Creating Positive Math Experiences for Learners

A recent article described how anxiety toward math can hinder mathematical progress. As parents and educators, how can we reduce or eliminate math anxiety through creating positive math experiences for learners? We’ve come up with some ideas.

1. Focus on math as a process rather than math as a single answer.
Many students view math as finding a single answer, where getting the right answer is good but getting the wrong answer is bad. When learners feel concerned with finding a single correct answer, they can develop anxiety toward math. In reality, math is a process that requires making conjectures, finding examples or counterexamples, trying new ideas, and collaborating. One way to help learners view math as a process is to ask learners questions such as “how do you know?” or “can you prove that?” rather than immediately confirming whether an answer is correct. Praise learners for their ability to explain their mathematical thinking, even if an answer is incorrect.

2. Ensure learners have material with an appropriate level of challenge.
If material is too difficult for learners, it can cause learners to feel anxious or discouraged. Choose problems with multiple entry points and provide learners with various tools to help solve such as manipulatives, graph paper, or colored pencils. Knowing a learner’s Quantile measure can also help educators choose materials with an appropriate level of challenge.

3. Avoid using math as a punishment.
Many of us have probably had a teacher who assigned extra math problems when the class was misbehaving or a parent who made us do schoolwork when we didn’t complete a chore. When math is used as a punishment, it leads learners to associate negative feelings with doing math rather than feelings of accomplishment, intellectual curiosity, and joy. Find creative ways to use math as a reward instead of a punishment, for example by spending one-on-one time playing a math game with a learner or allowing a learner to use special technology such as a tablet for the purpose of doing math.

4. Remain calm.
Parents and educators may feel anxious themselves about math, and learners can sense this feeling and replicate math anxiety from adults in their lives. If you feel math anxiety as an adult, try to remain calm when working with learners. It may help to review materials on your own first, prior to working with students, to give you a chance to review concepts before explaining those concepts to a learner.

What are some ways you create positive math experiences with learners in your life?

New Partnerships Increase Use of Quantile Measures

A series of new partnerships have greatly expanded the reach of the Quantile Framework for Mathematics. In the last year, Quantile measures have been added to Pearson’s aimswebPlus and Istation’s ISIP Math. Quantile measures have also become available through state assessments in Kansas and to the 15 member states of the Smarter Balanced Assessment Consortium. These new partnerships are in addition to the numerous state level assessments and assessment products that already report student mathematical ability in Quantile measures, including Kentucky’s K-PREP, North Carolina’s NC READY, Curriculum Associates i-Ready, HMH Math Inventory and Imagine Math. Also this year, new materials and textbooks from Pearson, McGraw-Hill, Origo Publishing and Big Ideas Learning have been calibrated to the Quantile scale, adding to the dozens already featuring Quantile skill or concept measures.

Quantile measures accurately match students with instructional materials by measuring both mathematical capability and the complexity of mathematical skills and concepts on the same developmental scale. There are two types of Quantile measures: a measure for students and a measure for mathematical skills and concepts. The Quantile student measure describes what the student is prepared to learn next. The Quantile skill or concept measure describes the difficulty, or demand, in learning that skill or concept. Both measures are represented as a number followed by the letter Q (e.g., 640Q) on the Quantile scale. Quantile measures can improve mathematics teaching and learning by helping educators target instruction and determine if students are on track to pass year-end assessments and succeed in college and careers. Visit www.Quantiles.com for more information about the Quantile Framework.

Celebrate Pi Day with Rich Math Tasks!

Every year Pi Day is celebrated in classrooms across the nation. This year we are offering examples of rich math tasks on the topic of pi that have been calibrated to the Quantile Framework. Use these tasks in your Pi Day celebrations to help students make meaningful connections to the concept of pi. Visit quantiles.com/pi-day to access our Pi Day resources!

And with the roll-out of this new resource, we’re giving away a pie! What do you need to do to be eligible to win a free pie? Simply “Like” our Quantile Framework Facebook page by April 14th and you’ll be entered to win*.

*Pie giveaway for residents of the United States only. Winner will be contacted via Facebook.

Literature That Will Enrich Mathematics

Embracing literature to enhance mathematics instruction in the classroom or at home benefits students by providing a richer and more meaningful perspective of mathematics. Connecting children’s literature with mathematics is an effective avenue for promoting problem solving, communicating in mathematics, and make connections between the mathematics needed in multiple disciplines. The paper “Using Children’s Literature to Teach Mathematics” presented on The Quantile® Framework for Mathematics site offers teachers and parents helpful suggestions for identifying literature that will support mathematics instruction and engage students.

An appropriate book to enhance an effective mathematics lesson should have an authentic context that includes real-life experiences, multi-cultural components, and enjoyable plots that unite mathematics and literacy. A report titled “Making Informed Choices: Selecting Children’s Trade Books for Mathematics Instruction” by S. J. Hellwig, Eula E. Monroe, and James S. Jacobs (2000) offers suggestions for identifying books that will support instruction and create meaningful and explicit connections to engage students. The article offers pointers for choosing appropriate children’s literature with mathematics topics. An appropriate book should:

  • represent mathematics and other information accurately and depict mathematics relationships correctly.
  • presents factual information, uses terminology appropriately, and portrays mathematical principles accurately.
  • includes a format and presentation that are visually and verbally appealing.
  • offers interest and pleasure without overpowering the text with mathematical processes and terminology.
  • provides a context for learners to make meaningful connections between mathematics and personal experiences.
  • easily connects the mathematical process or experience to the resolution of the story.
  • presents concepts in a way that appeals to a range of audiences and abilities.
  • appeals to a variety of interests, cultures, and/or experiences.
  • offers layers of richness beyond the predictable or expected and presents exciting new views or ideas.
  • engages students with a story that layers the unexpected with original insights or surprising events.

The study of mathematics is not just about learning mathematical processes and memorizing facts and algorithms. Mathematics becomes more visible in everyday life when students discuss the uses and advantages of applying math in various situations and recognize the necessity of mathematics in careers, personal budgets, traveling, and even games. What better way to promote those discussions when so many children’s books are available to add fun and interest to topics in mathematics?

Math Circles Help Develop Students’ Problem Solving Skills

At MetaMetrics, we get excited when we see enthusiastic students and educators in our community! Just down the street from our offices is exactly what you can find on Saturday mornings: students, parents, and educators working together to solve challenging math problems as part of the Chapel Hill Math Circle headquartered at the University of North Carolina at Chapel Hill.

What is a math circle? A math circle is a group of students of any grade level coming together to share their passion for math through exploring challenging math problems or special topics. Math circles benefit students by providing the chance for them to solve unfamiliar problems in unique ways. In traditional math classrooms, students often learn a new skill and then immediately apply that skill to a set of practice problems. This process does not give students the opportunity to determine which mathematical concept or solution strategy should be applied to a given problem. In math circles, students see problems out of context from classroom instruction, which helps them develop the ability to solve problem, make arguments, critique others’ reasoning, and persevere through difficult tasks.

In the Chapel Hill Math Circle’s beginning group, students in first- through third-grade solve problems such as this one:

A male parrot and a female parrot are talking. The one with a yellow tail says, “I’m a boy.” The one with a blue tail says, “I’m a girl.” If at least one of them is lying, who is who? Explain your answer.

This is an example of the type of problems the advanced group of high school students would solve:

A polyhedron is made up of pentagons and hexagons. How many pentagons must there be? Prove that no other number of pentagons is possible.

These problems are designed to solicit deep thinking and require students to try multiple solution strategies, collaborate, propose and test conjectures, and communicate ideas using valid mathematical arguments. At the end of the school year, the math circle concludes with a Julia Robinson Math Festival, a full day of problem solving, games, and prizes, all related to math!

For more information about math circles, including how to find a math circle near you or how to start your own math circle, visit the National Association of Math Circles at https://www.mathcircles.org/. For more information specifically about the Chapel Hill Math Circle and the corresponding Triangle Math Teachers’ Circle that provides professional development for local teachers, visit https://chapelhillmathcircle.org/. For more information on the Julia Robinson Math Festival, visit http://jrmf.org/.

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Photo Courtesy of the Chapel Hill Math Circle

Celebrate Storytelling in Mathematics

September 25th is Math Storytelling Day! MetaMetrics® offers Lexile “Find a Book” so that educators and families can use student Lexile® measures to make informed decisions about reading materials that both interest children and are at reading levels appropriate for them to understand the material. Likewise, on quantiles.com MetaMetrics offers Math Literature Guides that accompany children’s books so that teachers and parents can use student Quantile® measures to engage children with appropriate topics in mathematics. Because this is the week of storytelling in mathematics, we want to share some Math Literature Guides that serve as samples for a variety of mathematics skills and concepts.

A simple topic for the early mathematics learner is working with ordinal numbers, such as first, second, third, and fourth. A fun book to read is Trouble on the T-Ball Team by Eve Bunting. The Math Literature Guide for this book offers ideas for using ordinal numbers at sports events (third quarter of a football game), in routine events of the day, or when losing the first tooth. In the Math Literature Guide, notice the blue title of the book. This means that when you click the title, you will be taken to the Lexile “Find a Book” page for that book.  On that page in the right-hand column is a drop-down menu called “Find This Book.” Select “World Cat” in that drop-down list to see libraries near your home where you might find the book. You can also select “Barnes & Noble” or “Amazon” to purchase the book.

For children a little older, another more challenging math topic is counting to a million, the subject of the book, A Million Dots by Andrew Clements.  Dots are everywhere in the book and the challenge is to find the dot that is indicated by the number on the page. The Math Literature Guide for this book offers ideas for questions that will encourage children to think critically when comparing such large numbers.

Geometry topics are the subject of many children’s books. One example is Sir Cumference and the Great Knight of Angleland by Cindy Neuschwander. This book includes some plays on words about angles and circles. By fifth grade, students are learning about right angles, acute angles, and obtuse angles. So the Math Literature Guide for the book offers ideas for finding different types of angles in the book and for thinking about where angles are found in architecture, design, and nature.

Mathematics is everywhere in our world but can seem to be invisible unless we take the time to point it out. Reading children’s books that accentuate the uses of mathematics offers insight and appreciation for the role of mathematics in our lives. Talking about the books we read makes reading more fun as well.  Sunday, September 25, is Math Storytelling Day, so take a trip to the library where you will find books that reveal mathematics in unexpected places to kick off a week of pleasure in reading books about mathematics. Read and enjoy!

Story Telling in Mathematics

Many people have fond memories of mom or dad putting them to bed with favorite bedtime stories. I recall the precious memory of a parent reading a fun story just before I snuggled into bed for the night. I also have a special memory of the bedtime hour when my dad was home to tuck me in. He did not read stories to me. He gave me “algebra” problems. From the time I was in third grade and up, he would ask, “A number plus 8 is 15. What is the number?” Now as a grandmother, I play “Mystery Number” with my grandchildren at bedtime. They never fail to follow their answer with “Give me another one, Grandma!”

My bedtime memories were a good combination of mathematics and literacy. The benefits of reading to our children are enduring. Through books, children appreciate experiences of others that often relate to their own experiences, expectations, and dreams. Children’s books can also help to teach the concepts and uses of mathematics.

Math Storytelling Day is coming up! According to their website, September 25 is set aside every year to celebrate the many ways that mathematics is used in our daily lives. “Math Storytelling Day is a great opportunity to get children excited about math through stories and games. Math stories can include logic, patterns, puzzles and numbers.”

A great place to find mathematical resources, such as games, activities, websites, tutorials, and videos is quantiles.com. Parents and teachers can access resources that are targeted to a child’s mathematical ability level based on The Quantile® Framework for Mathematics.  This learning community for teachers, parents, and students also includes helpful articles such as “The Quantile Framework for Mathematics in the Home.” As well as those ideas listed in the article, another simple convenient way to encourage a strong appreciation for the mathematics people use every day is to read books about math topics that inspire children to appreciate and enjoy mathematics.

The website quantiles.com lists children’s books that teach mathematics and offers Math Literature Guides that detail specifics about how to connect mathematics and literature. Each Math Literature Guide includes a series of questions and activities that promote ways for parent to talk about mathematics with their children. One example is the Math Literature Guide for the book Keep Your Distance, a fun and humorous book about measuring lengths with inches, feet, and miles by Gail Herman.

To celebrate Math Storytelling Day this year, the Quantile Team at MetaMetrics will share more book titles and Math Literature Guides about various topics in mathematics. Math storytelling can be an enjoyable experience for parents, teachers, and students as they focus on the ways mathematics is used daily. Stay tuned!

Gold in Math Olympiad

The 2016 Rio Olympic Games finished almost a month ago with the U.S. winning a total of 121 medals, which is almost double that of Britain in second place.  While we are still celebrating our nation’s athletic prowess, we should also be touting our academic success — the U.S recently won its second consecutive gold medal at the International Mathematical Olympiad (IMO). The IMO is an annual competition for high school students held each year in a different country. The two-day competition requires students to complete 3 problems each day in 4 ½ hours. Here is an example problem:

“In Lineland there are n ≥ 1 towns, arranged along a road running from left to right. Each town has a left bulldozer (put to the left of the town and facing left) and a right bulldozer (put to the right of the town and facing right). The sizes of the 2n bulldozers are distinct. Every time when a right and a left bulldozer confront each other, the larger bulldozer pushes the smaller one off the road. On the other hand, the bulldozers are quite unprotected at their rears; so, if a bulldozer reaches the rear-end of another one, the first one pushes the second one off the road, regardless of their sizes. Let A and B be two towns, with B being to the right of A. We say that town A can sweep town B away if the right bulldozer of A can move over to B pushing off all bulldozers it meets. Similarly, B can sweep A away if the left bulldozer of B can move to A pushing off all bulldozers of all towns on its way. Prove that there is exactly one town which cannot be swept away by any other one. (Estonia)”

In the podcast “Count One More Gold for The U.S. — In MathJody Avirgan interviews Po-Shen Loh, the U.S. team coach. Loh, once a team member and now a professor at Carnegie Mellon University, thinks that just as the U.S. Olympics inspires young athletes, the IMO can likewise encourage students to be interested in mathematics. “I think that mathematics is similar to sports in the sense that if you do more practice, you actually get significantly better,” states Loh. “And the big question then becomes, ‘How do we convince people that doing that practice in mathematics is a fun, fruitful, exciting thing to do?’”

Good question, Professor Loh. One way we can encourage fun mathematics practice is through the use of math games. A quick internet search yields hundreds of math game sites. For a more precise approach to finding math games, teachers and parents can use the free resources available on quantiles.com.  At the site, click “Use the Quantile Framework” at the top of home page. Then select “Math Skills Database” and “Keyword Search.” Enter a keyword such as “Operations.”  A list of Quantile Skill and Concepts (QSCs) targeted to the topic will appear. Suppose you want to practice “Order of Operations.” Click the QSC “Use order of operations including parentheses and other grouping symbols to simplify numerical expressions.” Then click” Show 18 Resources” to view the free resources calibrated to that skill. There are several math games listed to help students practice math AND have fun.  

Productive Failure

“If at first you don’t succeed, try, try again.” Babies learn to walk in this way. Preschoolers learn to button, tie, and zip to dress themselves in this manner. However, the idiom can now apply even after children enter school. In the article, “How ‘Productive Failure’ In Math Class Helps Make Lessons Stick,” Katrina Schwartz explains that productive failure is not just the idea that persistence pays off. Rather productive failure is an effective teaching strategy that involves “careful lesson design, a strong classroom culture and an instructor trained in getting results from small failures so his or her students succeed when it matters.”

The idea is that teachers are trained to develop math tasks that students will not be able to solve but that evoke a students’ prior knowledge relating to the task. Teachers also receive training to gain deeper content knowledge to assess student ideas and misconceptions as well as learn how to set the classroom environment to foster failure as a natural part of learning and not an embarrassment.

The Quantile Framework can help teachers to develop tasks that promote productive failure. Using the tools available on Quantiles.com, teachers can select activities to both develop challenging tasks and tasks that ensure prior knowledge. Here’s how:

  1. Go to Quantiles.com.
  2. Click “Use the Quantile Framework” at the top of home page.
  3. Select “Math Skills Database.”
  4. For the State Standards search, select the state in the dropdown list.
  5. Select the grade level or name of the math course in the Course dropdown list.
  6. Select the specific standard in the Standard dropdown list. Click “Search.”
  7. A list of Quantile Skill and Concepts (QSCs) targeted to the standard will appear.
  8. Click a QSC to view more details including its Knowledge Cluster. The Knowledge Cluster provides insight into Prerequisite, Supporting and Impending Quantile Skills and Concepts.
  9. To help create challenging tasks, click a QSC number for a Supporting or Impending QSC to see free challenging resources.
  10. To access resources to build prior knowledge, click a QSC number for a Prerequisite QSC to see free resources calibrated to a prerequisite skill or concept.

To learn more about productive failure, read the research of Manu Kapur, Professor of Psychological Studies at The Education University of Hong Kong.

Teaching Math with Storybooks

By reading and discussing stories with children, you can gain some insight to how they think. Herbert Ginsburg, a professor of psychology and education at Teachers College Columbia University suggests that reading and discussing math storybooks with your child can help set the stage for meaningful mathematical achievements in school.

Certain books, such as counting and shape books are centered on learning math. However, there are also many books that have embedded mathematical ideas in the stories. For example, when Goldilocks sees Baby Bear’s bed and realizes it is too small, she compares the size of the beds to the bears. By doing this, she then realizes that there is a simple correlation between the two: the smaller or larger the bear, the smaller or larger the bed.

Storybooks deal with mathematical information informally with patterns, spatial relations, measurements, addition, subtraction, multiplication, and division. When reading books with your child ask questions about what’s happening in the story, make predictions of what will happen next, and try to find the embedded mathematical skills.

The following ideas may promote your child’s math learning:

  • Read books that you both find interesting.
  • Talk with your child about what is happening in the story.
  • Use mathematical language to describe and explain events in the book, (this square has four sides and they are all the same length, this is the biggest, which weighs the most) this should also keep your child engaged.
  • Think about your own math experiences and if they are negative, try not to transmit those feelings.

Reading stories is a wonderful way to help your child understand new mathematical skills. To help you along, we have math literature guides on Quantiles.com that can be used to introduce new mathematical skills. Literature guides are provided as a resource for the Quantile Skill and Concept (QSC) they are associated with.

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Ginsburg, H. P. (2016, February 2). Finding the Math in Storybooks for Young Children. KQED News. Retrieved from http://ww2.kqed.org/mindshift/2016/02/02/finding-the-math-in-storybooks-for-young-children/

 

MetaMetrics is an educational measurement organization. Our renowned psychometric team develops scientific measures of student achievement that link assessment with targeted instruction to improve learning.