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.

Common Standards

     Well, I've held out this long.  I've tried to stay away from politics in this blog.  But I've talked about grades and grading; I've talked about national testing; and I've actually talked about Common Core before.  However, this time I want to share my thoughts about Common Core and address some of the counter-arguments that (in my opinion) are not sufficient to justify a school district or a state to refuse to use them.

      I support the use of the Common Core standards for English/Language Arts and for Mathematics.  I also support the common standards for Science that are coming to our public schools.  I support these standards because they were created by experts; they were vetted by experts; and they give all 50 million U.S. students a fair and equitable education.  We all know that education throughout the U.S. is not uniform because individual state standards vary widely.  Common Core sets a level playing field for all.  Additionally, these common standards are consistent with those from countries that produce students with the highest academic abilities.  We all love competition and we all love to win; so I would think that we would all want our students to be able to fairly compete with anyone in the world for 21st century jobs.  Common standards allow us to do this.

     So here are some bad reasons for turning away from common educational standards:

1) I'm a Republican and Common Core is a Democrat thing--so I'm against it.

     We live in a partisan country.  Some people are strongly Republican and some are strongly Democrat.  If a cause aligns to a particular political party, then the loyal will support it no matter the cause and no matter the details.  But Common Core is not a Democrat thing and it is not a Republican thing.  It came from the National Governors Association and Council of Chief State School Officers.  Just as No Child Left Behind was not a Republican thing (Edward Kennedy co-wrote NCLB), Common Core is not a Democrat thing.

2) Common Core is too hard.

     Compared to the academic standards in some states, Common Core will appear to be more rigorous, less rigorous, or about the same.  Since different states had different standards in the past, this comparison will look different to people in different parts of the country.  But the goal of school is to teach and prepare students for the world that they will inherit.  The goal is not for students to get good grades.  We want our students to be successful, but too many of our students have been very successful in high school only to fail in college.  That is a national shame on our nation.  Common Core is trying to prepare students for both higher education and for the word of work.  If it is hard, then students are being well prepared for their future.  Isn't that something we all want?

3) It was implemented too fast.

     States were given four years between state adoption of the Common Core standards and the actual implementation of the Common Core standards.  I think that a lot of people feel that the Common Core came all of sudden--one year we didn't have it, and the next year we did.  There was a lot of planning behind the scenes that the general public may not have seen.  This is why it seems to be so sudden to some.  If there were ten years between adoption and implementation, some people would feel the same way.  Why should we wait to give our students a world-class education?  And why give up on it just because it was fast?

     Also, public education is often accused of moving too slow.  Fifty million students and three million teachers comprise a very large group; and it is often slow for this group to change.  If we drag out the change and take our time, it might never happen.  We have to "rip off the band-aid".  Now is the time

4) (This bad reason hasn't occurred yet, but it will towards the end of this school year.)  See, everyone did poorly on the test.

     This year, for the first time, the PARCC and Smarter Balanced tests will be administered to students in grades 3 to high school.  In all likelihood, overall student scores will be low
compared to their class grades in math and English/Language Arts; or compared to past standardized test grades.  And there will be all sorts of renewed calls to cancel Common Core.

     In fact, whenever a new standardized test is administered, scores are often low at first and then increase over time.  Remember, the content of the courses are more difficult, so naturally the tests will be more difficult and some students won't be able to rise to that challenge as well as other students.  Once again, the goal of school is to teach and help students to be prepared for their future.  We are not helping students by giving them easy tests and then telling their parents that they are smart and then having these same students struggle after high school.  Colleges will recognize these new tests that same way they recognize the SAT and ACT tests.  They have to be the sort of tests that really prepare our students for college.

     We have a real chance to improve the education of millions.  And it could happen to this current generation of students.  We can say that we were there when U.S. public schools took a bold new step toward becoming the new standard in world-class education.  This is education's "moon shot".  Let's make a real difference; let's give our kids the best!

The Value of National Testing

     Chapter tests, unit tests, and final exams have been around (seemingly) forever.  These are tests that happen in school.  But what about the nationwide tests that students take?  I'm talking about the SAT, the ACT, the NAEP (National Assessment of Educational Progress), and the new PARCC and Smarter Balance tests.  What is the value of these tests?

     Let's start with the SAT and ACT, because most people know about these tests.  The purpose of the SAT test is to reliably predict an individual's success in their first year of college (see report here); and the SAT does a pretty good job of doing this--particularly for mathematics.  The stated purpose of the ACT is:

     Your ACT composite score, together with your high school grades, indicates how prepared you are for   college. In addition, the scores from the various sections of the ACT will help your college place you in the right classes, matching your skills with course requirements. (citation)

     Of course, aside from these "official purposes", we know that lots of people attribute much more importance to these two tests.  And, to be fair, some colleges have "cut-off" scores; if you score below a cut-off score, then you won't be considered for admission.  Still, my feeling has always been that there are plenty of colleges in the U.S. and unless you are determined to go "ivy league", there is a college out there ready to accept your money...uh...uh...I mean...to accept you.  Also, I believe that the SAT/ACT do a good job of showing what you know and are able to do.  Let's face it, a lot of students are good at "playing school".  They know what to do to get an "A".  But some student get an "A" because they understand the material and other students get an "A" because they are good at "playing school".  The SAT/ACT helps to separate these two groups of students.

     The NAEP, on the other hand, probably does the best job in determining what our nation's student know and are able to do.  This test is given to a sample of students in every state.  Colleges don't look at this test and parents don't get individual scores from this test--so it is a "low-stakes" test.  Students don't feel external pressure to do well on this test and nobody hires a tutor to do better on this test.  The PARCC and the Smarter Balanced tests--the new tests to be used to assess the Common Core standards--are supposed to be more like the NAEP tests.  Colleges aren't asking "What did you get on your PARCC Algebra 2 test?" yet, but I believe they will in the coming years.

     The value of these new tests are really the same as the value of the old SAT/ACT tests; they are supposed to show what students have actually learned in school.  We have to brace ourselves for students who get good grades in school and bad grades on PARCC and Smarter Balanced.  It will happen to the students who are good at "playing school" but not so good at learning.

     Students who do well on these tests should do well in their college courses.  Students who don't do too well will know where they stand and will enter college (I think) with a better idea of what they need to do to succeed.

     Sometimes I worry that the reason more than 50% of students that start college and never finish is because their teachers and school counselors and parents made them feel that their good grades in high school meant that they would be academically successful in college.  Their PARCC and Smarter Balanced grades may give them a different point of view--and that's OK.

     The value of national tests is an unbiased view of a student's academic ability.
          

Common Core and Our Desire to Give the Best to Our Students

     During my 25 years in education, I've seen ideas come and go; I've seen programs come and go; and I've seen movements come and go.  I used to think that the education system was constantly dreaming up ideas that were initiated with great fanfare and then were let go as failures.  But I've come to realize that education is not a static thing; certainly National Education is not a static thing.

     A lot of thought and research and debate goes into new initiatives and I think that it is fair to say that educators are constantly thinking about students and the best way to help students.  Education is also constrained by limited funds and (sometimes) limited research.  Also, big problems that require big solutions are often very complicated.  But it is not an excuse to "do nothing" just because the task at hand is difficult.

  After the landmark report "A Nation at Risk" came out in 1983, our education system did their best to respond to the issues that were raised in this report.  Some problems have been addressed and some remain.

     We have to remember that time does not stand still.  The world is changing and that means that our schools have to change also.  The form of that change can be numerous and diverse; but change it must.

     I am living and working through the transition to the Common Core standards.  Once again, this is a big change that is responding to a big problem in a big way.  Change can be scary at times, but this change is very, very necessary.  I am confident that I will look back at this second decade of the century and say that I was part of the beginning of something big.  And I am proud to be involved in this change.

     This isn't the end of change.  Programs and ideas will continue to come and go.  Each one will do its part to help our students and to improve on the last change that occurred.  I've come to believe that change is good and it should be embraced.