A battle often ensues between who is the champion of the core courses in education. Whether it is social studies claiming the “history repeats itself” mantra as the way to live; or it is English/Language Arts highlighting literature as the true representation of society, therefore the most important; science itself claims the facts and statistics in life help discover the cold hard truths; finally, mathematics focuses on the logical and methodical as the true means to understand one’s purpose.
This certainly does not take away from all of the other academic areas in education, but it does spotlight the multiple philosophies that exist in varying components of courses. Educators often reflect on the types of curriculum, instruction, and assessments that make students successful. Because these can be such different philosophical components, let’s focus on the math area of assessment.
Why Traditional Assessment Methods Limit Some Students
With so many research-based discoveries about how students learn, the challenge lies in the ability of math instructors to move away from simply teaching math facts or relying on traditional “skill and drill” instruction and assessment methods. The paradox lies in the idea that when students don’t understand or cannot perform math functions, they are given more examples to practice. But if they do not comprehend what they are doing, adding more items to practice doesn’t accomplish anything but frustration and an eventual shutdown of the learner. This is only one of many limitations placed on students when learning in this design.
For those students who can learn by way of the repetitive rote memory methodologies pertaining to numbers and formulas, it can be a strong method. And rote memory can be a useful skill in some situations. But what about those students who do not cognitively process this way and need to be assessed differently?
Elementary-age students are curious and learn by questioning. Posing questions through discussions opportunities is a significant form of comprehension for students and a terrific formative assessment. If students had opportunities to problem-solve real-world applications through small or whole group discussions, they would be able to apply those mathematical concepts that are not necessarily understood through an immense amount of practice problems. In fact, they could even be enhanced through the written form, ranging from essay exploration to small paragraph reviews. Better yet, applying those mathematical formulas through discussion and lab practicum projects could ultimately enhance learning.
Without these opportunities, simply hearing a word or theory with a definition does not work well for the majority of learners. Most students won’t equate prediction skills or see the relevancy of understanding differences in the world or even know the true importance of subtracting and adding outside of theory learning. And assessments in the traditional math sense will only prove a deficiency in their abilities but not improve them.
Creative Ways to Assess Math
There is no doubt whatsoever that one of the fastest ways to student learning is through treats, no matter the age of the student. So using M&Ms in a math lab to highlight ratios, work with fractions, make predictions, etc, can support so many levels of learning and assessment.
Before even opening the bag, predictions can be made about numbers of M&Ms in a bag, how many colors could be contained, short writing bursts to explain why there might be more of a particular color, and maybe partner discussions about the type research that goes into designing and distributing these types of candies. And teacher observation can be the most powerful assessment in these cases.
After these predictive types of activities, the hands-on moments of opening the bags and separating colors, sizes, types, etc. provides an engaging and tactile experience. It’s a lab that can apply so many of the math concepts they have learned without even knowing they are using those types of math skills. Providing more depth in a lesson, such as with engineering careers or factory-based skills, can provide a work corridor for students as they research these occupations.
Another example pertains to equipment throughout the school. Measurements can be an additional tactile way of understanding important math concepts, whether it is an elementary-based lesson using rulers on different objects by way of a scavenger hunt or a high school lesson on the different angles in which a water fountain stream can occur. Again, formative assessment plays a role in conjunction with instruction.
This last example is a neat way to incorporate some physics training, if a math instructor desired to do so. After theory introductions of angles, typically students see problem after problem focusing on those angles. Instead, have students move to water fountains throughout the hallways to apply their theories in understanding water pressure, angles of the water streams, what-if scenarios; then they can be applied to classrooms discussions about their findings or further research about angles and pressure in dams around the world. Again, engineering concepts or the controlling of natural elements can be true math applications, and solid assessments can originate from these projects.
Another example of using classroom manipulatives deals with building blocks, which can be utilized in several ways. One example relates them to Pythagoras’s Theorem. Students are creative, and using building blocks to highlight this theorem is an easy way to get visual and tactile learners to understand a formula such as this. It breaks up the monotony of the repetition of drilling through exploration of the angle in a physical way. Assessments can be built on these examples, from pictures of their own work that students may recognize on quizzes to short explanations about the process they experienced.
Including technology allows students to apply math theorems in their own projects and can open up a world of excitement. An educator can implement a particular math-based software program for students to apply their current classroom curriculum or, better yet, allow students to create their own projects to show their comprehension of theorems. This opportunity may also support the teacher’s professional development in that they can flip the classroom and learn from the student. Again, creating project-based assessments with rubrics, possibly even collaborating with students in their designs, moves away from the traditional assessment procedure.
It’s time to build upon creativity and transition away from the traditional way of learning and assessing math.