1) Mathematical computation is the main focus of a math lesson.
Many people interpret “doing math” as performing various computations and calculations to find a solution. As a math course writer, it can be easy to emphasize mathematical computation in a lesson without assessing a student’s conceptual understanding of the content. Just because a learner can regurgitate a theorem or algorithm doesn’t mean they mathematically comprehend a concept. Including examples and assessment items that focus on understanding and reasoning as well as computation provides students the opportunity to not just find a solution but to make sense of the math itself.
2) Teaching argumentative writing is the responsibility of an ELA Course Writer.
While the responsibility of teaching syntax and grammar rules does not necessarily fall on math course writers, they are accountable for teaching math learners how to prove and justify math concepts through writing. Knowing how to form a sound and cohesive math argument is a skill expected of all learners today, as one of the Common Core Standards for Mathematical Practice revolves around constructing and critiquing mathematical claims. What’s more, the math standards themselves are full of directives such as explain, show, and analyze. Course writers must consider how to properly incorporate and model argumentative writing into content as a means of achieving these standards, such as introducing mathematical sentence frames or opportunities to critique an existing argument.
3) Multiple-choice items are not rigorous enough.
Oftentimes an open-ended question is considered a more rigorous assessment than a multiple-choice item. But a well-written multiple-choice question can require just as much critical thinking as an open-ended question given the appropriate distractors. Using “multiselect” multiple-choice items is one way to up the rigor, as they provide math item writers the opportunity to introduce various methods or representations of a solution and challenge students to look at a problem from different perspectives. These sorts of tasks also prevent students from searching for the one “correct” solution.
4) Less is more when it comes to solution methods.
While less may be more when it comes to the breadth versus depth debate of math curriculum, it is beneficial for math course writers to include various strategies of approaching a particular concept or task. Keep in mind that the same problem does not need to be addressed five different ways; solving two separate problems using two different methods can be sufficient. Especially in an era of math education that encourages students to analyze a problem from different perspectives, highlighting several solution methods in instruction and examples offers students multiple entry points to the same task.
5) Students need to be presented with all information upfront before they try examples.
Many curriculums are designed so that the instructor first presents all content necessary to meet a lesson’s objectives before allowing a student to try an example on their own. There is definitely a place for direct instruction in each lesson, but math course writers should remember that the 21st century learner is expected to think critically and problem-solve. Providing an opportunity for student inquiry and exploration before or during the instructional part of a lesson engages students in the learning. Course writers should think about when it might be appropriate to let learners make their own conjectures to arrive at a particular property or formula instead of just stating it for them.
Avoiding these misconceptions when developing math content can provide teachers the tools to thoroughly instruct, assess, and empower learners to take more responsibility in mastering mathematical concepts.