Praise and Intelligence

As you watch your student taking their Peaksmart quizzes, you've probably noticed the Peaksmart goat praising your child's efforts as they progress through the quiz.

Praising your student when they do well is always a good thing, right?  It can be, but the way in which you offer the praise can surprisingly have unintended side-effects.  According to Carol S. Dweck, a social psychology professor at Stanford, and author of Mindset: The New Psychology of Success, the way we praise children can instill in them a "fixed" mindset or a "growth" mindset. 

A "fixed" mindset relates to a person's belief in their innate abilities.  If a student does well and their parent or teacher praises them with phrases like "you are so smart" or "you are a genius", this can reinforce the child's belief that they are naturally intelligent.  Surprisingly, this can prevent some kids from trying harder problems for fear of risking failure.  In fact, some children that believe they are smart will purposely avoid situations in which they might fail [1].

On the other hand, a "growth" mindset can be instilled in students by praising the child's effort or hard work.  This type of praise has been shown by Prof. Dweck and others to help children become more adaptable and less fearful of failure.  The end result is a student that achieves more than one whose intelligence is praised directly.  Students instilled with a "growth" mindset are less stressful of setbacks and failure and see them more as opportunities for improvement.

Some valid ways to praise include, based on Prof. Dweck's research [2]:

• praising the approach or strategy ("You figured out an good way to solve this problem!")
• praising specific actions ("You scored very well on the quiz!")
• praising hard work or effort ("You really practiced these math facts!")

The Peaksmart team has taken care to ensure that we praise the child's effort as they work through their quiz problems.  We want to see our Peaksmarters full of confidence in their abilities to work hard and increase their math skills without fear of failure. 

References

1. http://nymag.com/news/features/27840/
2. http://www.parentingscience.com/praise-and-intelligence.html 

Multidigit Computation Strategies Amongst Grade School Students

This post is second in a series examining how students learn whole number operations and  multi-digit computations. For the first post in this series, please see this.

Research [1] indicates that students introduced to multi-digit computation develop three distinct strategies for solving problems, which we call decomposition, jump, and vary. 

Let's take 28+42 as an example to illustrate these strategies.

1. Decomposition: In this strategy, students break down both numbers into simpler tens and then add the remaining numbers.

20+40=60

8+2=10

60+10=70

2. Jump: In this strategy, students keep one number whole and simplify the second number to arrive at the solution.

28+40=68

68+2=70

3. Vary: This involves changing the problem in a way to make it simpler and then compensating for this simplification.

30+42=72

72-2=70

Research [2] also indicates that each student may develop thier own strategy for solving these types of problems, but as they are exposed to more problems over time, students veer towards the most optimal strategy. It therefore is recommended that students be allowed to discover strategies on their own and "struggle" towards their optimal technique so they gain an understanding of the underlying number system. Once the optimal strategy is developed, this will serve as the building block for more complex number operations.

Peaksmart aids this approach to numbers and operations in two different ways.

First, the Peaksmart system ensures that students get repeated exposure to several types of problems on a given topic. This gives students an opportunity to exercise their strategies in different contexts and arrive at their most optimal technique. For example, not only is multi-digit addition exposed as a simple computation exercise but also in form of money problems and word problems.

Second, timing plays an important role in Peaksmart quizzes. The time constraint gradually guides the students towards the most optimal strategy. Timing is very important! The student does not simply master a topic because he or she got all the questions correct. The topic continues until students arrive at the best technique to solve the problem within the time constraint.

References:

 [1] Verschaffel, Lieven, Joke Torveyns, and Pol Ghesquiere. "Simple Addition Strategies in a First Grade Class with Multiple Strategy Instruction." Cognition and Instruction. unknown: Unknown, 2005. 1-21. Print

 [2] Verschaffel, Lieven, Brian Greer, and Eric De Corte. Whole Number Concepts and Operations. Charlotte, N.C: Information Age Publishing and National Council of Teachers of Mathematics, 2007. Print. 

.

Why Repetition Works

In his book, Why Don't Students Like School: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom, Daniel T. Willingham discusses how and why math drills are so effective. Note that Mr. Willingham purposely uses the term "drill" which has fallen out of favor with some educators. But the repetition that drilling of math facts provides is a vital tool in ensuring math facts are stored in long-term memory, where they provide students with the most benefit.

Mr. Willingham points out that our working memory, the short-lived memory that we use to hold information in our brains to do complex, short-lived tasks, like reasoning and comprehension, is very limited in terms of capacity. According to his research, there's no way to expand working memory. The way around this limitation is to engage the brain's long-term memory, which can potentially store information for a lifetime.  Interestingly, the letter "c" takes up as much space in your working memory as the word "cognitive" - as long as you've learned and committed to long-term memory the meaning of "cognitive."  

When kids drill math facts regularly, as they do in Peaksmart [1], they are effectively adding to their long-term memory. If a student practices effectively and commits 7 + 9 = 16 to long-term memory, when they see this math fact in the future, there is essentially no toll on their working memory. The student's recall function becomes automatic and engages only the student's long-term memory, bypassing the less-efficient working memory. The only way this information can be committed to long-term memory is through dedicated practice.

Mr. Willingham also discusses his findings that drilling works better if it is spaced out over time. The optimal spacing between practice sessions is a subject researchers are still exploring and we will take a deeper look at the state of this research in a separate blog post.  However, Peaksmart parents have the ability to set their child's quiz schedule to a frequency appropriate to their child's needs.  And of course, students always have the ability to practice any Peaksmart topic [2] in between quizzes.

References

1. http://www.peaksmart.com

2. http://www.peaksmart.com/ps/topics/K

A shiny new release - Peaksmart 5.1!

The Peaksmart team is excited to announce our latest release, which is available...now! Release 5.1 includes:

• New look and feel. The first thing you'll notice is our brand new home page. We're very proud of the new design - and we think you'll appreciate it too.

• More sharing options. Your feedback continues to help us evolve Peaksmart to be an even better math enrichment tool for your kids. Thanks for helping us get the word out to your friends and family via emails and word of mouth. With the new website, we've made it even easier for you to spread the word about Peaksmart - post our link on Facebook, Tweet about us, or use any of the other of dozens of sharing options we've baked in - all from the comfort of our home page.

• Updated Learn More. The Peaksmart FAQ page continues to grow in length and quality. Have a question about how the Peaksmart system works?  The answer is probably here!

• Adaptive algorithm enhancements. Of course, we've been doing more than just making Peaksmart prettier! The adaptive algorithms that allow our assessments, quizzes and practices to target exactly where your child should be in the curriculum have been tuned, to ensure all of our Peaksmarters feel challenged and engaged at just the right level - at all times!

• Easier navigation of curriculum topics.  Our curriculum topics page has been overhauled to make it even easier for you and your Peaksmarters to find specific topics to practice before a big test (or before the next Peaksmart quiz).

• Lots of bug fixes, tweaks, and polish!
  

As always, the Peaksmart team is very excited to bring you these improvements. We can't wait to hear from you and your Peaksmarters! Thanks for choosing us to help your child reach their math potential. And thanks for cheering us on!