Exceptfor a brief time during the “New Math” fad in 1960s, math was taught throughrote memorization and practice. Too much focus was on learning procedureswithout any connection to meaning, understanding, or the applications thatrequired the procedure. When the Common Core Standards were introduced, thefocus on math instruction went from the rote practice to student centered. Thenew standards were based on the mathematical understanding that studentsconstruct their own understanding when solving math problems.
In Common Core, mathstandards changed from placing math standards haphazardly and with no priorconnections to previous grade levels to spiraling and building on each priorgrade level. Each grade level builds upon the math foundations learned theprevious year. Rather than covering the excess of topics taught before, the CommonCore requires deeper understanding and the ability to apply mathematics toproblems students may not have encountered before. The Common Core StateStandards for Mathematics begin with eight Standards for Mathematical Practicethat describe ways in which students should engage with the content, processes,and proficiencies of longstanding importance in mathematics. To meet the learningoutcomes of the Common Core State Standards for mathematics, teachers need tofocus on providing students problems to solve in order to build conceptualunderstanding in math, not just procedural knowledge and step memorization. Itis important for student understanding that teachers present lessons andactivities that activity involve students in solving and discussing tasks that encouragemathematical reasoning and problem solving and allow varied solution strategies.
Teachers should not provide narrow pre-taught strategies but instead need tosupport different perspectives and strategies so students build on each other’sunderstanding of problem solving. Effective teaching practice for the standardsinvolve encouraging students to apply math through a variety of differentapproaches, including modeling and making and critiquing strategies.An important aspect ofCommon Core involves students constructing viable arguments and critiquing thereasoning of others. Teachers need to facilitate meaningful mathematicaldiscourse through purposeful questioning and discussions in every lesson.Effective teaching of math enables class discussion among students to buildshared understanding of math strategies and ideas by analyzing and comparingstudent approaches, strategies and arguments. The teacher is needed not to leadthe discussion, but to guide by applying purposeful questions to assess and advancestudents’ reasoning and connections to important math ideas and relationships.
By utilizing these methods, teachers ensure students develop a foundation ofconceptual understanding over time and become skillful in using procedures flexiblyas they solve new math problems. Asa fourth grade teacher, I already use a student centered problems solving approachto math. After my school sent me to CGI training, I changed the way I presentedmy lessons.
I open every lesson with a problem that relates to what I want mystudents to learn. Students share their strategies with the class where wediscuss strategies, create equations to match our strategies and discuss thesimilarities and differences between students solutions.