Peaksmart Parents: Challenging our Kids at Home

The Peaksmart team is happy to present a guest blog by one of our earliest Peaksmart moms, Summer Lynch. Summer is a super-busy, stay-at-home mom to two boys ages 8 and 5. On top of being a full-time mom and part-time student, Summer somehow balances many other activities such as writing, planning epic birthday parties, cheering her favorite college basketball team, traveling, reading, exercising, photography...you get the picture!

One of my 8 year old’s favorite statements is “Mom, I need a challenge.” He is one of those kids that tends to get bored when things get too easy or mundane for him. My kids have always loved numbers and letters, from an early age. While other kids tended to go for the cars and blocks, both my boys would sit for hours at a time, going over and over any puzzle, book, or game that had these elements. I've always encouraged them to watch and play with things that would challenge them.

When my boys started school I found that they were ahead of most of their peers in math and reading.  Unfortunately, most teachers don’t have the time or resources to challenge the small group of kids that are ahead in math and science. The average first-grade classroom, says Deborah Ruf, author of Losing Our Minds: Gifted Children Left Behind, can have as many as 12 grade-equivalences and an IQ range of up to 80 points. While the No Child Left Behind initiative in the US was meant to help many kids reach proficiency in math and reading, "gifted" students are hitting barricades and not being pushed to go further. “Seventy percent of the kids who are high ability are underachieving,” says Rider University professor Ambrose.


So it seems, now more than ever, parents need to keep challenging their kids - at home.  I've found computer-based programs such as Peaksmart are a great way to challenge my son. He finds that the quizzes offer him just enough challenge. The curriculum is customized for him in such a way that he can work on things he should be working on and go over things that he may want to brush up on.  He is continually pushing himself to do better so that he can move up and receive the medals and other rewards that Peaksmart offers. When he gets frustrated at what he does not know, it makes him want to work harder to get past that section. Having to show his work for many of the quiz questions, as opposed to picking from multiple choices is great - showing his work ensures me that he really understands the problem and the way to work towards a solution.


I'm very concerned about making sure all of our kids are getting the resources they need to achieve at their own levels and pace - at school and at home. Its nice to know that sites like Peaksmart exist to help busy moms like me.

Algebra in Elementary School

Most students in the United States do not study algebra until high school. The reasons why algebra instruction has been postponed are varied, but some of the most popular ones include:

• it is assumed that younger children aren't developmentally ready for the type of abstract thinking that algebra introduces
• even teenagers have trouble with algebra, so introducing it earlier doesn't make sense
• the current curricula in most schools do not emphasize the need for or benefits of introducing algebra in elementary school

In their paper, Arithmetic and Algebra in Early Mathematics Education [1],  David W. Carraher, Analúcia D. Schliemann and Bárbara M. Brizuela describe their research indicating that algebraic concepts could quite easily be introduced at an earlier age and may even be beneficial to students' mathematical learning processes.

The authors conducted a 30-month study of second through fourth graders in which they introduced activities designed to emphasize the algebraic nature of arithmetic, including addition, subtraction, multiplication, and division.

By exploring the commonality between arithmetic and algebra, both flavors of mathematics can be enhanced for pre-teens if the parent or teacher is aware of the overlaps. Some examples of opportunities for exploring both arithmetic and algebra at the same time include:

• arithmetic can be thought of as a part of algebra - the part that deals with numerical concepts, number lines, as well as functions involving numbers
• arithmetic operations can be described as functions in an algebraic sense 
• many concepts in algebra can be thought of as a generalization of arithmetic operations

Number lines, for example, can be used to describe the most basic algebraic concepts, like additive linear functions. The authors used number lines to help the children in the study start internalizing algebraic concepts and thinking at an earlier age than thought possible.

Word problems can also be used to bridge the divide between teaching pure arithmetic and algebraic concepts. Replacing a number in a word problem with a symbol helps teachers reinforce the generalizations that algebra introduces. Tufts University provides a lot of great resources on their Early Algebra site, including creative ways to use word problems to introduce algebraic functions for third graders [2].

The National Council of Mathematics Teachers (NCTM) supports the authors' research findings and encourages teachers to find ways to integrate more algebraic reasoning when possible in elementary school. "As a collection of mathematical understandings develops over time, students must encounter algebraic ideas across the pre-K–12 curriculum. At the elementary school level, teachers help students be proficient with numbers, identify relationships, and use a variety of representations to describe and generalize patterns and solve equations." [3]

Because Peaksmart's curricula for pre-K through third grade are based on NCTM standards and recommendations, our students naturally encounter many of the overlapping concepts described in this post, like number lines and word problems. In fact, you'll see a specific algebra topic in each grade - starting in Kindergarten - that builds on the idea that introducing algebraic concepts in elementary school is a natural way to reinforce mathematics learning.

References

1. http://ase.tufts.edu/education/earlyalgebra/publications/2006/earlyMath.pdf 
2. https://wikis.uit.tufts.edu/confluence/display/EarlyAlgebraResources/Formulas+and+Stories
3. http://www.nctm.org/standards/content.aspx?id=23273

An Introduction to the Common Core State Standards

Have you heard of the common core state standards initiative (CCSSI)[1]? If you're a math teacher in the United States, you may already be familiar with the goals of the common core standards initiative, but many parents are not sure what this means for their schools and their kids.


Essentially, the CCSSI is an educational initiative in the United States that attempts to align the myriad state standards for math and English into a comprehensive set of national standards that will define the knowledge and skills that all students should have at every step of their education - from Kindergarten through 12th grade. The standards will also allow teachers and parents to understand exactly what students should be learning and when in an attempt to better prepare all students for college and beyond [2]. The common standards will make it easier for both parents and teachers to assess their student's achievements across the country as well as against international standards. 


The National Council of Teachers of Mathematics (NCTM) fully supports the goals of the common core standards initiative and has been at the forefront of its development [3]. The NCTM has been a key partner in developing the common core standards and is actively working with teachers and administrators nationwide as implementation of the standards begins (and continues through 2015). 


NCTM standards and research already play a significant role in the Peaksmart curricula. The Peaksmart team has been watching the development of the common core standards for math as we continue to evolve our math ecosystem. We will continue to monitor the roll-out and implementation of the common core standards initiative and provide you with more details to help you understand the impact for your schools and kids. In the meantime, the Peaksmart team is happy to provide practices, quizzes, and lessons that can be used to help promote the goals of this wide-reaching initiative to improve math education in the U.S.


References
1. http://corestandards.org//
2. http://en.wikipedia.org/wiki/Common_Core_State_Standards_Initiative
3. http://www.nctm.org/news/content.aspx?id=26109

Geometric Thinking Skills in Early Childhood

In the National Council of Teachers of Mathematics (NCTM) journal, Teaching Children Mathematics, Carmen S. Brown describes in her article More Than Just Number [1] how children in preschool and younger are already well-versed in thinking about shapes and using geometry in their everyday lives. In fact, Brown's research suggests that in early childhood, geometrical thinking skills are stronger than basic number skills and help the the young mind prepare for more abstract number concepts. By providing a fun and encouraging learning environment for geometrical learning, parents and teachers can provide a strong mathematical foundation for their students as they begin to comprehend shapes, their attributes, and how they all relate to numbers in general.

In fact, geometry skills are developed most naturally during play - starting in infancy. All the time spent with building blocks and shape-sorting toys is good fun, but it's also the first and most efficient way that children can begin to comprehend the basic concepts of geometry, like matching and sorting, that they will build upon when they enter elementary school. As they are learning about squares, circles, triangles, and rectangles, even infants are beginning to see relationships between the shapes, their colors, and their other attributes as well as formulating ideas around symmetry and the spatial relationships of the shapes.

Brown describes the characteristics of ideal environments for children to learn geometry. It's important to use geometric language, like point, lines, angles, and corners, to encourage the development of a math vocabulary and introduce the terminology so it can be used in everyday life. This is especially important when using Peaksmart with children who may not yet be able to read. We described some of our experiences with one of our earliest and youngest Peaksmart users in earlier posts. Whether the parent or teacher reads the questions out loud or uses the audio button available in all Peaksmart quiz quesitons, it is important to use the correct terminology when describing shapes, even if the student is just beginning to understand the concepts behind the new terms. 

Brown goes on to describe how playing and experimenting with shapes in multiple ways at an early age allows children to conceptualize things like height, width, length, volume, and weight. Of course, once these concepts are learned, the ability to compare and contrast the attributes of these shapes is not far off. Peaksmart supports our learners with plenty of practice problems aimed at classification by color, color and shape, as well as sorting by color, shape, size, and type.

Peaksmart continues to add to the toolkit our parents and teachers need to help guide preschool through 3rd grade students through the basic concepts of geometry with practices and lessons. Here are some of our practices involving shapes, symmetry, and spatial relationships that are excellent for younger Peaksmarters. Additionally, we have new lessons available to help explain the geometric concepts that Peaksmart provides regarding 2D and 3D shapes.  

References
1. Teaching Children Mathematics, Carmen S. Brown, Teaching Children Mathematics, April 2009, Volume 15, Issue 8, Page 474

Helping Your Child Find Their "Element" in Math

In his book, The Element: How Finding Your Passion Changes Everything, Sir Ken Robinson [1], a world-renowned speaker, consultant and expert on education, describes the magic when an individual's innate talents and passions overlap to put them in their "element". Many of his stories in the book describe people finding their "element" at very early ages. One in particular, is Terence Tao [2].

Terence is a professor of mathematics at UCLA. Born in Australia, he taught himself basic arithmetic skills at age 2 by watching Sesame Street. Soon after, he began teaching older playmates math too. When he was 7 years old, he was tested by an expert in mathematically gifted children (see the questions he answered, correctly, here [3]). He received his Ph.D in mathematics at the age of 20 and has been awarded numerous honors including a MacArthur Fellowship and a Fields Medal.

Interviewed for The Element, Terence believes that the most important aspect in developing a real interest in math is to have the freedom and ability to play with mathematics, to be able "to set little challenges for oneself, to devise little games". He also emphasizes the importance of being able to experiment with math in different ways.

Stories like Prof. Tao finding his calling so early in life are inspiring, yet he insists that he doesn't have any magical math skills. He does admit to being very stubborn when trying to find ways to solve math problems, though. Sometimes he would be taught a topic in school, not really grasp it immediately, but work on it in a dedicated fashion outside of the classroom, coming at it from different angles until it "clicked" for him.

Whether or not you have a math prodigy in your house, you probably have someone that would benefit from the same type of tools and approaches that Prof. Tao uses. Peaksmart allows for unlimited experimentation with mathematics with our practice topics. Our topics are chock full of lots of variety too, so if one approach doesn't make sense, another perspective given in another question type may do the trick. 

The Peaksmart team is also working on building out lots of other ways to learn math skills in the upcoming months, including our new lessons pages.  Check them out and let us know what you think!

References

1. http://sirkenrobinson.com/skr/the-element
2. http://en.wikipedia.org/wiki/Terence_Tao
3. http://www.nytimes.com/ref/science/20070313_PROF_GRAPHIC.html