a majority of the students are "A" with 5 and 6, using models. However, when assessed without models, only two students reached the "A" level. When you responded earlier to what a typical first grader knows, were you speaking with or without models?

Thanks again.

Answer
from Kathy Richardson

Children in first grade typically need models in order to think about the parts so they usually are lower on Part Two than Part One. This becomes less of an issue for most second graders.

First grade teachers need to help the kids move to this level by asking them "what if" questions once in a while.. What if you had 4 cookies and you gave me 2, how many would you have left?  They should do this with smaller numbers that the children know well with models. 

f this is still an issue with 2nd graders, direct teachers to the tasks where the kids are asked to "pretend". Developing Number Concepts Book 2: 3-6 through 3-12.

Kathy
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Question
Re: AMC Anywhere Hiding Question

"I administered a Hiding Assessment yesterday (using AMCAnywhere web-version) and have a question.... I wanted to assess starting at five and no matter what happened, I wanted to assess ten.  Typically, kids can do ten before 7, 8, and 9.  Also, in the new Framework, sums to ten will be an expectation.  I was unable to skip around within one assessment session and when I did ten by reassessing, the other data disappears from some reports.  I am pretty sure that there is only one report where I can retrieve the information. "

Answer
from Kathy Richardson

The Assessing Math Concepts Assessments are intended to help teachers determine the instructional needs of their students. The Hiding Assessment is based on the idea that when a child knows the parts of numbers so well that they can immediately identify the missing parts, they essentially know the "basic facts" for that range of numbers. That means the assessment can be used to determine what addition and subtraction "facts" the students knows and what facts they still need to learn. In order for the assessment to really hone in on what students know, we designed the path through the assessment to identify all the numbers the child is Ready to Apply from the smallest number to the largest number. Children generally learn the smaller numbers before the larger numbers. The exception to this is the number 10. Students do often learn parts of 10 before they learn parts of 8 and 9. However, 10 is just a small part of the whole picture, so we did not set up the assessment to assess only that number out of the context of what else the child knows or doesn't know. A child who knows the parts of 10 without knowing parts for 7, 8, or 9 is at a much different level than one who knows parts of 10 and all the parts for the smaller numbers. This seems to be the important information that would not show up if you skipped those numbers to assess 10.

If you are required to assess whether your students know parts of 10 specifically, you could assess everyone on 10 and end the assessment after getting that information. The class summary report always shows the last assessment given so if you go on to assess other numbers without including 10, it would not show up on that report. You could however, save that report as a PDF before reassessing your class on other numbers. You can also retrieve that information on the Student Progress Reports.

Please let me know if you have any additional questions.

Thanks,
Kathy
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Question
Re: 2nd Grade Assessments

In 2nd grade, we are going to give Hiding Assessment at the beginning of the year and then in mid-October, we are going to give Grouping Tens after the place value instruction because we believe those understandings are foundational and need to be mastered before starting addition/subtraction instruction in early December.  So…if a student gets A's on all the tasks in Grouping Tens and at some point during the year gets all A's on parts 1 and 2 of Hiding, which assessment is the logical one to give the student next?

Answer
from Kathy Richardson

Before I answer the question about which assessment to do after Grouping Tens and Hiding, I want to comment on something you said. Did you mean you will have teachers give Grouping Tens AFTER the place value instruction? In case you did, let me tell you what I would recommend instead.  The AMC assessments are primarily designed to give teachers the information they need BEFORE they begin instruction.  This is a big shift from what we are used to doing. We usually teach and then "test" to see who got it and who needs more instruction. However, because the AMC assessments determine the level of thinking a child has reached and the level of proficiency they have achieved, they can really help teachers provide appropriate instruction for each child. So for example, if a teacher gives Grouping Tens before instruction, she would know which children are still needing to count by ones, who is counting by tens, who can combine tens and ones but counts on to add or subtract 10 and who already thinks of numbers as composed of tens and ones and needs to move on to a different level.  The children would all be working with the stations but she would be watching for different things and interacting with the children differently depending on what the children need.

So, let's think about what this might look like in the classroom:

The whole class is working with a set of 8 Place Value stations. I stop to observe the children who are working on Paper Shapes.  I know that each of the children working there at the moment have different instructional needs.

I know that Matthew Needs Practice because he counted on to add 10 and counted back to take 10 away during the assessment. So I interrupt him in the middle of filling his Paper Shape and ask him how many tens and ones he has so far.  Then I ask him how many he would have if he made another ten.  I know he will probably need to count on to find out, but  I will continue to ask him that question for a few days knowing that he will eventually realize he knows the answer without counting. My questioning focuses him on thinking about what is happening and not just doing the task without thinking. 

I know that LeeAnn was Ready to Apply on the assessment because she could add 10 and take 10 away without counting. I challenge her by asking her to tell me how many she has on her Paper Shape so far and then to think about how many more tens it might take to finish the Paper Shape. I want her to begin thinking more about the actual quantities she is working with and the relationships between the numbers. So if she has 2 tens and 3 ones on the Paper Shape, I could ask her to think about what the total might be.  Or if she had filled the Paper Shape up about half way, I would see if she noticed that she could double the number to get a reasonable estimate. In the next day or two, I could ask her to add two Paper Shapes. Over time, I would be looking to see if she needed to actually move the counters to see how many tens and ones there are all together or if she could reorganize the cubes mentally. 

I know that Eddie Needs a Prerequisite. But I don't want to isolate him from the class. So I want him to do the stations along with the other children but I know that I can't expect him to answer the same questions I might ask Matthew or LeeAnn.  I listen to him count all the cubes on his Paper Shape to make sure he is counting correctly.  In a few days, I could begin asking him to snap the Unifix cubes together into ten sticks and see how many sticks he could make. 
If teachers realize that the assessments are to inform their instruction and not just "judge" their teaching, I think they will find them more useful and over time will find better and better ways to help each of their children to move along in their understanding.

So…if a student gets A's on all the tasks in Grouping Tens and at some point during the year gets all A's on parts 1 and 2 of Hiding, which assessment is the logical one to give the student next?

I would suggest going on to Two Digit Addition and Subtraction. If a child has some difficulty (gets an N or an I), I would go back and assess them on Ten Frames.

I met with all of my 2nd grade teachers recently about their Hiding Assessment data and this question came up.  They noticed that while assessing the number 7, the assessment also assesses one or two of the combinations of 6 and wondered why. 

Other numbers are included in the What if section of the assessment as a way of checking retention of combinations the children  learned previously and to see if they are flexible in thinking about the combinations. Children have a tendency to focus on what they are learning at the moment without connecting it to what they know so we want to continually ask them questions that will help them see how it is all related. I discuss this very briefly on p. 39 under Section 1 heading in The Hiding Assessment book. 

Kathy
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Question
Re: Strategies for Two-Digit Addition and Subtraction

I am confused between the top three choices we are given to choose from for the strategies they used. The choices are:

  • Knows parts to make/add tens
  • Counts to make/add tens
  • Visualizes written problem

What kind of answer would get the top strategy? I keep thinking that they have to know parts to ten (for instance, in 28 + 16, 8 + 2 more gives me ten and 6 ones are left over), but my fellow teachers are saying that if they know to combine the tens and then combine the ones and then regroup then I could choose the first strategy.

Here is an example of what most of my kids tell me when they explain:
(28+16)

First, I added 20 plus 10 to get 30. Then I added 8 + 6 to get 14. I can't have 14 ones, so I added the ten from 14 to the 30 to get 40 and then I have four ones left over so the answer is 44. 

Is this kind of answer worthy for the top strategy choice? 

As for the second strategy (counts to make/add tens) I am just not sure what the difference is between that one and the first one.

Answer
from Kathy Richardson

First, I want to give you some information about the thinking behind the assessment that I think will help you interpret what the kids know. 

First of all, this assessment is different from most other assessments of 2-digit addition and subtraction because we are looking for the level of understanding of the underlying mathematics rather than the ability to get right answers. We are looking to see if the children think of numbers as tens and ones and use that knowledge to arrive at the answer. 

-Knows parts to make/add tens
The child is making and adding tens and knows the combinations used. (So if they added 8 and 6, they would know the answer is 14 without needing to count. Or if they made a ten they would know they needed 2 to make a ten and 4 ones would be left over.)

-Counts to make/add tens
The child is making and adding tens but needs to figure out the combinations used. (For example, they might count on to add 8 + 6 or if they took 2 of the 6 to make a ten, they would need to figure out that 4 ones would be left over)

The assessment does not distinguish between different ways kids use tens and ones to add.

So kids might add the tens and then the ones and then add the 30 and the 14.

They might add ten to 28 to get 38 and then break up the 6 to get 40 + 4.

They might pretend that 28 is 30 and add 16 to get 46 and then take off the 2 they added on to change 28 to 30.

All of these would be the first or second choice depending on whether they knew the "facts" or not. You are right that adding the tens and then the ones is not as sophisticated as breaking up the 6 to make a ten would be. I would make a note of that. Then, I would challenge the kids to see if they could find a way to add the 16 without breaking up the 28. Some won't be there yet so it won't be a requirement. I would just say, "I am wondering if anyone can figure out a way to add the 16 to the 28 without breaking up the 28." I would have them all build the 2 tens and 8 ones and see what they can come up with. 

-Visualizes written problem
The child is not thinking about the model in front of them but is thinking about the symbols as though the problem were written down.

What concerns me most about the response you say is typical for your students is that it seems like the kids are thinking about "doing a problem" rather than about combining tens. 

Do you think they are visualizing a written problem when they answer or are they just using the language they are used to using in the classroom?
It is very subtle, but I think it would be easier to tell they were thinking about groups of tens if they said:

First, I added  2 tens and 1 more ten and I got 3 tens. Then I added the 8 and the 6 and I got 14. Then I took the ten out of the 14 and put it with the other tens and that made 4 tens and I had 4 left so that makes 4 tens and 4 left over. That makes 44.

Remember, the assessment is intended to give us information so we can provide kids with the instruction they need to move forward.  It is not about judging you or the children. As you give the assessments, try to think about "What do they need from me?" 

I hope this helped. I really love getting questions from teachers. Please feel free to send me any other questions that come up.
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Question
Re: AMC Anywhere Reports: What do the shapes mean?

My school is using the web-based version of Assessing Math Concepts (AMC Anywhere). When I'm looking at my class summary report generated by AMC Anywhere, I see that there are different colored shapes that indicate the instructional level. What do the shapes mean? I can't find that information anywhere.

Answer
from Kathy Richardson

Here is some information about the new symbols on the Class Summary reports.

The shapes and colors were added to give you a visual picture of how your kids are doing.

I think you will see the real value of these symbols if you look at the Instructional Report.

On the Instructional Report, the children are organized by level so you can see at a glance which children are at the same level.

N ( Reddish Square) Needs Prerequisite
I (Blue Triangle) Needs Instruction
P (Yellow Circle) Needs Practice
A-(Yellow Circle) Not Quite Ready to Apply
A (Green Rhombus) Ready to Apply

The shapes are used to highlight what the child knows (highest A) and what they need to work on (the lowest P - or I or N in those cases where the child has not reached the P level yet).

The particular colors and shapes have no meaning. They were just chosen arbitrarily.

I hope this is helpful. If this is not clear or you need more information, let me know.

Best wishes for a great school year.

Kathy
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Question
RE: Two Digit Addition and Subtraction

I have a question about AMC Assessment 9, Two Digit Addition and Subtraction.  I am struggling to find the connection between the student responses from the interview and the recommended stations.  In the other eight AMC assessments it is easy for me to see where a child's instructional level is an I or a P what stations to use based on the Linking Assessment and Instruction section of the AMC Concept book.  Those connects are not so easy for me to make in AMC Assessment 9.  For example, on Part One of Student Interview, the heading in the Summarizing Instructional Needs is Adding Up Tens, With Model, and Relationships/Procedures.  When I look on pages 62-65 of the book, trying to find stations to connect, it lists Forming and Counting Groups (Instruct and Practice), Two-Digit Addition and Subtraction (Practice), Comparative Subtraction (Practice), and Combining and Separating 1 Ten and Some More (Practice).  I do not see experiences that are recommended from the Assessment 9 book that are instructing and/or practicing the critical learning phases that are being asked in the interview.  HELP!

Answer
from Kathy Richardson

I hope the following information will help make things clearer. 

At this level, children need to apply what they have learned about parts of numbers, number relationships, and numbers as tens and ones to solve problems. It is really integrating and using what they have learned thus far.

I think the Goals in this case are as important as the Critical Learning Phases when planning instruction. 

Goals

  • To use what is known about single digit numbers to add and subtract two-digit numbers
  • To use what is known about numbers as tens and ones to add and subtract two-digit number
  • To describe how they solve problems

Critical Learning Phases

  • Tells how many to make the next ten
  • Combines numbers by reorganizing into tens and leftovers when necessary
  • Breaks apart tens when necessary and reorganizes them into tens and ones

Children solve problems in the following ways:

I • Counts all or on. Children are thinking of numbers as a collection of ones instead of as groups of tens and leftover ones.

f they count all- they need more work with learning about tens and ones.  Go back to Grouping Games and Organizing into Tens and Ones.  They need to practice organizing into tens and ones until they can make tens and know the total number of tens without counting. 

P • Uses tens and ones when solving problems but they need to figure out the combinations needed to make tens and leftovers and do not easily keep in mind the number of tens they have formed or have left.

If they have to figure out the number needed to make a ten or need to count by tens, or need the model, they need to practice adding and subtracting. (p. 64-65) If they really struggle, they can practice using 1 ten and some more as listed on p. 65).

They need to practice adding and subtracting using models until they can do the problems without models. And can apply what they know to problems presented symbolically.

A• Adds and Subtracts using tens and ones without needing to figure out the combinations or totals and without needing a model.

 

AMC Two-Digit Addition/Subtraction assesses the following levels:

1. Making Tens: Going Back( + 20 and + 12)
, See p. 61 - 62

I• Needs instruction
Counts all or on
Need experiences learning to form and count groups 

P• Needs practice
Figures out tens or counts by tens (See p. 63)
Needs experiences organizing into tens and ones

A• Ready to apply
Adds with ease
Move on - and provide instruction according to what they did on the rest of the assessment

 

2. Making/ Breaking Tens Using Models 

I• Needs instruction

Counts all or on
Needs experiences organizing into tens and ones (see p. 63)

P• Needs practice
Figures out tens or counts by tens (See p. 64)
Needs experiences adding and subtracting 2 digit numbers 

A• Ready to apply
Adds with ease
Move on - if need models, continue practice to point don't need
models (See p.  64).
Also go on to Comparative Subtraction (See p. 65).

Making/Breaking Tens - Presented Symbolically
Children need to apply what they know about adding and subtracting tens when using models to what they do with symbols. 
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Question
Two Digit Addition and Subtraction – Going back?

I am using AMC Anywhere. I completed Part 2 of Assessment 9, Two-Digit Addition and Subtraction with a student, and they received an "N".  Do I go back to do another assessment or go back to Part 1 of the assessment if Part 2 was given first? Ex: I assessed using  Part 2 of Two-Digit Addition and Subtraction. Do I go back to Assessment 8, Grouping Tens,  or Part 1 of Two-Digit Addition and Subtraction?

Answer
from Kathy Richardson

If a student gets an "N" on any assessment, it means they need a prerequisite because they show no understanding of the concepts in that assessment.  In the case of Two-Digit, it is appropriate to go back to Grouping Tens to see if there is any understanding of tens and ones.
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Question
Re: Counting Objects

A kindergarten student received a "N" on Counting Objects, Part 2,Task 3, One More/One Less. The teacher gave the assessment using AMC Anywhere, the web-based version. What does the N mean? Did the program not allow the teacher to continue on to Task 4 because of how the student scored on Task 3?

Answer
from Kathy Richardson

A child who "Needs Prerequisite (N)" is incorrect 2 or 3 times out of the three questions asked. The assessment results would show what range of numbers the child was working with when they received an N and whether it was for One More or One Less. The child does not go on to Task 4 if they got an N because Task 4 assumes proficiency with Task 3. In Task 3, the child is asked to tell one more when the numbers are presented in sequence. In Task 4, they are asked to tell one more when the numbers are not in sequence.
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Question
Re: Comments and Notes Section of AMC Anywhere

When one of our teachers enters comments into the assessments, using the web-based version (AMC Anywhere), the comments do not "stick" to that question. The comments show up on subsequent questions as well, even if they don't apply, and my teachers have to undo them. Is there a way around this?

Answer
from Kathy Richardson

Unfortunately, the program cannot link comments or notes to just one answer. The comments are to summarize the assessment in general. It is probably best to enter the comments at the end. However, if you do mark something during the assessment, you need to know it will show up at the bottom of the report and not be linked to any particular question. The same is true for the notes. If you type in a note, it will show up at the end of the report, so you need to be specific, since those will also not be linked to any particular question.
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Question
Re: Grouping Tens

On the Grouping Tens Assessment the question states, "Does this help you know how many altogether?" Our second grade staff is thinking the question should read (so that the student has a response that we put into the system) "How many altogether?"

Answer
from Kathy Richardson

The question in Grouping Tens is written in that way so that a child who does not know the answer does not feel they should know.  However, I have never had a child who didn't tell me how many altogether if they knew. If they should happen to just say, "Yes", then ask, "How many?"
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Question
Re: Using Assessment Information/Data

1. If a student scores an *N on the first section of the assessment, should the teacher go back and begin with the previous assessment (i.e.: Starts with Train Combinations so go back to Number Arrangements)?

2. When starting to plan for activities and grouping, should the students be grouped according to their level of performance within the benchmark? For example: If a teacher assesses seven students, is it feasible that the teacher would then break those seven students up into 2-3 groups?

3. Is it reasonable to expect that a teacher would meet with her targeted groups one time a week, possibly two times a week?

Answer
from Kathy Richardson

Here are my answers to your questions:

1. If a student scores an *N on the first section of the assessment, should the teacher go back and begin with the previous assessment (i.e.:  Starts with Train Combinations so go back to Number Arrangements)?

Yes. Going back to the previous assessment is exactly what you want to do. 
This will help you identify any pre-requisite understandings that the child does not have. 

2. When starting to plan for activities and grouping, should the students be grouped according to their level of performance within the benchmark?  For example:  If a teacher assesses seven students, is it feasible that the teacher would then break those seven students up into 2-3 groups?

Most of the time, the teacher will not need to break the children up into little groups unless she has determined that the children need very different things to move forward. I try to use what I call "expandable tasks" so each child can work with the same tasks but will work with the numbers that are appropriate for them.

So if the children were working with parts of numbers, using toothpicks, for example,  some might be making arrangements of 4 one day and 5 another day; another group might be working with 5s most of the time as well as beginning to work sometimes with 6s as well. I would be interacting with the children differently depending on their level. For example, if a child was an I on 5 and a P on 4, I would ask the following types of questions:  "What parts do you see in this arrangement? Can you find any other arrangements that have the same parts? Can you find any that have different parts?" If a child was "ready to apply" for parts of 5 and almost ready to apply for parts of 6, I would ask the following types of questions: "What parts do you see in this arrangement?" If the child said they saw 2 and 3, I might challenge them by asking, "What if you had 6 toothpicks instead of 5 toothpicks and one part had 3 toothpicks, how many toothpicks would be in the other part?" 

3. Is it reasonable to expect that a teacher would meet with her targeted groups one time a week, possibly two times a week?

I would try to meet with targeted groups three or four times a week but for very short periods of time. I think daily short sessions will be more productive than occasional long lessons.  I would probably do the same set of activities over and over with them. For example, if a group of children needs to learn parts of 4, I would do a couple of minutes of The Tub Game and then a couple of minutes of The Cave Game and a couple of minutes of Number Shapes: On and Off. I would do the same the next day and maybe add in Grab Bag Subtraction to see if they are remembering any of the parts. I would try to keep it simple and short and frequent. 

I hope this helps. Let me know if you have any additional questions. 


Kathy
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Question
Re: Changing Numbers

Kindergarten is looking at implementing Assessment #2:  Changing Numbers and we were wondering why this particular assessment doesn't provide a choice of what set of numbers (range of numbers) to begin assessment with.  For our kindergarten students, we were thinking that starting with set 2: 2,5,4,6 would be more appropriate as these are smaller quantities and more students would have entry into task.  We were a little concerned that starting with set 1:  5,8,6,10 might end up frustrating some students.  Can you share information for the reasoning behind this sequence of numbers sets?

Answer
from Kathy Richardson

Here is my thinking behind having all children start with Numbers to 10 for the Changing Numbers Assessment. 
We want to know how children think when they are presented with the task of changing one number to another. We can learn much more about what a child knows about numbers when we start with numbers to 10 than when we start with numbers to 6. It is important to remember that we are trying to find out what a child does and does not understand. Children will just do whatever they know how to do and will not realize they are doing anything wrong even if they make a new pile or add on to the existing pile -but teachers will gain much more insight into children's thinking. The numbers to 6 can help complete the picture but do not give the whole picture by themselves.
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Question
Re: Ten Frames: Subtraction

I have a question about the Ten Frames – subtraction (13 – 6 frames/questions).
Are we to show the turned-over ten frame (pretend ten frame) when it asks, "If 13 stars ... and use them to fill this ten frame, would you have some left over?"

Also, are we to show the ten frame with 3 stars when it asks, "Take away 6...."?  Is this frame supposed to be turned over?

We have different interpretations of what to do.  Some feel we are not supposed to show any ten frames for this problem.

Answer
from Kathy Richardson

The problem 13-6 is using "pretend ten frames," so there should be no ten frames in view of the child at all.

The wording should be, "If you had 13 stars and you used 10 of them to fill a ten frame, would you have some left over?"

"If you needed to take away 6 stars and you took away 3 first, would you still need to take some away?"

I never noticed before that we used "this" and "these". I will have that fixed. 

Thanks,
Kathy
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Question
Re: Grouping Tens

I have a question about the Grouping Tens assessment.  When I asked the question for the student to add/subtract 30, the student got the answer correct.  When I asked him how he figured it out, he basically told me that he stacked the problem in his head and added the ones and then the tens.  Which strategy would this fit under?  The strategies choices are: Add 10, Count by 10s, Count by 1s, Guesses.  

Answer
from Kathy Richardson

Since it is impossible to list all the responses a child might make, I have a rule of thumb on how to handle it.

I think back to the instructional levels and what they mean.

Ready to Apply (A) means the child fully understands and does not need any more instruction on this concept.

Needs Practice (P) means the child understands what is happening but needs more work to become proficient.

Needs Instruction (I) means the child has just an inkling of what is going on and needs quite a bit of support from the teacher.

Needs Prerequisite (N) means the child needs to work on something else before he is ready for this concept.

Those levels correspond to the following responses:
A Adds tens
P Counts by tens
I Counts by ones
N Guesses

Since there is not a response that fits, I would choose the instructional level that fits. I would pick Counts by tens which means the child Needs Practice. I chose this because he would not have gotten to this part of the assessment unless he had a pretty good idea of tens and ones. 

Then, I would make a note under comments that he used the standard algorithm to get the answer. Then during instruction, I would work on having him see that he can add groups of tens to any number without using the algorithm- but just by thinking about how many tens he would have if he added them.
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Question
Re: Hiding Assessment

I wanted to assess a student on specific numbers: 4, 5, and 10 on Part 1.  So I begin with 4 and then go to 5.  In order to do 10, I have to end the assessment and then enter again as a new assessment.  I am thinking that the first session isn't being recorded.

Yesterday, I assessed a number of students and the information is not being recorded.  I am wondering if it is because of going out of one session and starting another.

Answer
from Kathy Richardson

There is an explanation for why you are not seeing the session where you assessed children on 4 and 5. The class summary always shows the latest assessment which, in this case, is the assessment on the number 10. You would have to go to the child's progress report to see both sessions. The only thing I can suggest if you really need to assess every child on the number 10, no matter how they do on numbers from 6 through 9, is that you assess all the children on 10 first. You could then make PDF copies of the class summaries that show these results. Then you could assess 4 and 5, and because it would be the latest assessment, those results would show up on the class report.

I think it would be useful for you to know why the Hiding Assessment works the way it does. I designed the assessment so teachers could find out what number combinations a child knows without counting and what number combinations the child still needs to work on. It is not really intended to find out whether a child knows or does not know any particular number. This is because it is possible for one student to know 4 and 5 quickly and easily, but not to be able to do 6 at all, and for another child to know not only 4 and 5, but also 6, 7, and 8.  These children are at very different places and need very different instruction.

If you want to set a benchmark for knowing 4 and 5, you can do that and find out which children meet the benchmark and which children do not.  

Le t me know if you have any further questions about the Hiding Assessment or any others. 

Kathy
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Question
Re: Combination Trains

I made an observation. The student seems to catch on to the types of questions being asked and is therefore ready to answer the questions quickly. So for example, while I am entering the information to the question, “How many blue cubes?” it seems to me that he is able to count the yellow ones so that he can quickly tell me the answer. I am not positive that he counted (as that can be done quickly and quietly in his head), but it does seem as something that can happen. I have also noticed that same thing on other assessments. For example, in the Hiding Assessment, while I am asking how many are hiding, it seems that some of the students are doing the math in their head and then can give me a quick response. As I said before, I am not sure if that is what they are doing, but it does seem to be a way of "cheating" the test. Just wondering if you have addressed this problem before and what I should do?

Answer
from Kathy Richardson

It is good to be aware of what the children are doing to get an answer. Body language and the length of pauses give you some important information that you can't get by just listening for the answer. If you suspect a child is counting, ask, "How did you think about it?" If the children know you are truly interested in what they actually did, they will tell you. If they say something like, "I just knew," but you don't think that is true, I would again say, "How did you think about that?" The critical factor here is that the child knows that you want to know how they did it - even if they counted.

In a truly safe environment, is not necessary for them to hide what they did. They may need some reassurance that however they got their answer is okay. You just want to know what they did.
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Question
Re: Ten Frames Assessment

When I give the Ten Frames assessment, I find that it goes on to the next question when I think it is clear the child will need to count to get an answer. Shouldn't it stop?
 
Answer
from Kathy Richardson

The Ten Frames assessment gives the instructional level for 4 areas:  1: Adding Ones to a Ten (10 + 9 and 6 + 10); 2: Knows Parts of Numbers;  3:  Making a Ten and Adding Ones (8 + 7 and 7 + 6 and using a pretend ten frame 8 + 5); and 4: Recognizing Ten More (18 + 5).
 
There are several stopping places built into Ten Frames. Generally speaking, if the child shows any awareness of 10, the assessment will continue.

The first stopping place occurs after the first 2 questions (10 + 9 and 6 + 10).  If the child knows at least one answer without counting, or counts on for both problems, the assessment will go on so teachers can find out how the child determines the total after making a ten. If you do not want to go on, however, you can end the assessment and get the instructional level for that part.

The next stopping place is after 8 + 7 and 7 + 6. If the student counts all or counts on from 8 or 7, the assessment will stop and he will not be asked to work with a "pretend" ten frame. However, the 3 problems go together to make one instructional level, so you can't stop it yourself without getting an “Incomplete”. 

There is one more stopping place. The assessment will not go on after the "pretend ten frame" question if the student counts all or counts on from 8 for that problem.  It will go on if the child counts on from 10. If you do not want to go on after that response, you can end the assessment there yourself. 
 
I also suggest you go into demo mode and see what happens when you end at different points before you actually try stopping the assessment yourself while assessing a student.

Kathy
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Question
Re: AMC Counting Assessment

In a recent administration of the Counting Objects (#1) assessment with Kindergarteners, the following question arose:

Sometimes, students will miscount the quantity presented (ex. we present 12 blocks but they count 13) but can name the miscounted quantity easily when asked "How many did you count?" (ex. they say "13"). The options for recording are "Knows, Recounts To Find Out, or Doesn't Remember". While they are able to recall the quantity they counted, they counted the pile incorrectly to begin with. How can this be accurately recorded?

We are considering using "Doesn't Remember", as we see that we are able to document the inconsistency in the following question related to Rote Counting (skips 1 number or sequence is incorrect). Is this the best way to do this?

We appreciate any thoughts you can provide regarding this.

Answer
from Kathy Richardson

I understand the confusion, but let me share my thinking.

There is a stage of thinking that I refer to as Count and Land. At this stage, the child is focused on the process of touching each object, saying the sequence, and telling where they landed. The number has no meaning to them, so if you ask them, "How many did you count?', they will either shrug their shoulders or recount. The student you are describing was able to hold the number he "thinks" he counted and is able to tell you that number. The fact it is an incorrect number is a different issue. As far as the child is concerned, it is the number he counted. So the response that describes this is "Knows". The fact the child lost track will show up when you choose the indicator that describes that: Loses track.

I know it feels "wrong" to give a child credit for a wrong answer, but what we need to do is analyze what we are trying to find out and if the child is or is not able to do that.

Let me know if you have further questions about this or have any other questions.

Best,
Kathy
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Question
Re: AMC Anywhere Reports: What do the Shapes Mean?

My school is using the web-based version of Assessing Math Concepts (AMC Anywhere). When I'm looking at my class summary report generated by AMC Anywhere, I see that there are different colored shapes that indicate the instructional level. What do the shapes mean? I can't find that information anywhere.

Answer
from Kathy Richardson

Here is some information about the new symbols on the Class Summary reports.

The shapes and colors were added to give you a visual picture of how your kids are doing.

I think you will see the real value of these symbols if you look at the Instructional Report.

On the Instructional Report, the children are organized by level so you can see at a glance which children are at the same level.

N ( Reddish Square) Needs Prerequisite
I (Blue Triangle) Needs Instruction
P (Yellow Circle) Needs Practice
A-(Yellow Circle) Not Quite Ready to Apply
A (Green Rhombus) Ready to Apply

The shapes are used to highlight what the child knows (highest A) and what they need to work on (the lowest P - or I or N in those cases where the child has not reached the P level yet).

The particular colors and shapes have no meaning. They were just chosen arbitrarily.

I hope this is helpful. If this is not clear or you need more information, let me know.

Thanks,
Kathy
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Question
Re: Students Passing the Tests


I am doing a small professional development with some teachers on Monday. 10 teachers k-2 grade. I am struggling with some comments the first grade teachers are making: “we can’t get them to pass the test for concept 3!” “they need more practice counting backward so they can pass the counting test” (When I asked them about this, they said for the one less part).

I am having them re-read some pages from the beginning of the assessment books pages 3-10 to have a deeper understanding of what and why we do stations. I am also going to have them dig into each concept and unpack the critical learning phases a bit.

What else would you suggest? I need your wisdom. Questions I could ask to nudge some adult thinking??

Answer
from Kathy Richardson

Here are a few random thoughts to start with.

Each assessment is designed to identify a wide range of levels. The counting assessment helps identify instructional levels from the child who cannot yet count to 4 to a child who knows one less than 80. This is so teachers can determine through one assessment the instructional needs of all her students. That is not the same as a "goal" for all students. The right goal for each student depends on what they already know- not on what someone else has decided they should know. If teachers want to help children develop the idea of one less, they need to know where to start... In other words, a child who does not know 1 less than 7 does not need to practice one less than 14. The goal is not to memorize one less, it is to have an understanding of the structure of numbers even to the point they see that 1 less than 8 must be 7. Learning one less is much, much more difficult than learning one more. This is because young children do not have the concept of "reversibility." They can't conceptualize what comes before - they have trouble thinking "backwards."

When a whole group of teachers are having a problem with a concept, it is bigger than a particular teacher's teaching abilities. There is something else going on. My recommendation is that the goal be changed to one that most kids develop with meaningful counting experiences and some practice with activities like Book 1: 1-16 One More/One Less, 1-17 Give and Take, Level 1, 1:1-8 Grow and Shrink.

The comment that troubles me the most is the idea they have to "pass a test". That is contradictory to the idea that children are "developing number concepts." They are building a web of interrelated ideas - not climbing a ladder of skills.

Off the top of my head, I am thinking of some exercises you might try. You might ask all of them: If they were to "set their own goals" for what they think is reasonable for most of their kids (with good instruction), what would they set? If they knew they were accountable for reasonable goals, how would that change what they do?

What are the long term consequences of memorizing in order to pass tests?

If I think of more, I will let you know. Also, if you have some more questions that will nudge my thinking, let me know.

Thanks,
Kathy
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Question
Re: Notes/Comments on Web Version of AMC

There is only one Notes/Comment page per assessment on the Web Version, not one for each task. Teachers are finding it difficult to use this effectively because they have to note each task for each comment; comments don't correspond with tasks.
 
Answer
from Kathy Richardson

The comments were intended to be generalizations, not specific to each question. Your question is timely since I have just finished a document explaining the thinking behind the comments.
Download PDF Document | 350 KB

Kathy
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