Hm.

Do we live in the 21st century or not?  Teachers are so reticent to embrace new technology, yet so eager to bring students back to “our generation.”

My curiousity was peaked by this column in the L. A. Times.  I’m not trying to (re)ignite the tech war here, but really?  Rather than teach kids to “follow the slower rhythms of classroom dialogue,” shouldn’t we be embracing the technological innovations available to us?

My favorite?  Students “will chronicle their experience in journals.”  It would be a shame to use a blog, wouldn’t it?

Hm.

From a recent article in EdWeek.  I’m not finding fault, I really enjoy their content.  See if you can find the problem with this graph (the fact that the percents don’t add up to more than 100% doesn’t count).

Why Teachers Leave

Educators know the value of quality professional development.  Teachers left to rely on the skills and strategies acquired during a four- or five-year undergraduate program are ill-prepared to help students master key concepts (in math, reading, or any other subject).  That is why we subject ourselves to continued learning.  Sometimes it’s good, sometimes it’s not.  However, quality professional development is critical to changing the way we do business.

Other countries get this.  Teachers spend significant time in professional development and lesson study activities.  This is one factor contributing to the success of the primary Singapore mathematics program.  Some districts in the U. S. get this, too.  But then we get news like this.

There are two underlying factors in this situation:

1. Parents – 100 (or more) of them signed a petition.  Their main (although unstated) concern: My kids aren’t in school and so I have to pay for daycare for an extra three hours every Wednesday.  This is indicative of our culture.  I’m not going to say more about that now.
2. Teacher organizations.  My favorite quote on this topic from the article: “The kids need to be in school….  If they needed to do the meetings, the teachers should be paid to go to the meetings after school, you know, not take it out of time for the kids.”  This is really about pay, not what’s best for kids.  It’s an unfortunate pattern that emerges in district after district.

Unfortunately, the winner of Round 1 in Laramie County is classroom time – time that could be more productive if teachers were able to participate in training on a regular basis.

You might ask, “Why does he care about math education so much?”

And then I come across something like this:

If you see what’s wrong with this, you get my point.  If you don’t see what’s wrong with this, you’ve made my point.

If you need a hint, let me know.  I’m still a teacher at heart.

(Image from eggindustry.com)

Take a look at this article in the Salt Lake Tribune.

Yet another example of people missing the point: it’s about instruction.

The State of Utah would be much better off spending their money on competitive grants to districts to provide training for their teachers in concept-based mathematics.

I won’t rant about this anymore.  I think this says it all.

My son is in first grade.  He loves it most of the time.  Every Friday, the first grade teachers at his school send home a packet of homework, five days worth, that is due the following Wednesday.  I would much prefer that they send it home during the week and leave the weekends alone, but that’s how it is.

The homework tasks are usually very similar.  They consist of:

• A set of spelling words.  Students need to use each one correctly in a complete sentence.  The set consists  of some spelling words and fewer high-frequency words.
• A sheet of words with the same vowel sounds to cut out and glue into the correct category.
• An addition facts practice sheet, usually themed around one common fact (e.g., adding zero, or 2+3 = 3+2 = 5).
• A nice Venn diagram activity that involves frogs and rabbits.  They have used this one all year, categorizing the frogs and rabbits in several different ways.
• Some other reading or writing activity appropriate the current literacy theme.

Homework is good.  I have made my feelings about drill and practice quite clear in previous posts.  Here’s my question: What are the teachers doing with the information?  For what purpose is the homework issued?  What is the intent?

This became a concern for me when my son turned in his spelling words one week.  In a rush to get the assignment completed on Tuesday night, I had not reviewed his work.  One of the words was “so.”  His sentence was, “I am so never going to pet a snake.”  Homework returned with the comment, “Nice job!”

Here’s what I’m getting at: Give homework.  But make it meaningful, and be sure to give productive feedback to kids.  Does it double the teacher’s time in grading?  Yes.  But that’s what we do.

We had an opportunity to welcome Dr. Kevin Feldman to our school district last week. He presented a day-long session on “Narrowing the Lexical Divide: The Critical Role of Vocabulary & Academic Language in Improving Secondary Literacy Across the Curriculum.” His focus on academic vocabulary was of great benefit to the teachers in attendance.

One thing that really caught my attention in his presentation was the discussion about where we find Academic English – that Hayes and Ahrens (1988 ) used a measure of “rare words per 1,000″ to evaluate the frequency of word use. They found that the everyday adult speech of college graduates is at approximately the same level as preschool books, and that most informational texts are at a level comparable to newspapers and magazines.

This reinforced my belief that we have to talk about math before we write about it, and also supports the notion of developing formal spoken language as one path to formal written language (see Pimm (1991)). It also made me wonder about the level of spoken English in math classrooms, both by teachers and by students. Then Dr. Feldman showed us this website, which will analyze passages to determine rare words per 1,000.

Those who know me will likely guess what I’m thinking: research. This should be fun!

From the ASCD Blog:

“More math, particularly Algebra, in California high schools has yet to pay off. Last week’s most-clicked Smartbrief story reported that enrollment in remedial math courses still remains high in California Universities, leading many to question why high school reforms are not transferring to college-preparedness.”

Are we surprised? This is much less an issue of what we teach than an issue of how it is taught.

Standards are not the problem. Expectations for student learning and the pervasive “sit and get” culture of high school mathematics teaching are the culprits. Our focus needs to extend beyond the curriculum to include sound instructional strategies.

While I may be somewhat critical of the lack of new information in Foundations for Success, I do agree with the findings and recommendations of the National Math Advisory Panel. Which is why I’m so troubled by this article by David Thornburg. The basis for Thornburg’s argument is this:

Recent pronouncements from Washington regarding math education have suggested that pedagogical points of view don’t matter in the teaching of mathematics. For example: “There is no basis in research for favoring teacher-based or student-centered instruction,” Dr. Larry R. Faulkner, the chairman of the panel, said at a briefing last Wednesday. “People may retain their strongly held philosophical inclinations, but the research does not show that either is better than the other.”

Thornburg goes on to cite two “counterexamples” to refute this claim, both from “Rising Above the Gathering Storm“:

1. Statewide specialty high schools (e.g., IMSA ), and
2. Inquiry-driven project-based learning.

This is a wonderful example of the misconception of inquiry as being something totally student-centered, with little or no teacher input. Granted, part of the ownership for this misconception lies with the math education community – we do not often enough discuss the concept of inquiry using the word “inquiry.” Instead, we use terms like “problem solving,” “reasoning and proof,” or “connections.”¹ It is the stubborn insistence of some educators that math is math and science is science and never the two shall meet.

The science education community, on the other hand, gets it. They understand inquiry.² It’s part of their standards. In fact, the National Science Teachers Association (NSTA) describes scientific inquiry as

a powerful way of understanding science content. Students learn how to ask questions and use evidence to answer them. In the process of learning the strategies of scientific inquiry, students learn to conduct an investigation and collect evidence from a variety of sources, develop an explanation from the data, and communicate and defend their conclusions.³

Sounds to me a lot like the process standards:
Reasoning and Proof:

Instructional programs from prekindergarten through grade 12 should enable all students to–

• recognize reasoning and proof as fundamental aspects of mathematics;
• make and investigate mathematical conjectures;
• develop and evaluate mathematical arguments and proofs;
• select and use various types of reasoning and methods of proof.

Problem Solving:

Instructional programs from prekindergarten through grade 12 should enable all students to–

• build new mathematical knowledge through problem solving;
• solve problems that arise in mathematics and in other contexts;
• apply and adapt a variety of appropriate strategies to solve problems;
• monitor and reflect on the process of mathematical problem solving.

Connections:

Instructional programs from prekindergarten through grade 12 should enable all students to–

• recognize and use connections among mathematical ideas;
• understand how mathematical ideas interconnect and build on one another to produce a coherent whole;
• recognize and apply mathematics in contexts outside of mathematics.

Not to mention the communication and representation standards.

But this isn’t the issue at hand; the real issue is how to teach it.If we approach this from a logical perspective, then we understand that students will not develop these skills of scientific inquiry without some direction from the teacher. Inquiry is developed along a continuum, beginning with structured or directed inquiry, moving to the broad category of guided inquiry, and finally – often after much support and scaffolding – to open or student-initiated inquiry. One can also think of this in terms of the Gradual Release of Responsibility model for literacy instruction.

In other words, Thornburg’s argument is entirely irrelevant. His counterexamples fail miserably to disprove the findings of the panel with regard to student-centered v. teacher-directed instruction. What we know is that a balance of both is critical so that students have the opportunity to develop a solid conceptual foundation of school mathematics.

—
¹See the National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics, with particular attention to the process standards. [back]

²Some science resources and organizations that discuss inquiry:

• BSCS
• Northwest Regional Education Laboratory’s Science Inquiry Model. They also have a great problem-solving model for math.
• National Science Education Standards.
• Inquiry and the national science education standards: A guide for teaching and learning.
• The Valle Imperial Project in Science. [back]

³From the NSTA Position Paper on Inquiry. [back]

File this under, “Stuff I meant to post last week and didn’t.”

The National Mathematics Advisory Panel released its final report last week, titled Foundations for Success. You can find the report and sub-reports in a variety of file formats at the NMAP home page.

The report is heavily grounded in “high-quality” research and includes six key elements that I would summarize as follows:

1. Curriculum Focal Points;
2. How students learn;
3. Teacher content knowledge and pedagogical content knowledge;
4. Quality first instruction;
5. Quality, focused assessment; and
6. Education research.

Remember, these are my summaries, not theirs. I would suggest looking at the report if you’re at all interested in what the group had to say, as they are much more verbose than I.