Cross-Curricular Math Instruction

We know that some students think that math “doesn’t matter.”  If math is too conceptual for some students, applied math could make the subject seem more useful. This is easier accomplished on the elementary school level where one teacher teaches all subjects, however collaboration between teachers can incorporate cross-curriculum activities. 

There have been peer-reviewed studies, which show the benefits of incorporating teaching mathematics in a cross-curricular context. Applications for math education incorporated in a variety of fields have been discussed in academic literature, including history, art, drama, and physics. 

While this blog is mostly concerned with K-12 education, cross-curricular education has been successfully implemented in a college setting. Dartmouth University offered the Mathematics Across the Curriculum (MATC) program, which sought to ensure mathematic competency for all Dartmouth graduates regardless of degree program.  The objective of the program is straightforward, and in many ways is the goal of all mathematics education: In the same way that all students should be able to write an essay in any subject they have studied, all students should be able to look at a problem or situation or experiment and ask suitable mathematical questions.

There are multiple cross-curricular guides and lesson plans online. Education World has a great resource for cross-curricular instruction. Scholastic offers a variety of “authentic” math lesson plans. Scholastic also has a special section that offers cross-curricular instruction focused on the nexus of math and sports.  The Discovery channel offers educational activities that focus on math, science and social studies.

Does cross-curricular education work in your experience? Does it enhance the experience of students, allowing engagement of a variety of student interests? Or does it water down the material, leaving students distracted or struggling? How can you best incorporate a cross-curricular approach to mathematics?

Impulsivity and Math Achievement

Could impulsivity lead to better math skills in children? Could this impulsivity be a reason behind the historic gender gap in K-12 STEM education? In the past, boys often scored higher on standardized testing in math than their female peers. The reason for the gender gap in mathematical performance may be based on a tendency towards impulsivity, according to a new study by Drew H. Bailey, Andrew Littlefield, and David C. Geary. The report, published in the Journal of Experimental Child Psychology, found that boys were more likely to make errors, more likely to call out answers in class, and more likely to answer from memory. The study found that girls were more deliberate, less likely to answer in class, more likely to count out on their fingers, and less likely to commit answers to memory.  As a result, students who were less concerned about making errors and participated more, performed better in math.

The takeaway from this study is not a comment on the nature/nurture debate in education, but an insight into how learning styles affect math achievement.  In this blog, Carolyn Kaemmer has already pointed out that the “gender gap” has been mostly erased on the Trends in International Mathematics and Science Study (TIMSS) and Program for International Student Assessment (PISA).  While the new study found a tendency for female students to be deliberate and male students to be impulsive, individual learning styles will vary across the spectrum. This study shows that students should be encouraged to actively participate in class and not to fear answering a question incorrectly.  Consider Dr. David Dockterman’s blog entry about trial-and-error, or “loop learning,” where failure is an engine for success.  Of course, taking chances isn’t enough.  Managing math anxiety and perseverance are also essential behavior ingredients for learning.

What do you think? Are these different learning styles the reason for the gender gap? Share your thoughts. 

President Obama Announces 1 Billion in Funding for STEM Master Corps

Many K-12 STEM educators do not hold a certification in their fields. In response to this, as well as to new CCSS standards, President Obama has announced one billion dollars in funding for training of 20,000 new K-12 STEM teachers in his 2013 budget. This funding will create a “Master Corps” of educators designed to not only have the teaching expertise required of all K-12 educators, but specific training in upper-level science, technology, engineering, and mathematics. Members of this STEM Master Corps will receive a $20,000 yearly federal stipend in addition to their base salary.

This commitment is part of a larger program, the RESPECT Project (Recognizing Educational Success, Professional Excellence, and Collaborative Teaching), a five billion dollar program designed to increase the quality of K-12 STEM education. The Master Teaching Corps and RESPECT programs are a set of strategies for advancing STEM education.  The President has made STEM education a focal point of his educational platform, even mentioning it in his last State of the Union address.

Do you think that this will improve the state of STEM education in this country? Share your thoughts about this initiative. Are you a studying to be a teacher? If so, would you consider joining the Master Corps?

Math Solutions Introduces New Titles for CCSS Prep

The Common Core State Standards offer the benefit of ensuring that all students receive the levels of instruction that will provide them the tools to be successful adults. However, these new standards create challenges for students and educators alike.

Math Solutions® has introduced five new titles designed to help with the transition to the new CCSS for math:

1. Solving for Why: Understanding, Assessing, and Teaching Students Who Struggle with Math by John Tapper
This title uses a response to intervention (RTI) approach that incorporates mini-assessments and targeted strategies for addressing deficits.  A resource for grades kindergarten through eighth grade.
2. Teaching Preschool and Kindergarten Math: A Multimedia Professional Learning Resource by Ann Carlyle and Brenda Mercado
This resource offers 26 videos and 150 lessons. A resource for pre-K and kindergarten.
3. It Makes Sense! Using the Hundreds Chart to Build Number Sense by Melissa Conklin and Stephanie Sheffield
Designed for kindergarten through second grade, this is the second book in the It Makes Sense! series. The title features games and creative methods of teaching with the CCSS math in mind.
4. It's All Connected: The Power of Representation to Build Algebraic Reasoning by Frances Van Dyke
A resource for older students, grades six through nine, this title focuses on using graphic representation of algebraic concepts. This features forty creative lesson plans.
5. Number Talks: Reproducible Dot Images and Five- and Ten-Frames by Sherry Parrish 
This resource is designed for kindergarten through fifth grade. It features downloadable content with over 250 reproducible exercises for students.

Have you used any of these resources? If so, leave a review in the comments section. If you know of any other resources that can help students and teachers prepare for the Common Core State Standards, share them here too!

A Big Problem? The Role of Childhood Obesity and Math Performance

A child’s acquisition of math skills may be related to health factors, a new study by Sara Gable, Jennifer L. Krull, and Yiting Chang.  The study followed thousands of K-5 students and found a relationship between poor mathematical performance and childhood obesity. Consistently lower mathematical performance in obese students was noted. However, the reason for this correlation remains unknown. Does childhood obesity lower cognitive skills? Or are obesity and low math performance symptomatic of another condition, such as poverty, parental involvement, or emotional health?

This echoes previous studies that have linked mental ability and physical health. A 2009 study in The Journal of School Health found that as levels of passing scores on physical fitness test rose, so did scores on standardized exams in math and English.

These studies seem to imply that the health of the body is linked to the acuity of the mind. What do you think? Have you found that you can "think clearer" after moderate exercise? It is tempting to link these findings back to earlier Math Hub discussions about student coping strategies around math anxiety and turning math fear into mastery. Do these studies support a holistic approach to childhood education? Or maybe there is no causation; maybe obesity and poor math skills are both symptoms of a larger problem. What are your thoughts?

Using Technology to Teach Connections between Math and Music

Researchers at Drexel University have teamed up with the Philadelphia Philharmonic to help students conceptualize music in mathematical terms. The team designed a software program, iNotes, to accompany live musical presentations at the Philadelphia Philharmonic. The technology also can provide cultural, historical, and technical information about the score. For example, a student using iNotes to accompany Tchaikovsky’s "1812 Overture" might view information about Napoleon’s failed invasion of Russia in 1812, the event that inspired the score. Or iNotes may provide information on the type of drum used in a live performance that emulates the characteristic cannon fire of the overture. 

In addition to the development of this application, the team has created the Summer Music Technology program (SMT) at Drexel University. This program uses technology to teach middle school and high school students the connections between mathematics and music. For example, students are exposed to technology that enables them to "see" music as a graph or an algorithm. This information is then applied by showing how web-based music services such as Pandora use the mathematical interpretation of music toidentify a user’s musical taste and make corresponding song recommendations.

Visit Musicalgorithms >

This is not the only program that explores the mathematical interpretation of music. The website "Musicalgorithms,"  hosted by Eastern Washington University and funded by the Northwest Academic Computing Consortium (NWACC), allows users to upload audio files and receive algorithms that correspond to components of the music.

Linking music and mathematics may help students see the relevance in math education, may increase the "fun" factor while learning about algorithms, and in this blogger’s opinion – is downright interesting.  Share your thoughts below.

Adventures in Literary Math

By Guest Blogger: Kazia Berkley-Cramer

As summer reading programs start across the country, it’s a good time to explore books for children and young adults that deal with mathematical concepts in a significant and accessible way. Here are two books that are compelling, creative, and will spark a little math thinking.

For the middle grade reader, a great option is Chasing Vermeer by Blue Balliett. Balliett’s first book (along with sequels The Wright Three and The Calder Game) is a Chicago-based art mystery that also features mathematical concepts. As someone who has can be intimidated by all things mathematical, I can assure that Balliett is exceptionally good at making these concepts exciting, fun, and accessible for young people.

Sixth grader Calder (co-protagonist with fellow sixth grader Petra) constantly fidgets with his set of pentominoes, which he finds helps him think and often sparks new ideas. A pentomino, Balliett explains before the story begins, consists of five squares in different patterns (named after the letters of the alphabet that they resemble) and is used by mathematicians to help them think about issues related to numbers and geometry. Although Calder’s set is three-dimensional, it is also possible to make them out of paper or cardboard (see this helpful page on Scholastic’s website). One of the goals of playing with pentominoes is to get a certain number of pieces to fit on a board, and Scholastic’s website has an online version of a pentomino board with varying degrees of difficulty.

Calder is also particularly fond of codes. He and his best friend Tommy create their own code system based on the pentominoes, which they use when they write letters to each other. Balliett includes these coded correspondences and requires readers to decode each message the friends send to each other. The back of the paperback edition includes many extras, including a guide with suggestions for how to create your own code system.

John Green’s young adult road trip novel An Abundance of Katherines features more traditional math: formulas and graphs. Child prodigy Colin Singleton, a recent high school graduate who has been dumped nineteen times by girls and women named Katherine, believes that the world’s population is divided in two: those who have a tendency to dump (“the dumper”), and those who have a tendency to be dumped (“the dumpee”).  Working from the idea that all romantic relationships result either in a breakup, a divorce, or death, Colin works obsessively on creating a formula that can predict the outcome of romantic relationships.

Green supplements his book with a real mathematical formula created by mathematician Daniel Biss, and the book features an appendix by Biss that explains Colin’s formula in clear and understandable detail. If you want to see what the formula looks like but don’t have the book on hand, here is a page from Green’s tumblr where he briefly discusses the formula. Although by the end of the novel Colin realizes that human relationships are much more complicated than a formula can allow, it is interesting to think about what other everyday situations could or could not be graphed.

Both of these books have potential for great interdisciplinary lessons in school, but they are also excellent ways to keep kids and teens thinking mathematically beyond the classroom. What are some of your favorite books that feature math in some way?

Common Core, the Quantile Framework, and Math Excellence

Blog by:
Malbert Smith III, Ph.D.,
Co-Founder and President of MetaMetrics

 

Just last week, I was invited to speak at the CCSSO Rural Chiefs Conference in Kansas City on the topic of “Supporting Math Differentiation in a Common Core World”.  While there is much written and discussed on the idea of differentiated instruction, in practice there are limited tools and resources to support math differentiation, a deficiency well-documented in this recent Ed Week article, ‘’Educators in Search of Common Core Resources”. 

A theme permeating much of my presentation was the neglect of math in our country.  By almost any measure, e.g. instructional time, professional development, number of assessments, instructional programs, etc., math runs a distant second to reading in the amount of instructional attention given.  At least part of the challenge we face in addressing our math crisis in K-12 education will require that we remedy this neglect.

In my suggestions for addressing this imbalance I focused on four critical strategies. While the adoption of the CCSS is a significant first step in the right direction, its real success will rest upon how effectively we implement these standards.  It is critical that we recognize that math – like any other skill - can be learned.  Too often we subscribe, consciously and unconsciously, to the notion that math achievement is an inherent ability, as if math achievement was based on a “math gene”.  If we take more of a Carolyn Dweck growth perspective, as opposed to a fixed mind set, we will go a long way toward promoting the idea that math achievement is possible for all of our students.

Secondly, we need to build math tools and resources that support differentiated instruction.  Once, when leading a math workshop for a school district, the head of the math department informed me, tongue in cheek, that all math teachers know how to differentiate instruction:  “We say it louder and we repeat it.”  Yet I suspect we have all seen variations of this model, this when we continue to drill a student on a math problem or concept to no avail.  Meaningful differentiated instruction is really only possible when we are able to measure a student’s math level and the difficulty of the math concepts and skills on a common scale.  This possibility is now a reality with the Quantile Framework for Mathematics.  Once you know a student’s Quantile measure you know what math skills they are ready to learn.  And just as importantly, one can make sure that the learner has acquired the necessary pre-requisite skills.  Unfortunately, we often continue to employ the “repeat louder” model and fail to provide differentiated content and instruction to meet the unique needs of the learner. 

A third and critical step towards applying the math growth trajectory for all students is mitigating the devastating effects of summer loss.  While summer loss in reading mostly impacts our low income students, summer loss in math impacts students across socioeconomic levels.   During the summer months, we need to draw the same attention to math as we currently do to reading.  On our website (www.quantiles.com) we have built a free utility, Math at Home, which teachers, parents, and students can use to address this issue.

Fourth, students need access to personalized learning platforms that promote the basic elements of deliberate practice. Differentiated instruction through personalized learning platforms enable the learner to move through a learning progression of math skills at the right time, pace, and level.  The underlying engines for the delivery of content within these platforms will require the use of vertical scales, like the Quantile scale, so that the math level of the learner can be matched to the appropriate mathematics material.  Computer adaptive delivery of content and assessment require a common vertical scale that links student to skills.  And the Quantile Framework for Mathematics provides that link.

With the advent of the CCSS we are starting to have the right national conversations about mathematics instruction.  At MetaMetrics, we are dedicated to building the resources and tools to support differentiated instruction and help all students improve their math skills.

Engaging Middle School Students in Math

In a recent article published by MindShift, journalist Annie Murphy Paul questioned, “What is it about middle school and mathematics?” Indeed, research shows that it is during the middle school years that students begin to lose interest in math.  This disengagement often persists, which puts these students at a disadvantage in later schooling and even in their future careers.

Researchers from the University of Sydney in Australia investigated this middle-school phenomenon, looking specifically at factors that caused students to switch on or switch off in mathematics.  The Journal of Educational Psychology recently published the findings, based on data drawn from over 1,600 Australian middle school students.

One of the primary factors the researchers identified in turning students onto math is self-efficacy—students’ perceived capabilities to learn or accomplish mathematical tasks.  According to the published article, teachers can foster self-efficacy in students by maximizing opportunities for achievement.  For example, educators should build on skills students have already mastered and help students develop appropriate goal-setting (i.e. goals that are challenging but still realistic).  

Another critical factor they identified stems from students’ perception of the value of math.  Educators and parents can emphasize the importance of math and the development of math-related skills by demonstrating its usefulness in the real world.  In addition, it is important that educators and parents model positive attitudes toward math.

Improving Mathematical Problem Solving: A Research-Based Practice Guide

What Works Clearinghouse (WWC), a division of the Institute of Education Sciences (IES), publishes research-based education practice guides that address current educational challenges.  The most recent practice guide, Improving Mathematical Problem Solving in Grades 4 Through 8, provides five recommendations that educators and curriculum developers can use to help students in grades 4 through 8 develop better skills in mathematical problem solving. 

Unlike many of the mathematical educator guides floating around the Web, these IES publications are developed through rigorous research and the validity of this research is also evaluated.  After reviewing all available studies pertaining to the topic at hand, the authors of the practice guide assign a “level of evidence” (strong, moderate, or minimal) to each recommendation.  During this evaluation process authors examine individual studies and then consider the whole evidence base, evaluating factors such as the number, quality, and design of the relevant studies.  For more information on the role of evidence and the criteria for each level, see page 3 of the practice guide.  

Check out the practice guide and let us know what you think!  How helpful are the five recommendations?  Is the strength of evidence rating important to you? Does the evidence surprise you in any way?