Asking Questions, Forming Equations

Some part of the ARRA money allocated to the Lowell Schools is being used to give teachers time to look at assessments and collect data about how our students best learn.  Grade level teams and cross-grade level data teams have formed since late summer all with the purpose of methodically looking at our assessment data and making decision about what to do next.  We use the ORID protocols to analyze our data while the mechanism for assessment of our own teaching is the process of Learning Walks.My grade level, Grade 3, has been contemplating a mathematics inquiry that will help us improve our instruction and, ultimately our students' learnings.  The development of the question has taken us in a circuitous route through methods for comprehending a particular operational skill (multiplication) to the question we've agreed upon this morning: What does best practice look like when we are teaching our students to generate or identify a correctly constructed equation matching a word problem situation.We've noticed that our students, particularly our ELLs, meet the standards for whole number computation.  However, many students, regardless of whether or not they are ELLs or native speakers, cannot for the life of them select a reasonable equation to match the word or story problem.  This is critical mass for our kids -- the bulk of the MCAS testing that will take place in the Spring requires students to decipher story problems in just this way.Those of us who have a strong background in Constructivism dislike the very idea of teaching students "key" phrases:  for example, in all means to use an addition equation. Personally I feel that there are other ways to get kids to comprehend the problem and generate equations from their understandings.  I want my students to visualize the events in a story and be able to logically create an equation that will get them to an answer.But what about of kids who have so many language issues that visualizing is not a strength? Is there another, better way? The data analysis tells us there has to be - at least with the students we are currently working with. As my colleagues and I work through this cycle of inquiry, we will be peeling away our preconceptions; this can be pretty scary.Our next meeting will begin the process of researching what might work with our students, and maybe, we'll invent something new.  Now that would be something!

Two Lessons From Master Teachers

Every year we scour our standardized test scores wondering what we can do so that our students look as good on paper as they appear when we are assessing them day-to-day.  I hate that standardized testing, in this case MCAS, is considered the measure for success.  I think of some of my colleagues who took the National Teacher's Exam -- does that test still exist -- a grueling all-day summative paper assessment by which prospective teachers were judged to be worthy or unworthy of hiring.  People I admired performed poorly on this test -- the single measure used to judge employability.  In the same way, I dislike the high-stakes tests that judge our students and judge our teaching effectiveness. Should one measure be the end-all of whether or not students are learning?Off of the soapbox now, the topic I'm considering is what magical intersection of ideas and conditions will help my students acquire mathematics?  And that's what this section of the blog is about.Once upon a time - at least 15 years ago -- I was a participant in a summer course designed by Math Solutions and developed by Marilyn Burns.  Marilyn Burns is not only a master mathematician, but she is a master teacher -- and unlike other experts/consultants in education, she puts her money where her mouth is: she actually teaches the lessons using the methods she advocates by volunteering in public schools in her area of California.  Right there she had my respect -- no theoretical ivory tower.One of the presenters said something sage that has stayed with me all these years.  When we are shifting the teaching of mathematics, or any topic for that matter, to a more constructive, meaning-based model, it can take up to 5 years for our students to "get it".  The presenter, whose name has escaped me, told how her school in Texas had adopted using replacement units for basal math texts -- unit based on deepening students' comprehension of mathematics. And while the test scores (remember them?) were disappointing at first, after several years, there was a delightful, vindicative jump showing that students had not only acquired math concepts, but were now flexible in applying them.Isn't that what we h0pe for? The current frenzy of testing and accountability of teachers for what students can and cannot show in a single-shot standardized high-stakes test, doesn't allow us much time for developing a program in a methodical way.  Lesson #1:  Things take time.The second lesson was an idea planted in my brain by a brilliant and gifted mathematician, Andrew Chen of Edutron.  I had the privilege of being a student in one of Andrew's Intensive Immersion Institutes, a mathematics class to strengthen/clarify/stretch mathematical thinking for teachers.  Andrew's words, that our students are just as bright as their suburban and high-achieving counterparts, were like a breath of fresh air.  Generally urban teachers are told either outright or through insinuation, that they can't be as good as counterparts in less troubled teaching environments -- or the students' test scores would be higher (how insidious is that!).  Here was an MIT mathematician telling us that our students (and teachers) can achieve much, but sometimes other things (socio-economic ills for example), get in the way.  Lesson #2: Don't give up on students or yourself.Both of these ideas have been in the back of my mind as I've been working with our Math Resource Teacher and Coach to tweak the third grade teaching resources this year.  As we develop materials that work for our kids, we'll use this space to document some of the things we've learned about teaching mathematics in an urban school system.