Tag Archives: math

Engineering the education of future engineers

Too few students are becoming engineers or working in scientific fields. A Wall Street Journal article from Nov. 2011, Generation Jobless: Students Pick Easier Majors Despite Less Pay describes how students may start college intending to become engineers but lack the motivation or skills to meet the rigorous curriculum or choose other fields offering more pay.

The article states, “Research has shown that graduating with these majors (engineering and science) provides a good foundation not just for so-called STEM (Science, Technology, Engineering and Mathematics) jobs, or those in the science, technology, engineering, and math fields, but a whole range of industries where earnings expectations are high.” Non-STEM fields seek people with quantitative skills and may pay more the than the engineering jobs.

Engineers create our technological gadgets. Science Foundation Arizona hopes to persuade more students to become engineers. photo: Steve Jurvetson-Flickr.com

But students are not prepared for college science or mathematics. Less than half of the graduating high school seniors were ready for college math and less than a third were prepared for college science courses according to an ACT report cited in the article.

Ironically, high-tech gadgets designed by engineers are embedded in the lifestyles of high school and college students, yet they choose not to pursue a career to make the gadgets and software, and perhaps earn a fortune they doing so.

Science Foundation Arizona has established the Arizona STEM Network to increase the number of students interested in STEM fields, increase student achievement, and hopefully inspire them to pursue STEM majors in college.

The Science Foundation of Arizona will manage the Arizona STEM Network to increase teacher effectiveness, get businesses involved in the schools, increase the amount of STEM learning and activities in schools and keep track of what initiatives works and their impact.

They have a five-year plan they hope will change the course of the state’s economy by increasing the number of citizens trained in science and engineering fields to attract employers seeking people with those skills.


Recreational math

A few weeks ago I saw an article in the New York Times, “How to Fix Our Math Education.” The authors suggest replacing the theoretical teaching of math with applicable math. “The truth is that different sets of math skills are useful for different careers, and our math education should be changed to reflect this fact,” mathematicians Sol Garfunkel and David Mumford wrote in their op-ed piece.

Most people never need to solve the quadratic formula or use complex numbers, so why do we spend so much time teaching so many children math skills they will never use? Sounds rational.

The authors suggest “teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations.” Again, entirely rational and reasonable. Perhaps if people understood math better on a relevant, everyday basis, fewer people would have signed mortgages they could never pay. (I have no proof of this, but I can’t help fantasizing about a couple ridiculing a mortgage broker proposing ludicrous terms.)

Kari Kling teaching a Math Mania class in her home.

I started teaching in 1993 at Aztec Elementary School in Scottsdale. One of the lead teachers responsible for designing the school, Kari Kling, is an expert at making curriculum relevant to students based on how their brains develop. She understands that awareness of the brain development in children should be driving what is presented in the classroom.

In 1997 she published a book called It’s Not About Math, It’s About Life. It relates math to the real world, where it belongs. The authors of the Times article would probably approve of her approach.

Kling says, “We use the language of math to communicate about something in real life. Numbers aren’t just random, they stand for things.” She teaches a class called Math Mania “to teach kids about numbers as a foundational piece so they understand math when it gets more complicated. Kids need to have real experiences with numbers. If they hear something weighs 14 pounds they need to know what 14 pounds feels like.”

When I taught third and fourth graders, we were learning about the Titanic. They read that the doomed ship was 882 feet long. I asked if that was bigger than a football field. Some said yes, some said no. I told them a football field was 300 feet, goal line to goal line. Silence. One kid who understood numbers said, “The Titanic is almost three times the size of a football field?” He was stunned. I asked if they thought the Titanic would fit on our playground. Some said yes, some said no.

Dice for generating sums.

The next day I brought my 100-foot extension cord to measure the playground. By the time we had got to 882 feet, they had a clear sense of how big the Titanic was. Teachers call this number sense and it is what Kling focused her second and third graders on. What good is manipulating numbers in an algorithm if there is no understanding what those numbers mean?

I went to Kling’s house a few weeks ago to watch her teach a Math Mania class for second and third graders. She had the kids come up with as many ways as they could to add two numbers to make 10 as a short cut to adding large columns of numbers. She calls this “bridging to 10.” It yielded a pattern as pictured in the photo at left. Hopefully the student will see the numbers on the left go from 1 to 9 and the numbers in the middle are 9 to 1 and apply this pattern for any sum.

Then they rolled two or three dice and added the numbers to discover what combinations the dice yielded. They kept track of the sums on a chart. In a subsequent class they would analyze which sums came up the most often, which pairs of numbers came up and why.

The kids were all doing math but they were playing with numbers and playing with dice and writing about the activities in their journals. It wasn’t more “kill and drill” of worksheets or page after page of problem sets. They were playing with numbers in their heads, on paper and with other kids.

There are parents who think math doesn’t need to be fun, it has to be learned. But these are kids, and kids — and adults, really — remember things that are fun because so many parts of their brains is being stimulated all at once.

Plus, it’s better to think of math as fun than as a chore.

Story and photos by Daniel Friedman

Students keep track of what number combinations and sums they roll.


Should the parent be the tutor?

Story and photos by Dan Friedman

With the school year starting up and the thicket of issues surrounding homework, academic achievement and responsibility sprouting from the lazy days of summer, parents are apt at some time to consider hiring a tutor. It might be a matter of wanting their child to score in the upper echelon of their class to better position themselves for admission to the college of choice, or just to avoid an F in math.

After I had had enough of teaching, I was a private tutor for a few years to a slew of kids whose parents hired me to help with their kids’ deficit in math, writing or study skills, or sometimes all three.

Tutoring can add a couple hundred dollars per week to the family budget, which I was all too happy to accept since I could buy food with the money. Some kids I tutored needed help, not because they couldn’t get the attention they needed in school, but because it was more convenient to rely on the tutor to pick up the slack. They knew I would be there to explain the concepts they had daydreamed through or re-explain the directions they hadn’t read.

In reality, when I was a classroom teacher in elementary and middle school, few students ever came in for extra help with lessons they clearly didn’t understand or assignments they had not a clue about how to complete. One-on-one teaching is very efficient and a lot can be accomplished in 10 minutes after school. But students had extracurricular activities that beckoned, and socializing with friends overpowered any desire to ask a question during lunch.

Parents shouldn’t have to hire long-term tutors for their kids to succeed in school. Teachers will generally make themselves available when one of their students is struggling. Parents need to talk to the teachers and find out when their student can come in for a few minutes of extra help.

Ask your kid’s teacher what they suggest. Often, the teacher will say, “If they would just ask a question in class, they wouldn’t be lost.” Really, this is a huge issue. If kids would just raise their hand and ask the question ricocheting around in their head, it would help immensely. Participating in class can save parents hundreds, if not thousands, of dollars.

Still, there are times when a kid just needs someone to explain how to divide fractions, or how to write a paragraph one more time in the quiet of their own home, for them to get it.

Marina Koestler Ruben’s book, How to Tutor Your Own Child (Tenspeed Press, 2011) proposes that indeed parents are the ideal tutors for their kids. She provides all sorts of strategies and approaches to make it work. Koestler says in her introduction, “Parent-tutors provide holistic, low-pressure academic support, engagement and enrichment for their children.” Well, yes, they can, but it isn’t that simple is it? In theory, the book is 192 pages of advice on how to be that holistic teacher with tips and methods to organize, explain, re-teach and enrich the lessons kids need to learn.

I guarantee you there will be times when, after a long day and many frustrating attempts to explain how to factor a polynomial, both parent and child will just be butting heads. The parent tutoring effort will be acrimonious and counter-productive.

So, examine your relationship with your child and decide if being the tutor is best. I made plenty of money being the scorned tutor who insisted the student show his or her work on a math problem, and being a pain in the ass about proofreading. But I persevered, the lesson was completed, I got paid and peace in the household was maintained because mean Mr. Friedman left, and the parent could be the good guy.

For the parent who has the energy to be an effective tutor, Koestler’s book is very valuable and useful for the right situation and parent-child dynamic.

Better to get the student to ask questions in class, and get extra help in school before relying on a tutor. Students need to learn how to be more responsible for their education by seeking help. Tutors are perfect for additional teaching and a personalized, fresh approach.

Veteran teachers offer test-taking strategies for college-bound students

Valley students can sharpen their test-taking skills through a PSAT preparation class offered several times throughout the year at the EAJ Institute, a division of New Vistas Center For Education.

The one-week class prepares students for the PSAT exams, also known as the Preliminary Scholastic Aptitude Test. The exam is offered to students in grades 10 and beyond as preparation for the National Merit Scholar competition and the Scholastic Aptitude Test (SAT).

The PSAT test measures a student’s critical reading skills, math problem-solving skills and writing skills. The test opens the competitive door to college entrance, scholarships and the National Merit Scholar Program, which qualifies and honors students who exhibit extraordinary academic capabilities.

Language arts teacher Stacey Trepanier. Photo courtesy of New Vistas Center for Education.

“There is such a thing as test-taking anxiety,” says Eleanor Jordan, Ph.D., director of EAJ Institute. “The only way to overcome this is to show students what to expect and equip them with reasoning strategies and tactics to arrive at the correct answers. When students take this five-session class they will be equipped, confident and prepared to perform at the pinnacle of their capabilities.”

The class is taught by language arts teacher Stacey Trepanier and math teacher Jim Barnette.

Trepanier is a Shakespearean coach and teacher of 18 years. She gives students tools to critically analyze reading passages and discern Greek and Latin root words to assess unfamiliar vocabulary. She also offers tips for constructing powerful essays.

Math teacher Jim Barnette. Photo courtesy of New Vistas Center for Educaiton.

Barnette, a 34-year veteran teacher, offers components of reasoning to give students the competitive edge in everything from simple math to data analysis, statistics and probability.

The PSAT is the preliminary requirement for taking the College Entrance Exam and serves as the initial step for participation in the National Merit Scholar Competition, an academic competition for recognition and college scholarships that began in 1955.

Class sizes are limited and specific schedules will be announced in September, 2011. Registration is required.

EAJ Institute, a division of New Vistas Center For Education, offers specialized classes and testing services to the Phoenix area at large. Its services include: academic and diagnostic testing, reasoning ability testing, PSAT/SAT preparation classes, gifted enrichment classes and workshops and a summer day school for pre-K through 2nd grade. The Institute is located on the New Vistas campus at 670 N. Arizona Ave, Suite 35, Chandler AZ 85225. For more information call 480-963-2313 or visit newvistasaz.com/eajinstitute.html.

Numbers, sensibly

10 CheeriosTeaching new skills and concepts depends on understanding what the student already knows. This applies to adults as well as children. When kids enter school and learn to read they need to know their alphabet and have an inkling that letters correspond to sounds. Most kids learn the alphabet by singing the ABC song as well as seeing letters in books, on signs, on television, etc.

Math is the same way. Before kids learn 1+1=2, they need to know what numbers are and what they represent. They must develop number sense, which is the understanding that numbers relate to the real world. Young children have number sense when they know that three people can fit in their family car, but 30 could not.

A study by David Geary at the University of Missouri confirms scientifically what parents and teachers know: that number sense is as essential to learning math as the alphabet is to learning reading. The study followed 177 elementary school kids for five years to track the differences in progress amongst the group of elementary school aged kids.

press release about the study reports, “A long-term psychology study indicates that beginning first graders that understand numbers, the quantities those numbers represent and low-level arithmetic will have better success in learning mathematics through the end of fifth grade, and other studies suggest throughout the rest of their lives.”

Number sense is part of the standards as set by the Arizona Department of Education for first grade but number sense is part of a youngster’s life when parents count things and play games with quantities.

When I taught third, fourth and fifth graders, I still taught number sense, though with a more advanced perspective than one would for a preschool student. When teaching multiplication, I needed to make sure my students understood that multiplying two numbers in the hundreds would necessarily be in the tens of thousands or in the millions — not just thousands. Number sense bolsters estimation skills also.

From the National Council for the Teaching of Mathematics: “Researchers note that number sense develops gradually, and varies as a result of exploring numbers, visualizing them in a variety of contexts and relating them in ways that are not limited by traditional algorithms (Howden, 1989).”broccoli5

Hmmm. That’s a complicated way of saying kids should know that the five pieces of broccoli they don’t want to eat is four pieces of broccoli after they manage to choke down one piece of broccoli. 5-1=4 means very little to children without number sense, even though they may be able to count on their fingers and get the answer right on a worksheet. Kids understand math when they have number sense.broccoli4

Before you rush out to find a cool number sense smartphone app, remember, number sense is a real-world, three dimension experience, not the flat screen of a smart phone or computer. Numbers count things. With your child, count the number of Cheerios that fit on a spoon or in a cereal bowl, or discover what 100 Cheerios looks like. Or count all the socks that have no mates. In the car count the number of orange cars compared to the number of white cars.spoon full of cheerios

“Cognitive Predictors of Achievement Growth in Mathematics: A Five Year Longitudinal Study,” will be published in the journal Developmental Psychology. But really, you don’t need to read it. — Dan Friedman

SRP grants fund innovative classroom projects

Learning Grants by SPR in action.

SRP is accepting applications for grants this month from teachers around Arizona, in hopes of enhancing learning in math, science, technology and social studies. The SRP Classroom Connections program is ready to provide up to $180,000 in funding for teachers with great ideas. The application deadline is March 31.

Learning Grants are available for programs that benefit learning in math and science. Each selected school will receive up to $5,000 to implement new plans that meet Arizona Academic Standards.

Last year’s 27 winners came up with a variety of ideas to make learning more interesting for students. Lone Mountain Elementary School created a LEGO Learning Lab so K-5 students could learn about structures, machines and design. Fountain Hills High School implemented a STEM (Science, Technology, Engineering and Math) class where students will participate in university-level lectures, use an MIT curriculum and receive dual credit through ASU’s college of engineering.

A Social Studies Grant is available to teachers looking to enhance history, geography, civics, government and economics classes. Teachers who are selected will receive up to $2,000 each. Last year’s winners included Madison Park Elementary School, which started a traveling Civil War trunk that contained Civil War artifacts, books and audiovisual items with which students could interact while learning about this period of history.

SRP will be holding a grant-writing workshop from 5 to 6:30 p.m. on Wednesday, March 16 at SRP’s Project Administrative Building, 1521 N. Project Drive in Tempe. To sign up call 602-236-2798.

Applications are due March 31 and winners will be announced in May. All public, private and nonprofit schools in metropolitan Phoenix, Pinal County, Gila County, Yavapai County, Page and St. Johns are eligible to apply. For more info visit: srpnet.com/grants.

Xavier recognized at JET TEAMS competition

The engineers of the future: Xavier's JETS teams took first place in their division.

Two teams of students from Xavier College Preparatory participated in the Junior Engineering Technical Society (JETS) Technology, Engineering, Applied Math and Science (TEAMS) competition last month at Arizona State University.

The Xavier teams participated in the 9-10 category for high school freshman and sophomores, and the 11-12 category for high school juniors and seniors. Participating high schools were placed in divisions based on the size of the senior class as well as the admissions criteria. Both Xavier teams placed first in their divisions.  The 9-10 team also won runner-up in the spirit competition.

The JETS TEAMS program is an annual high school competition challenging students to work collaboratively and apply their math and science knowledge in practical, creative ways to solve real world engineering challenges. After participating in TEAMS, students increase their knowledge of engineering, feel more confident about participating in engineering activities and increase their ability to work with others to solve complex problems. In recent years, countless reports have identified troublesome science and math achievement gaps in America, and signaled the need for renewed efforts to cultivate a competitive 21st century workforce. These reports point to the necessity of programs that foster STEM (Science, Technology, Engineering and Math) literacy in effective ways, and across a broader range of young people. The TEAMS Competition helps develop “STEM-capable” students in an engaging way by showing them how math and science, with an engineering focus, are used to make tangible differences in the world.

“What impressed me the most is the determination the girls showed applying problem-solving skills,” says Janet Mambrino, JETS/TEAMS faculty moderator at Xavier. “They did not give up when faced with complex problems. Instead, they worked together and kept plugging away until they were successful, walking away with a feeling of pride at their accomplishment.”

Focused on a theme each year, original academic and innovative concepts are developed for the competition based on the National Academy of Engineering‘s Grand Challenges. Tackling these challenges requires critical job-readiness skills such as collaboration, analytical thinking and multidimensional problem-solving. Students in the 2011 competition worked on the challenge of energy and the global need for diversification, efficiency, security and ecological sustainability.