As teachers, we all use some form of assessment to guide our teaching. After all, how would we know which questions to ask, games to play, or activities to plan if we didn’t have some idea about the level of children’s understanding in our classrooms? Differentiated instruction (providing individual children with instruction that matches their readiness to learn that material) is a hallmark of effective teaching in early childhood classrooms. But, there are a lot of them (children) and few of us (teachers), and that fact can make good assessment difficult. This handout provides efficient ways of monitoring children’s progress to better understand how to support their development. We will call this formative assessment.

More specifically, this handout makes use of curriculum-based assessment, in which children have opportunities to demonstrate their understanding through classroom activities, as well as through interactions with both teacher and peers. Teachers can keep track of these with checklists, portfolios, samples of children’s work, and observation notes. Accurately assessing children’s mathematical abilities can be difficult because we can’t really see inside children’s heads. If we hear a child say to another, “You have more dinosaurs than I do!” we can probably assume that child has some sense of number. But is their claim based on the size of the pile of dinosaurs, or the numerosity of both sets of dinosaurs, or maybe even some history of playing with this individual child? These different possibilities make it clear that more information is needed.

Before venturing into a list of techniques that can provide a deeper understanding of children’s mathematical abilities, a few suggestions will be helpful. What you hear at the surface of classroom conversation and interactions might not reflect a child’s true abilities and skills. It is frequently necessary to provide prompts or situations that might support a more accurate assessment. One prompt that has proven effective over many years and in many classrooms is, "tell me how you know." Other useful prompts are: "How did you figure that out?  Why do you think that? Can you show me how you know?" Be ready to follow-up with clarifying questions during the conversation.

Children’s math skills can be assessed in various ways. An example is counting objects (or movements or sounds). You could observe a child counting how many baskets they dunk on the playground, trains they can count when sharing with another child during free play, cotton balls they count out for a collage, times they can hop, or letters in their name. This section provides descriptions of some of the more common assessment formats.

CHECKLISTS
Earlier, checklists were mentioned as a possible way to conduct formative assessments. What would this look like for mathematics? A useful format is a table with rows for names of children and columns for assessments of specific mathematical abilities. It can be useful later if you also add a wide column for noting how you assessed the ability and ways you might support development (e.g., one-to-one correspondence, counting word order, or discussions of sides and corners of shapes).

Are observations in your classroom enough to complete these checklists? Frequently not. Another way of making sure that you can see a child’s understanding in action is by observing them playing or doing activities such as board games, counting games, Mother May I steps, basketball, or gross or fine motor activities involving shape sorters. A third method uses short interview questions. With these, it pays to know what really interests each child so that you can develop activities that will specifically engage them in using their mathematical knowledge.

SAMPLES OF CHILDREN'S WORK
Samples of children’s work can be saved in portfolios in individual boxes or folders and grouped by child or area of assessment (e.g., a folder for all of the children’s progress in geometry). Samples are particularly helpful in sharing with parents what their children are learning. Samples can include the actual work (for example, the collage of cotton balls with observations on counting progress attached on a sticky note or written on the back of the collage) or notated photographs of the work (either electronic or hard copy). Make sure to include some amount of notation in case the sample doesn’t ring any bells three weeks later when you are reviewing them for a parent-teacher conference!

OBSERVATIONS
Observations are a great way of keeping track of a child's progress. However, they can be tricky to keep track of. Developing a system to organize your observation notes is important. It could be done on sticky notes that are eventually attached to a piece of paper with the child’s name, one or several pieces of paper that include observations of all of the children on a specific skill, an electronic Word or text file with observations and photos (e.g., through use of an electronic tablet), or a more elaborate system with tables for specific mathematical skills. One excellent method of keeping track of observations is to pre-print labels or index cards with spaces for important details like the date, child’s name, type of skill/ability/knowledge you are assessing, level of knowledge you’ve observed, and notes. However you choose to record your observations, make sure that you can record the where, when, and what of your observation.

INTERVIEWS
Although perhaps one of the most effective tools of formative assessment, interviews can also be time consuming. Find a way to have in-depth conversations, either scheduled or at opportune times during the day. These can be your greatest opportunity to really understand what a child knows. It can also be tremendous fun. For this sort of assessment you’ll need similar tools to those that are useful for observation. The list of questions in the How Do We Know section above can also provide prompts for digging deeper into a child’s understanding.