Welcome to our blog!

The Center for Mathematics Achievement director, Anne M. Collins and staff Steve Yurek, Katie Aspell, and Matt Rogers welcome you to our center, our blog and our inaugural post. We are dedicated to transforming mathematics from rote recitation, symbolic manipulation, and procedural prowess to engaging student-centered experiences that build conceptual understanding, emphasize the inclusion of multiple representations and knowing which representation best represents a situation, and computations which can be justified, and through which the reasonableness of the solutions is discussed.

So, let’s look at an example. In my research, I have queried thousands of students to solve the following equation:

3 + 4 = ∆ + 5

The most common responses include   3 + 4 = 7 + 5; 3 + 4 = 7 + 5 = 12; and 3 + 4 = 7 + 5 = 17. One, thankfully the only one, actually neglected to honor the equal sign altogether and illustrated their thinking with something along the lines of the following:

3 + 4 = 7 + 5

7 + 11 +12 + 5

18 + 12 + 5

30 + 5

35

All of the solutions are incorrect but for different reasons. I contend that if, when equations were first introduced they were done so with balance beams, pan balances, counters, number lines, or algeblocks the misconceptions would not have occurred and intervention or remediation would be unnecessary.

Students who understand that an equation is simply two equivalent expressions set equal to each other would have little difficulty in solving such a simple equation. If taught, however, as a procedure then difficulties and misconceptions arise.

Let’s examine how parallel number lines might have prevented the expressed misconceptions.

                                                          3 + 4 = ∆ + 5

 

So, as you can see, this blog intends to discuss mathematical concepts, student misconceptions and ways in which to avoid them, share interesting problems, and discuss any and all mathematics issues of interest to our followers. We welcome you to comment on this post and/or to begin a new thread. We are looking forward to our on-going discussions and learning together as a community!

Anne

Common Core State Standards, MA Frameworks and the Work of the Center

Since it became evident that Massachusetts, as well as 45 other states, was adopting the Common Core State Standards (CCSS) we have struggled with how best to serve the needs of the teachers with whom we work. The staff of the Center for Math Achievement (CMA) at Lesley University is committed to supporting the mathematical needs of teachers in any way possible. We will continue to offer courses on site in districts and weekend workshops, participate in dine-and-discuss meetings with the Association of Teachers of Mathematics in Massachusetts (ATMIM), mentor/coach teachers, and publish materials that will promote effective teaching and learning.

Sol Garfunkel, mathematician, author, and professional development provider, in an email delivered through Jerry Becker’s list serve describes himself as “schizophrenic” when it comes time to deal with the CCSS. His dilemma, as with many mathematics educators, is how to reconcile an untested set of standards which he does not support with his commitment to best support teachers who have to implement them. I am in agreement with Sol, who went on to articulate how well-written the 1989 National Council of Teachers of Mathematics (NCTM) standards were and how we, as a nation, never truly implemented those standards as articulated. I would add that the revision of those standards as articulated in Principles and Standards for School Mathematics 2000 have also been largely ignored. Yet, after spending time at the International Congress of Mathematics Educators-12 (ICME-12) in Korea, I heard from many educators from around the world how much they value the work of NCTM and use their standards and publications religiously. In fact, many presenters from countries which out-perform the US on international assessments stated that the reason their students do so well is because their curriculum is based on the NCTM standards.

More information on the PARCC assessment will be released in the coming weeks and we will pass on that updated information as soon as it becomes available. Until then, feel free to ask any questions you might have, or to provide us with information you may have that we are missing.

Anne