Teachers Seeking Innovative Learning Strategies

       If students aren't learning, then the teacher isn't succeeding.

       This is a harsh statement.  Clearly there are lots of reasons that prevent students from learning.  Some of these reasons can be due to teacher actions in the classroom and some are outside the control of the teacher.  But the main goal of school is learning.  If the student isn't learning, than we haven't met this main goal.

       Of course, not all students learn in the same way.  When a teachers presents a lesson--be it via lecture, or a game, or discovery learning, or through the use of a task, or some combination of these methods--some students will "get it" and some will not.  And so our best teachers are constantly looking for different ways (different teaching strategies) to help students to learn.  This (indeed) is the part of teaching that very, very complex.  Trying to understand the best way to help students to learn--every student in every class--is the struggle of every teacher.

       Alas, the world of education is full of ideas to help us.  Some of these ideas fall into the category good suggestions that any teacher should use, such as:

• Scaffolding - breaking up the learning into smaller chucks and allowing students the time to learn one-piece-at-a-time in the effort to get them to learn the whole idea or standard.
• Graphic Organizers - providing students with different ways to organize information so that "many ideas or facts" are easier to see and to understand.
• Multisensory - presenting new information in multiple ways that help the students brain to store the information in multiple ways.  For instance, verbally explaining something while also writing the information on a whiteboard or computer screen, while also (perhaps) providing a manipulative or foldable for the student to hold and work with tactilely.  

Other ideas are more specific as to the sort of instructional style that may take place in a classroom.  A typical example of this would Direct Instruction or Lecture.  This is very typical in classrooms in the United States; particularly in our high schools.  Adults in their 70's and 80's probably received instruction in this manner when they were in high school and their grandchildren and great-grandchildren likely receive their high school instruction in this same mode.  Some people refer to this sort of instruction as Traditional classroom instruction--and it clearly is not effective for all students.

       More teachers are using a Discovery Learning approach to classroom instruction at least some of the time in their classes.  This approach allows students to build on past learnings by completing tasks and problems that require them to do so.  Students may work individually or in small groups of three or four while the teacher responds to students' questions and encourages students to think about other solutions.  This approach is common in some countries but is much less used in the United States.   

       I am part of a couple of math groups on Facebook and I posed the question, "Is Direct Instruction Necessary?"  I went on to ask if Discovery Learning could be the sole or major teaching strategy in a high school math class.  Of course the responses that I received were various and wide ranging, but I did learn a lot more about individuals and groups of teachers who use this approach with some success.  

       When teachers are continuously searching for more and better ways to reach their students, everyone wins: students, teachers, schools, society.

Teaching Mathematics For Understanding

       There has been a lot of debate in the U.S. about our student's ability in mathematics for the past decades--certainly for my entire career (which started in the 1980's). How do we compare with students in other countries? (see PISA results - 36th out of 70 for mathematics in 2012)  How do we compare with each other state-by-state?  (see NAEP results from 2013)

       What are the causes for these discrepancies?  What do other countries do differently compared to what we do in the U.S.?

       Ask a hundred people and (it seems) you would get a hundred answers.  Everything from "nothing's wrong" to "the system is broken".  Everyone has their point of view; there are experts on both sides of the every argument.

       Recently, I've read two sources on this issue that make a lot of sense to me.  The first is from Phil Daro.  He makes the point that many mathematics teachers in America have the goal of teaching students how to get the right answer.  In other countries the mathematics teachers have the goal of teaching students how to understand particular mathematical concepts.

       This makes sense to me because I've been that mathematics teacher and I've seen that mathematics teacher among my colleagues.  While I believe that our teachers want their students to understand and to gain a conceptual understanding, they are often fighting a battle against an accountability system that seems to reward "correct answers" more than awarding "correct understanding".  (Although the new PARCC and Smarter Balance assessments may have found a balance between these two competing forces.)  We are also fighting a culture of students who avoid the struggles needed understand these concepts and (instead) seek shortcuts for getting the right answer.

       The second source is an article by the education writer Amanda Ripley.  She took the PISA math test in an effort to understand the sort of thinking that it requires of students.  She also interviewed exchange students who spent time in schools in other countries.  From these interviews, she repeatedly heard these students remark about the following three differences between schools in the United States and schools in higher achieving countries.  These are:

1. School is harder. There's less homework but the material is more rigorous. People take education more seriously, from selecting the content to selecting the teachers.
2. Sports are just a hobby. In the U.S., sports are a huge distraction from the business of school, but that's not the case in other countries.
3. Kids believe there's something in it for them. The students in other countries deeply believe that what they are doing in school affects how interesting their lives were going to be. Even if they don't like a class, they see their education as a stepping stone to their future.

       I believe that we have to take a honest look at ourselves here in the U.S. and be open to these differences if we are ever to see a significant rise in the achievement of our students.  Our current climate of new standards and new assessments provide to us an opportunity to make this huge adjustment in our teaching and in our understanding of the true purpose of our mathematics class rooms.

       We can do this.  We must do this.  We must do better.