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)?
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.
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
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?
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.
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??
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.