Higher Level Thinking with Math Assessments
Location
Boston 1
Session Format
Presentation
Abstract
This paper examines the use of higher level thinking with formative and summative math assessments. Here, the foundational assessments include fact based knowledge and comprehension types of questions. Upon the demonstration of a solid math understanding, the assessment questions then begin to look at applying and analyzing mathematical understanding through real world problem solving. Assessments addressed at these levels of thinking look more deeply into student thinking. They apply mathematical knowledge by selecting problem solving strategies for non-routine challenges. The students discuss problem solving strategies with classmates to compare different methods of solving problems. Next, formative assessments are used that ask students to evaluate and create using mathematical knowledge. Here, they design projects based on foundational knowledge. They create models and useful applications using what they know about math. Examples include engineering projects and scientific studies using data. After feedback, these same projects can be used for summative assessment as well. This paper examines this framework with specific examples.
Keywords
Math assessment higher level thinking
Professional Bio
In August of 2003, Mary Kay Bacallao began as an Associate Professor of Science and Math Education at Mercer University in Georgia. There, she taught classes related to curriculum, math and science education, and early childhood. She also supervised student teachers in the field. Mary Kay Bacallao also became a consultant with the National Urban Alliance, an organization that worked with schools around the United States to strengthen teaching methods. Mary Kay Bacallao developed new manipulatives for mathematics education and wrote curriculum for a course called the Construction of Science and Mathematical Thinking. Some of these manipulatives include the equals game (a game of strategy for the basic facts), the gallon fraction measurement set, quadrilateral pieces, rainbow number puzzles, and star ten cards. Mary Kay Bacallao currently serves as a Professor at Mercer University in the Tift College of Education. Mary Kay Bacallao teaches problem solving, ESOL strategies, and math education classes. Mary Kay Bacallao also has served on a local board of education and follows changes in educational law and policy.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Bacallao, Mary Kay, "Higher Level Thinking with Math Assessments" (2026). Georgia Educational Research Association Conference. 7.
https://digitalcommons.georgiasouthern.edu/gera/2026/2026/7
Higher Level Thinking with Math Assessments
Boston 1
This paper examines the use of higher level thinking with formative and summative math assessments. Here, the foundational assessments include fact based knowledge and comprehension types of questions. Upon the demonstration of a solid math understanding, the assessment questions then begin to look at applying and analyzing mathematical understanding through real world problem solving. Assessments addressed at these levels of thinking look more deeply into student thinking. They apply mathematical knowledge by selecting problem solving strategies for non-routine challenges. The students discuss problem solving strategies with classmates to compare different methods of solving problems. Next, formative assessments are used that ask students to evaluate and create using mathematical knowledge. Here, they design projects based on foundational knowledge. They create models and useful applications using what they know about math. Examples include engineering projects and scientific studies using data. After feedback, these same projects can be used for summative assessment as well. This paper examines this framework with specific examples.
