In reality, no one can teach mathematics. Effective teachers are those who can stimulate students to learn mathematics.

Want to know why SCASD doesn’t use a math textbook for grades K-5?

Most traditional mathematics instruction and curricula are based on the transmission, or absorption, view of teaching and learning. In this view, students passively “absorb” mathematical structures invented by others and recorded in texts or known by authoritative adults. Teaching consists of transmitting sets of established facts, skills, and concepts to students.

Constructivism offers a sharp contrast to this view.

]]> http://pqme.org/uncategorized/would-you-buy-a-curriculum-from-these-people/feed/ 0 http://pqme.org/uncategorized/its-strategic-addition-strategies-video-3/ http://pqme.org/uncategorized/its-strategic-addition-strategies-video-3/#comments Mon, 15 Mar 2010 02:18:29 +0000 Barb http://pqme.org/?p=715 The latest informational video for parents posted to the SCASD K-6 Elementary Math web page walks the viewer through 4 possible strategies for solving 2-digit addition problems typically done in Grade 3. It’s a nicely done video that clearly lays out some of the potential strategies that third graders might use to solve math problems.

Referenced in the video is the Investigations’ Student Handbook that parents can refer to (pp. 20-24). Perhaps now each student/family now gets this handbook for reference? (This was not something I was even aware of when my son was in third grade, and each child definitely did not receive one).  Or perhaps this is something that is available in the classroom for reference only?

Different approaches and strategies can certainly be appropriate for solving various math problems. The video highlights that students need to select the most efficient approach for solving the problem. Just for fun, I categorized the number of steps required and time to completion for the simple word problem presented in the video, “Bridget went to Sticker Station. She bought 47 horse stickers and 74 space stickers. How many stickers did she buy altogether?”

Strategy A – Adding by Place: 4 separate steps (write the problem horizontally, write the tens addition 40+70=110, write the ones addition 7 + 4=11, write the combined addition 110+11=121), 26″ seconds to complete.

Strategy B – Changing the Number: 6 separate steps (write the problem horizontally, change 47 to 50 by adding 3, change 74 to 75 by adding 1, add 50 and 75 to get 125, calculate how much you added [4], and subtract it from 125 to get 121), 51″ seconds to complete.

Strategy C – Making an Equivalent Problem: 4 steps (write the problem horizontally, subtract 6 from 47 to get 41, and add that 6 to 74 to make 80, then add 41 and 80 to get 121), 31″ seconds to complete.

Strategy D – U.S. Standard Algorithm: 4 steps (write the problem vertically, add the ones, carry a ten, add the tens), 25″ seconds.

This is actually the first time I’ve seen the standard algorithm truly be embraced and I’m glad to finally see it. As for the other approaches, yes, it’s kind of neat to be able to tinker with numbers and shift them around. Fun stuff. Should kids have to solve problems three different ways, though? Repeatedly? Some Investigations homework sometimes seems to require it.

I hope that kids are no longer being penalized for using the standard approach as occurred for my third grader. If students can calculate effectively and get the right answer, I don’t care how they accomplish it as long as the strategy the use works for all problems, and works efficiently. That begs the question – how much more complicated would some of these approaches become if the problem was 89 plus 96, or 426 plus 789, or 7397 plus 4887? At some point, it would seem that ‘adding by place’, ‘changing the number’, and ‘making an equivalent’ might become a bit unwieldy and impractical.

Mastery and accurate recall of basic math facts is an essential component of mathematical problem solving. If we take that mastery as a given, what’s the most efficient method as far as fewest steps and quickest calculation? It may depend on the problem. In the example above, adding by place and the standard algorithm seem equivocal.

But this makes me wonder — which of those two approaches would be most efficient for a 4-digit plus 4-digit problem? I pitted Strategies A v. D for  that 4-digit problem above: 7397 + 4887 =

Strategy A – Adding by Place (all done horizontally as per the example: 7+7=14; 90+80=170; 300+800=1100; 7000+4000=11000) left me with a final calculation of:

11000+1100+170+14 = 12284 (definitely not so easy to do written like this. And yes, I DO know my math facts ). It took me 1:14″

Strategy D – US Standard Algorithm (done vertically, adding from right, carrying, etc). It took me 18″.

It seems pretty clear which is more efficient, doesn’t it?

America’s education advantage, unrivaled in the years after World War II, is eroding quickly as a greater proportion of students in more and more countries graduate from high school and college and score higher on achievement tests than students in the United States, said Andreas Schleicher, a senior education official at the Organization for Economic Cooperation and Development in Paris, which helps coordinate policies for 30 of the world’s richest countries.

… and lax local standards and poor curriculum choices are part of the problem:

America’s system of standards, curriculums and testing controlled by states and local districts with a heavy overlay of federal rules is a “quite unique” mix of decentralization and central control, Mr. Schleicher said. More successful nations, he said, maintain central control over standards and curriculum, but give local schools more freedom from regulation, he said.

If you think reading is a bit boring, well, you may be right.

But for one Pennridge 10th-grade English class, a hands-on architecture project has made reading exciting.

English teacher JoAnn Rubin uses a creative architecture project that teaches her students to use the precision of the English language and architecture as well as the freedom of artistic expression to help all types of students succeed in her English course.

“Not everyone is good at reading,” Rubin said about the project. “Some kids are really artistic.”

Okay, it actually wasn’t an article about English at all – here’s the real article about a geometry teacher.  Why is it acceptable for newspaper reporters to say math is boring and for math teachers to tell their students that not all of them will be good at math?  It’s this kind of thinking that provides a rationale for programs like Investigations that substitute writing and drawing and gluing for math.

See the C-Net video at the 1:08:45 mark.

The informational gathering was led by a senior corporate pitchman, who preached the wonders of Investigations, dazzled the congregation with Power- Point slides, numbers, data, mentions of Japanese superiority and slick humor— all the while informing the parents that they must remain faithful to the orthodoxy of Investigations.

Amherst, Mass., was also using Investigations but recognized the need for a change, identified alternative choices, and began a pilot test of a different curriculum in some of its schools:

First, a committee examined seven different math programs and narrowed the list to two (the new version of Investigations and an alternative). The committee then conducted a “pilot test” in which four elementary schools used one curriculum and the other four elementary schools used the other for one year, and all teachers reported their experience using a standardized rubric. The evidence collected from this one year trial strongly favored one of the curricula (which, interestingly, was not Investigations), and this new curriculum was adopted district-wide with substantial support. Note that no outside consultants were hired, as district personnel handled the entire process.

State College seems to be between the two Amhersts on this timeline.  A critical mass of SCASD Directors seem to recognize that there is a problem with the math curriculum,  but no plans are (yet) in place to try something new.

Students play at home and at school against other students around the world in live games of mental arithmetic. Each game lasts for 60 seconds and students can play up to 500 games, earning points for each correct answer. The students who answer the most questions appear in the Hall of Fame. Students cannot select their level but will move up as they progress.

Over the past 20 years educators have fought over the best way to teach numbers to kids. Advocates of traditional math tout the practice of algorithms and teacher-centered learning, whereas reform-math proponents focus on underlying concepts and student inquiry. In the face of continued declining scores in the U.S., these so-called math wars have heated up recently with the circulation of petitions, the release of contested curriculum guidelines and, in one case, the filing of a lawsuit. At stake is the ability of American high school graduates to perform everyday math tasks and compete in a global economy.

The piece doesn’t have much new information for those who have been following this issue, but there are some interesting comments from readers.  Here’s one:

The math wars are over.  Students need both arithmetic skills and a conceptual understanding.  In order to get both of these students need to practice math with the US algorithms until they are fluent with the procedure.  With this practice teachers can break down the algorithm to explain how and why it works.  And, then students can apply it to actual problems.

The problem with inquiry-based programs is that they are designed to only develop a conceptual understanding.  The spiral nature and lack of practice with efficient strategies (such as the US algorithm) leaves out the other half of the equation to develop students proficient in math.

Please review the work of the National Math Advisory Panel and the NCTM Focal Points.  Even the NCTM realized its 1989 approach was not working and published its Focal Points.

Here’s a comment from a reader who’s not happy with Scientific American consulting mathematicians for the article:

One principal flaw with this article is that the people quoted were primarily professors of mathematics.  As a group, professors know their subjects very well, but unfortunately few know much if anything about how educating a mind works.

The math wars are over.  Students need both arithmetic skills and a conceptual understanding.  In order to get both of these students need to practice math with the US algorithms until they are fluent with the procedure.  With this practice teachers can break down th ealgorithm to explain how and why it works.  And, then students can apply it to actual problems.

The problem with inquiry-based programs is that they are designed to only develop a conceptual understanding.  The spiral nature and lack of practice with efficient strategies (such as th eUS algorithm) leaves out the other half of the equation to develop students proficient in math.

Please review the work of the National Math Advisory Panel and the NCTM Focal Points.  Even the NCTM realized its 1989 approach was not working and published its Focal Points.

Me: “Can I erase this?” I pointed to the whiteboard, and he nodded. I erased the curve, and wrote a series of numbers on the board in a vertical column: 90, 85, 70, 65, and 50. “These are test scores,” I said, “How do you calcualate the mean, or average?”

Mark didn’t volunteer an answer.

Me: “Okay, let’s say the whole class takes an exam, and these are the scores. An average, or mean, tells me how well the class did overall. To calculate the average, I add all the scores, then divide by the number of scores. Here, you do it.” I have him the marker.

Mark added the numbers, then stopped.

Me: “How many scores are there?”

Mark: “Five.”

Me: “Okay, divide the total by five.”

Mark complied.

Me: “What’s the mean?”

Mark: “Seventy-two.” He looked at the numbers for a minute, then smiled. “I get it!” he said.

That’s when I realized what I’d suspected: Mark was a university freshman who had not, until just now, understood the concept of an average.

Reform math is known for several things. Instead of showing kids how to solve a problem, which Singapore Math does, reform math has them work in groups to discover ways to solve it. It wants them to explain how they did it, sometimes using a special vocabulary.

Sabrina Kovacs-Storlie, a supplemental math teacher at Schmitz Park, taught reform math for several years. “It is full of words,” she says. “So many words.”

Reform math also aims at exposing kids to advanced concepts at an early age. As a result, it jumps around. Kovacs-Storlie opens an Everyday Math book. Here is a lesson on calculating the perimeter of a shape. Next is a lesson about probability.

“It is teaching to exposure,” she says. “We are teaching to mastery.”