An Engaging Mathematical Environment

My mathematics methods class this quarter has prompted my thinking about the many ways in which math is taught and the importance of creating an environment that promotes learning among students.   I now realize that the teacher in my dyad placement last quarter, a fifth grade classroom at Einstein Elementary, was extremely successful at creating just such an environment.  Every student seemed to be engaged in the lessons he taught.  As an “observer” I wasn’t able to guess which students seemed more challenged by this subject than others.  They all actively participated.    Now that I’ve begun reflecting more on his teaching methods, however,   I  realize that he incorporated  many important  strategies into his classroom that  helped create this amazing “mathematical environment” (that I, of course, hope to replicate in my own classroom some day).  This blog is devoted to sharing some of these strategies.

One of the first things I noticed about his classroom was the level of attentiveness of his students.  Everyone was facing forward and quiet while he was speaking during his lesson.  They were also quiet and respectful when other classmates were speaking.  When I asked him about this he told me that he had established the rule early on that no one should talk over anyone else.  I later realized that this behavior didn’t happen by chance.  He would abruptly stop, mid-sentence, and look directly at an offending student if they were talking out of turn and would not begin speaking again until they were quiet.  This method was extremely effective.  It reinforced the message that each member of the classroom had something valuable to contribute and, therefore, should be listened to.   

Another effective strategy he used was his warm-up activity.  He always had the students play a math game that related to the lesson he would be teaching.  He usually asked for a student volunteer to come up to the document camera to play the first round with him, as he explained the rules, before handing out the game pieces and “boards” (papers) to play.  This seemed to generate excitement among his students.  The class would then be broken up into partner groups to play on their own.  During this center activity part of his lesson, when the students were in these table groups playing the math game, the teacher often called out a group that was on task.   This reinforced the expectation that all students were to stay focused on the game and not get sidetracked in conversions about anything other than math.  He also did this during student independent work time.  These “gentle” reminders seemed to keep his students on the right track.    

This teacher also taught very engaging lessons by using just the right mix of direct instruction and student involvement by asking students to volunteer to solve problems on the active board that reinforced the concepts he was teaching.   He was also adept at keeping the lesson moving at a comfortable pace by often checking in verbally with his students by asking them if they understood how he got a particular answer to an equation.  He’d ask for a “thumbs up,” close to their heart (so only he could see) if they understood.  If he didn’t see many thumbs he’d review the problem again.  This enabled him to “slow down” if necessary, but also to “skip forward” if the concept was understood by all.

He also had great strategies for involving all of his students.  When he asked questions about a solution to a problem he’d often wait until most hands were up before continuing on, and then he’d ask them to form partner groups to discuss the answer (instead of just asking one person to give it).  This method of student involvement was discussed in the Questioning Your Way article, by Mewborn (that was assigned reading in my class).  Per the article, “By sharing their solutions in pairs first, students can try out their ideas on someone else and practice what they are going to say to the class.  Students receive feedback on their solutions in a non-threatening setting, and their self-confidence is boosted.”  This seemed to be true as I witnessed this practice in my dyad placement classroom.  I noticed the “hands” of students that didn’t typically participate to offer a solution when the teacher brought the class back to attention.

This teacher was also very respectful of his students when handling “wrong” answers by calling on others to assist the student having trouble, so they could eventually be successful.  (A student that made a mistake on the active board was never permitted to return to his or her seat until they had successfully completed the problem.).  Another part of his lessons that I especially liked was when the teacher purposely made a mistake when solving a problem, and then asked for volunteers to find his “oops”.  (By doing this he kept the lesson light hearted.) He would also, on occasion, take on the entire class as his opponent during a math game to spur competition among his students.   They seemed to be especially involved and engaged during a lesson when they had the opportunity to “beat” their teacher.

I truly enjoyed observing these math lessons during my dyad placement.  This teacher modeled many of the strategies we’d been discussing in my mathematics classes.  I was able to watch as he put many of these effective strategies to practice in his classroom.