Will There Be Enough Food? Report Cards, Assessment and Inquiry

Whenever we had guests over for supper when I was a child, my mother would always worry that she did not have enough food. Despite decades of experience in cooking ‘for company,’ she still has that worry today. And we have never run out! I am reminded of that as my partner and I review all our assessment information to write an evaluative final report card. We feel like we just wrote the last one yesterday in some ways, and worry we won’t have enough “food” to share!

The Theory:

Young children show their understanding by doing, showing, and telling. Early Learning–Kindergarten teams need to use assessment strategies of observing, listening, and asking probing questions in order to assess and evaluate children’s achievement. (FDELK Draft Program, p. 28)

Observation, as well as the documentation of observations, is the most important method for gaining assessment information about a young child as he or she works and interacts in the classroom.

Observation should be the primary assessment strategy used in the early learning program. (FDELK Draft Program, p. 30)

Reporting should reflect achievement in the skills and strategies that the children are developing as they progress through the program. (FDELK Draft Program, p. 32)

The Practical:

  Working in an inquiry stance with students, where there isn’t generally one experience, representation, observation… that all did on a given topic as in the way we planned those ‘theme’ experiences in the past, we worry that maybe we ‘fed’ some too little. So at this time of year, when we really look at the sum total of what we know about ‘this student’s development in relation to…’ we were gratified to learn that all that documentation of their thinking was plenty of food.  Taking the Science strand as an example, we had many quotations of their thinking, their own drawn and written representations, photos of the learning in action… all in a variety of different experiences all over the classroom and in our notes.

This year we worked toward building methods of observation and making the childrens' thinking visible in the classroom. That will continue to be the journey. My learning as I write the report cards is to add a deeper layer of reflection on this. To take the bird’s eye view of our assessment information more often, maybe once a month next year. In looking at Science as an example, I notice that some students are more drawn to this strand, just as some are more drawn to visual arts, and note that we need to continue to invite and look for interests, questions and opportunities to provoke the engagement of those who gravitate more to other areas (and bring the ‘science inquiry stance’ there). Some students were more drawn to nature and environmental explorations (e.g. the snails that were carted in),

some to ‘substance’ exploration (e.g. cornstarch goop), some to investigations (e.g. the ‘wheels’ experiments),

 some to ‘curiosity’ explorations (e.g.  an individual Dollarama egg poacher put with a large paper to record thoughts about “What can this be used for?”), some to ‘design’ explorations (e.g. constructing a car; taking apart a real telephone), etc…

The ‘bird’s eye view,’ let us see that pattern of interests a little more clearly which of course becomes another stepping stone towards planning.

In conclusion, this report card is really bringing clarity to the value of our observations, the value of taking time to discuss those observations. For example,  standing back and looking at a documentation panel together and asking ourselves, “What is this telling us about what they know, strengths, interests, next and future steps?”

Now I really must get back to that report card writing… although this has been a worthwhile reflection… it has also been a procrastination LOL!

Playing with the Mathematics Itself

The Theory:

Knowing that I need to work on my own understanding of how math concepts develop (see last blog), I try as much as possible to ‘consult with the experts’ when planning. We are just swinging back into Geometry, so I went to Van De Walle’s  “Teaching Student-Centred Mathematics” (Grades K-3) and the K-3 Guide to Effective Instruction in Mathematics – Geometry and Spatial Sense (see link below) for support. Kindergarteners are learning to “explore, sort, and compare” as well as “identify and describe, using common geometric terms” two-dimensional shapes and three-dimensional figures. The “identify” is only one small part of that, the bigger part is becoming aware of geometric properties. “We know now that rich experiences with shape and spatial relationships, when provided consistently over time, can and do develop spatial sense” (Van De Walle, p. 187). Kindergarteners are generally working at Level 0 of van Heile’s Levels of Geometric Thought (see Guide, p. 12) where students identify identify two-dimensional shapes and three-dimensional figures by their appearance as a whole.

Students do not describe properties (defining characteristics) of shapes and figures. We are supporting them to work towards understanding that all shapes or figures within a class share common properties (e.g., all rectangles have four sides, with opposite sides parallel and congruent).  Progression from one level to the next is less dependent on students’ age or maturation than on instruction that promotes reasoning about geometric ideas.

Van de Walle and the Guide recommend that students have a lot of experience with sorting and classifying shapes.

 

The Practical:

Following ideas from the Guide about triangles, after a quick “Minds On” (telling a partner what shapes they could see in a piece of art), we began the “real triangles” problem. I gave pairs a baggie with about 10 different triangles (traditional and non-traditional forms) printed on paper. I did not say that the bag contained triangles, just that it had pictures of shapes. Their problem to solve was to find and bring back to the circle the “real triangles.” While they worked on sorting with their partners, I took anecdotal notes on the language that I heard.  For our consolidation, we sat in a circle with the “real triangles” on the floor in front of us to show others. A few students shared why they had picked these. The idea of three sides, and three “points” (vertices) was shared. The idea that they were actually all triangles was not. Hmmmm. Right in line with what I had learned about Level 0!

Our next step… Sort again, only this time, pose the question, “What are the other shapes?”

The Guide also has a great idea on page 18, to continue with shapes that are ‘trianglish’ (e.g. open three sides; soft corners…) and to ask why they aren’t triangles, and how they could be made into triangles!

We’ll see how that goes, then move to the “real rectangle!”

My key learning here continues to be the need for my own continued learning about the development of mathematical concepts, paired with effective problems that invite the students to engage with meaningful mathematics.

 

References:

 

K-3 Guide to Effective Instruction in Mathematics – Geometry and Spatial Sense

  http://etfo-ot.net/Site/wp-content/uploads/2009/05/geomspatsense-guideeffectinstrmathgrk-3.pdf

 

Teaching Student-Centred Mathematics, K-3, John Van de Walle and LouAnn Lovin.

Rethinking Mathematics

Thank you for the commentary posted to the previous blog:

Wondering if you have dug into math learning through the 3 part lesson? We are wondering what this would look like in our FDK class?

I would frankly have to say that math is an area of our program that I am not nearly satisfied with. However I am happy to share where I am at in my rethinking right now.

The Theory

My current key sources have been the Full-Day Early Learning Kindergarten Program (draft), a fairly hot-off-the-press literature review about “Mathematics for Young Children”, a Capacity Building Series article “Maximizing Student Mathematical Learning in the Early Years” and the EduGains.ca video on “Numeracy Through the Day” (see links below). That information gave me some reassurance, and some major pressure! Some highlights of my learning through quotes from some of these sources:

·         Good math experiences in the early years are vital! Here’s the pressure that is clear in the literature review undertaken by M4YC:

“There is ample evidence that a child’s Socioeconomic status (SES) is strongly predictive of mathematics achievement.” (p.10)

“For at risk children, early intervention and education, in the form of rich mathematical experiences, provide the only hope of closing the gap created by SES differences – a gap that widens without intentional mathematics intervention.” (p.13)

 “Children’s school entry mathematics abilities were not only consistently predictive of later achievement in mathematics but in reading as well.” (p.15)

“…robust studies point to the incredible importance of mathematics learning for young children to prepare them for school and life success.” (p. 16)

·         We (educators) need to grow our understanding!

“While children demonstrate remarkable facility with many aspects of mathematics, many early childhood teachers do not have a strong mathematical background. At this time when children’s mathematical potential is great, it is imperative that early childhood teachers have the competence and confidence to engage meaningfully with both the children and their mathematics.” (M4YC, p. 18)

·         Most children come to school with more mathematical knowledge and experience than previously believed but need “math talk” support to grow that understanding.

“Most young children come to school already knowing a great deal about mathematics. Children bring with them an intuitive knowledge of mathematics, which they have developed through curiosity about their physical world and through real-life experiences.” (FDELK Draft Program, p. 20)

“By modelling and fostering math talk throughout the day and across various subject areas, educators can provide the math language that allows students to articulate their ideas… increase growth in understanding of mathematical concepts.” (Maximizing Student Mathematical Learning…, p. 4)

·         Mathematics in the early years classroom requires both math that is found/ provoked/ supported in children’s play, and also rich mathematical instruction (we seem to think these are mutually exclusive, when in fact “overlap is natural and desirable” (M4YC, p. 24):

 “Sarama and Clements suggest that mathematical experiences can be narrowed down into two forms, play that involves mathematics and playing with the mathematics itself.”  (Maximizing Student Mathematics… p. 2)

“The Early Learning–Kindergarten team can create an effective environment to support young children’s learning of mathematics by planning daily hands-on experiences that focus on a particular mathematical concept and by identifying and embedding significant mathematics learning experiences in play, daily routines, and classroom experiences.” (FDELK Draft Program, p. 21)

“High quality instruction in mathematics and high quality play need not compete for time in the classroom. Engaging in both makes each richer and children benefit in every way.” (quotation in EduGains video)

 

The Practical

Here are a few ways that we are currently provoking play that involves mathematics:

1.       Inviting play with math materials

2.       Adding math materials to established play

3.       Acting on the teachable moment in play

4.        Our presence at centres, when we can build on mathematically-oriented in-the-moment play and talk.

Sometimes we notice the math happening, sometimes we look for opportunities to build on mathematical understanding or gaps previously observed. For example, we have a young JK student, who thinks that counting should begin with the number three. As a young soul, he also thinks that the world revolves around him, so I theorize that this obsession with starting counting at “3”may have to do with the amount of time he spent being three years old as numbers began to become relevant to his life. To support his development in play, we have incorporated many opportunities to count, highlight counting and numbers in his environment. We catch every opportunity we can to have him count, and notice numbers during his play!

 

Where we are currently at with playing with the mathematics itself:

With Kindergarten colleagues in my Board a few years ago, we looked at all the specific math expectations of our K Program, with an eye as to sorting which ones needed direct instruction through a highly-scripted transmission modelled math lesson vs. those that could be approached through a problem-solving model. Even I, who had set the others up for this activity, was amazed at how few we found that required the former. That made me a stronger believer in a problem-solving approach.

So what about the “3-Part Lesson?” Rather than working the math through an instructional practice formula, I consider the spirit of the elements of this instructional path that are important as we plan to “play with the mathematics” itself. Our last lesson happened to be a spontaneous example… all the kids were riveted… it had all the great characteristics: real-life context, engagement, stemmed from a student’s comment, and rich, open-ended, higher level math. It not only hit on nearly all of the numeration expectations as well as some of measurement, geometry and data management ones, but was also an example of proportional reasoning at its Kindergarten best, and yet was accessible to all! The problem-solving “How much toilet paper is enough?” question started with the new toilet paper dispenser that we received. The new holder ‘rolled toilet paper out’ with much greater ease and velocity than our previous one. This of course led to the discussion around our “clogging” issues. Little ‘Jen’ informed us that at their house they have a rule that “only 3 squares are allowed.” A mathematics 3-Part Lesson was hatched!

Before/ Getting Started (connect to schema)

How much is 3 squares of our toilet paper? We asked Jen to get us some, and counted out the squares. We also looked at the length of 5 and 8 (the amount/distance from dispenser to floor) squares.

During/ Working On It (problem-solving stage)

Key Question: How much toilet paper is enough? To support the thinking, we wadded up a three square strip into real life usage, and passed it around the group with the questions, “If you were sitting on the toilet, getting ready to wipe your bottom, does this feel like enough? (We also happen to be working on visualization as a reading strategy, LOL). Do you need more? A little more? A lot more?

The students did a Think-Pair-Share and told their partner their opinion and reasons. Students added their names to the ‘length of their choice.’

After/ Consolidation (sharing, reflection, highlights, summary)

"What did most people think was enough toilet paper?" We discussed our results, shared our reasons as a group, and recorded some of them.

Teacher Reflection: We want to look for more opportunities like these! The students were really engaged because the context was very real to them. We could have made further use of comparing mass by the non-standard “feel” of the crunched up balls of all three sizes. I would have liked more ‘hands on’ exploration to it. We could follow up with a post-practical-use survey posted outside the bathroom door!

“Through active participation in mathematics investigations, including problem solving and discussions, children develop their ability to use mathematics as a way of making sense out of their daily experiences.” (FDEL K Draft Program, p. 96)

Not all of our lessons happen to be an engaging spontaneous moment of course! I am trying to keep the idea of problem-solving towards an understanding of a big idea in the forefront of my mind as I comb resources, real-life contexts, literature, etc… for jump-points.

This is where we are at right now… I am sure of more growth as we continue!

Resources:

Full Day Early Learning Kindergarten Program, Draft 2010

http://www.edu.gov.on.ca/eng/curriculum/elementary/kindergarten_english_june3.pdf

Mathematics for Young Children (M4YC), Literature Review

http://sim.abel.yorku.ca/wp-content/uploads/2012/10/M4YC-Lit-Review-2012.pdf

Maximizing Student Mathematical Learning in the Early Years, LNS Capacity Building Series, 2011

http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/CBS_Maximize_Math_Learning.pdf

EduGains.ca, Kindergarten - “Numeracy Through the Day” video

http://www.edugains.ca/newsite/fulldaykinder/videoa.html