Assessment in the Mathematics Classroom

 Author: Julie Johnson

 Introduction

            Common core math standards for kindergarteners are fairly basic, but they set the foundation for all future mathematics in the subsequent years of education. Identifying numbers, counting, comparing numbers, beginning to understand the concept of addition and subtraction, and describing, comparing, and classifying objects and shapes are among the expectations that kindergarten aged students should be able to master. In Module 1, I explored several of the common core standards for kindergarten that I perceived to be more difficult and subsequently developed a tool kit of activities to address those standards in the classroom. In this paper I will review and expand upon those instructional strategies by developing assessment strategies for each activity. Accurate assessment of the crucial common core standards is important because early intervention for struggling students can go a long way toward ensuring their success in the classroom over the course of their academic career.

 

Common Core Math Standards For Kindergarten and Assessment

            After reviewing the common core math standards for kindergarten, I identified four that I thought would be the most challenging to the children. They included K.OA3, K.NBT1, K.G4, and K.G6 (National Governors Association Center for Best Practices and Council of Chief State School Officers, 2010). Contemporary assessment practices call emphasize documenting children’s demonstrated knowledge and growth. There is a focus on progress and the holistic view of the child. Unlike traditional early child assessments, it is beneficial to record feelings, ideas, and teacher interpretations of what is being observed (Arndt, et al, 2015). Students should also feel empowered to self-correct and take control of their learning. They should be actively involved in formative assessments and allowed to self-regulate their learning whenever possible (Andrade, H., 2010). It is based on these evidence-based concepts that I have developed my assessment strategy for each of the activities in my tool kit.

Tool Kit of Activities

            In Module 1, based on the standards identified above, I developed three research-based activities to address those standards that I think the students might find difficult and detailed them below. In this paper I have expanded the activities to include assessment strategies.

 

Activity 1 – Using colored squares to make different combinations of 5

Grade Level: Kindergarten

Content Area: Mathematics – Decomposing Numbers

Common Core Standard Addressed: K.OA3 “Decompose numbers less than or equal to 10 into pairs in more
than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1) (2010).”

Materials: Colored blocks, 15 yellow squares, 15 green squares, 1 piece of paper with squares, and a glue stick for each student.

Activity Description: In this activity the students will use colored blocks then paper squares to decompose numbers and find how many different combinations of the number 5 they can make using two different colors. Introduce the lesson by showing the students a line of five red blocks. Ask the students to count how many blocks there are and introduce the equation 5+0=5 by writing it on the board. Next trade one of the red blocks for a blue block. Ask the students to count the blocks again. Explain that there are still five blocks but the new equation is 4+1=5. Repeat the entire process changing one block each time until all of the blocks are blue. Have the class look for patterns and make observations of all of the equations on the board and have a discussion about why it happened like that. Let the children try to make their own combinations of five independently using different colored blocks. When you have observed their understanding of the concept using the blocks, allow the students to try to make their own worksheet using the concept and paper squares illustrated in the example photo. This activity can be modified by making the combination number higher or lower for example using 3 instead of 5 to make things easier.

Assessment Strategy: To assess this activity, the teacher will observe the students as they are completing the activity. To encourage the students to self correct, if the teacher witnesses a mistake, they can ask the student if they are sure that their work is correct. The teacher should make notes of which students are self regulating their errors, as well as a record of what mistakes the students are making to determine if many students are struggling with similar concepts or if everyone has understand the concept that has been taught. In this activity, the completed worksheet can also be assessed for accuracy and appropriate intervention can be provided to students who still have errors at the end of the assessment process.

Activity Adapted From: Gavin, M. (2012). Getting Interactive with Common Core: Decomposing Numbers. Kinder Craze. Retrieved 23 August 2016 from http://kindercraze.com/getting-interactive-with-common-core/.

 

Activity 2 – 3-D Shape Museum 

Grade Level: Kindergarten

Content Area: Mathematics – Shapes and Comparisons

Standard Addressed: K.G4, “Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length) (2010). ”

Materials: Assorted Classroom Toys, Examples of Target Shapes, Display Area

Activity Description: In this activity the students will search through the classroom toys to find different 3 dimensional shapes. Some example photos can be seen below. 

The activity will begin with the teacher introducing the target shapes and the characteristics of each shape. The children will then search the classroom to find toys and other objects in the shapes they have discussed and sort them into their relative categories in the display area. At the end of the shape hunt, the students will compare all of the objects of one shape, for example, spheres, and have a discussion about what makes each object a sphere, and why all the objects in this category are spheres when they are different sizes and colors. The discussion can then be extended into comparing 3D and 2D shapes, ie spheres and circles and discussing their similarities and differences.

Assessment Strategy: The assessment strategy for this activity is largely observation and discussion. The teacher will observe and record notes on how successfully or unsuccessfully the students are sorting the shapes. To gauge true understanding, you can ask they children to explain their thought process on why the they are putting specific objects into each category, to make sure that they are sorting the objects by shape and not some other factor like color or size. Also when differentiating between 2D and 3D shapes, the teacher should ask the students to describe their thought process, for example, why are you sorting this object into the ‘pyramid’ category instead of the ‘triangle’ category? 

Activity Adapted From: Katherine, K. (2012). Math Problem Solving. Kindergarten Kindergarten. Retrieved 23 August from http://www.kindergartenkindergarten.com/math-problem-solving/page/2/.

 

Activity 3 – How Many Different Ways Can You Fill a Hexagon?

Grade Level: Kindergarten

Content Area: Mathematics – Shapes and Combinations of Shapes

Standard Addressed: K.G6, “Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?” (2010).”

Materials: Hexagon Template Worksheet, Shape Tiles

Activity Description: In this activity the students will attempt to create hexagons using a multitude of different shapes. The students will be given hexagon templates and many different shape tiles and will then use the tiles to attempt to fill in the hexagons in as many combinations as possible. An example photograph of the activity can be found here. By creating hexagons, or other simpler shapes, the students will be able to see the relationship between different shapes and understand how some shapes can be combined to form different ones. This activity can be adapted in many ways to explore different kinds of shapes.

Assessment Strategy: The assessment strategy for this activity involves a lot of discussion and observation. The teacher should ask questions that allow the students to explain their thought processes when creating new shapes and record the different combinations that each student is using – in this activity, patterns will emerge and some students will find it easier to visualize how certain shapes can be combined while others will have difficulty incorporating other shapes. The teacher should ask questions to encourage them to think about using other shape combinations, for example, how might you use a triangle here? The teacher will encourage the students to be creative and try different combinations while self correcting and evaluating themselves.

Activity Adapted From: Katherine, K. (2012). Math Problem Solving. Kindergarten Kindergarten. Retrieved 23 August from http://www.kindergartenkindergarten.com/math-problem-solving/page/2/.

 

Common Core Sample Test Items

            Next, I accessed several common core sample test items from the Smarter Balanced Assessment Constortiuim and Partnership for Assessment of Readiness of College and Careers and tried out the grade 3 assessment test. Both of these tests seem to align quite well with the common core standards and specifically test the students using problems that address the standards that they should know and be able to do. The SBAC tests seemed to have a more significant alignment with the common core standards, but both tests seemed useful in terms of both formative and summative assessment in helping to determine what the students know, what areas they may need to work on, and what they have learned over a period of time in terms of growth and in relation to relevant standards.

As educators, it’s important to know where your students are going in terms of what things they need to know in order to be successful in school and in life. This way you can design lessons and learning objectives around what you want the students to accomplish during your lessons and to make sure they have mastered their grade level skills as many of these skills are cumulative. Students will need a firm understanding of these skills in order to learn the more complex skills emphasized in the following grade levels.

Conclusion

            Teachers should always have a wide range of activities and assessments in their tool kit to best accommodate the different learning styles and abilities of the students in their classroom. The activities and assessments discussed in this paper are just a few of the many ways that these standards can be addressed and evaluated. It is important to do thorough and accurate assessments to make sure all the students are acquiring essential knowledge and so that early interventions can be provided to struggling students to prevent long term problems. Observation, student self-assessment, and questioning from the teacher should all be a part of the early childhood educator’s assessment tool kit.

            

 

 

 

References

Andrade, H. (2010). Students as the definitive source of formative assessment: Academic self-assessment and the self-regulation of learning. Paper presented at the Northeastern Educational Research Association, Rocky Hill, CT.

Arndt, S. s., & Tesar, M. m. (2015). Early childhood assessment in Aotearoa New Zealand: Critical perspectives and fresh openings. Journal Of Pedagogy / Pedagogický Casopis, 6(2), 71-86. doi:10.1515/jped-2015-0014

Black, P., & Wiliam, D. (2009). Developing the theory of formative assessment. Educational Assessment, Evaluation and Accountability, 21, 5-31.

Gavin, M. (2012). Getting Interactive with Common Core: Decomposing Numbers. Kinder Craze. Retrieved 23 August 2016 from http://kindercraze.com/getting-interactive-with-common-core/.

National Governors Association Center for Best Practices and Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics (pp. 6-8).

Katherine, K. (2012). Math Problem Solving. Kindergarten Kindergarten. Retrieved 23 August from http://www.kindergartenkindergarten.com/math-problem-solving/page/2/.

Lang, L. B., Schoen, R. R., LaVenia, M., Oberlin, M., & Society for Research on Educational Effectiveness, (. (2014). Mathematics Formative Assessment System--Common Core State Standards: A Randomized Field Trial in Kindergarten and First Grade. Society For Research On Educational Effectiveness,