If I had a dollar for every time I’ve heard someone say, “I am not a math person,” well… I might not be rich, but I’d have a decent amount of spare cash to invest (that’s what we math people do with our spare cash … no, not really, but we should).
But this statement makes me wonder: Would this same self-proclaimed innumerate person also claim to be illiterate? What’s so scary about mathematics? And do we assume our students share this “irrational” fear of mathematics (pun intended) and therefore use tricks to make it less scary?
Math tricks do NOT help kids learn and can even hinder their progress!
We know the tricks – we learned them. Remember them? If not, Google them – they are everywhere! For example: order of operations (Please Excuse My Dear Aunt Sally); the butterfly method for comparing fractions; and multiplying by 6, 7, 8, and 9 using only your hands.
There are many more math tricks, and if used correctly, always result in the correct answer, but these tricks allow students to “skip” conceptual thinking that the College and Career Ready standards demand for students to be successful in life.Math tricks can be fun, but understanding WHY they work is key to conceptual understanding of mathematics. It's the thinking and justification behind the answer that allow for deep learning of #mathematics concepts. Click To Tweet
Integrating the Standards for Mathematical Practice (www.corestandards.org/Math/Practice/) into daily instruction is critical to students’ conceptual understanding of mathematics. Using math tricks does not really convey actual mathematics. The mathematical practices require students to problem solve, reason, communicate, and make connections through conceptual understanding, procedural fluency, and “productive disposition” – seeing mathematics as useful and worthwhile and the belief in one’s own efficacy to use mathematics to solve real-world problems (modeling with mathematics!) If students are asking, “Why do we need to know this?” then it is time to reassess how mathematics is being taught.If students are asking, 'Why do we need to know this?' then it is time to reassess how mathematics is being taught. Click To Tweet
Simply stated, children (and adults) learn mathematics (insert any process or skill here – engine repair, cooking, computer coding, laundry, etc.) when they’re allowed to discover their own approaches to solving the problem – and fail. My favorite quote is from Thomas Edison: “I have not failed; I have just found 10,000 ways that do not work.” Mathematics is about understanding concepts, not getting the right answers. We want students to make sense of problems and persevere in solving them.
Tools not Tricks
Although estimation is one of the most powerful mathematics tools, it can be a challenging task for young children because it requires them to conceptually manipulate numbers, and use appropriate tools strategically. When estimating, students have to analyze each number in the problem and make a determination as to round up or down. Estimation skills assist students in determining the reasonableness of their answer, which requires them to reason abstractly and quantitatively.
This ability to reason allows students to recognize computational errors. For example, if a student is asked to multiply 624 x 32 and their answer is 195,248, we want them to independently recognize that 195,248 is not a reasonable answer because they conceptually understand that using the estimation of 600 x 30 to arrive at 18,000 is a reasonable estimation of the product. Estimation is a useful tool for adding, subtracting, multiplying, dividing, and calculating time and distance.
It is important that we teach our students that estimation does not replace the need to come up with accurate answers (and attending to precision), especially when modeling with mathematics and integrating real-world problems and solutions in the fields of engineering and science to represent ideas and explanations.
So what “tricks” should teachers use?
None! Engage your students in the learning through mathematical practices. In addition to the practices identified in the previous section, here are some “look-fors” for student behavior and engagement.
- Students should ask questions, define problems, and predict solutions/results.
- Students should analyze and interpret data to draw conclusions, apply understandings to new situations, and continually ask themselves, “Does this make sense?”
- Students should use mathematics in problem situations that require computational thinking in a creative and logical way (e.g., diagrams, mathematical representations, computer simulations, etc.).
- Students should obtain, evaluate, and communicate information by constructing viable arguments based on evidence, critiquing the reasoning of others, and designing solutions.
- Students should be actively engaged and work cooperatively in small groups, to test solutions to problems, organize data, use mathematics and logical thought processes, use effective communication skills (writing, speaking and listening), and look for and express regularity in repeated reasoning.
The “trick” is ensuring our students take ownership of their learning, and the learning of their peers, through inquiry, problem solving, critical thinking, collaboration, and communication. And integrating mathematical practices into daily instruction will ensure they have the tools they need to be successful in life.
Dr. Speake loves science, technology, engineering, and mathematics (STEM geek!) and believes that everyone can learn through inquiry and habits of mind. Her 20-year teaching career ranges from high school teacher, district curriculum specialist, state of Florida Department of Education science and mathematics program specialist, and senior director for instructional services. Dr. Speake has presented to administrators and teachers on inquiry, STEM, and embedding the mathematical practices and literacy standards into all content areas, including science, social studies, and Career and Technical Education. She holds a B.S. in Biological Sciences from the University of Maryland, as well as a M.Ed. in Secondary Curriculum/Instruction and a doctorate in Education Leadership and Policy from the University of South Florida. Previous to teaching, she was a field biologist for the Maryland Department of Natural Resources, a water chemistry lab technician at the National Aquarium in Baltimore, and a research biologist with the Florida Department of Environmental Protection.