Common Core Math + Families = Student Success

A Context to Connect with Families

In the last 3 weeks Core Learning has had the opportunity to support math instruction through Parent Math community engagement events in several Alameda County districts. Two of our Parent Math nights coincided with American Education Week and certainly facilitated communication between schools and the public in order to ensure that the successes and needs of schools are celebrated and met, respectively. Beyond AEW, the need for clear and regular communication with families around the Common Core math standards has become increasingly evident as parents and districts begin to experience the implications of the transition to the new standards.

One of the most frequently asked questions that we have heard from parents, whether they have children in the elementary or secondary levels, is why are we teaching math to students in this new, seemingly inefficient way?  As parents encounter ways to “do” math that diverges from their own math learning experiences, they may be discovering that their own mathematical understandings are being challenged as they try to support their children’s mathematical development.

As is often the case with new things that we don’t fully understand, it may be tempting to dismiss the different ways that math is being taught. Adjectives we have heard in reference to the Common Core standards include “confusing,” “dumbed-down,” “inefficient,” and “impractical.” However, we have found that as parents engage in the new mathematical models that elementary students are using to understand the why of mathematics, and as they encounter the limitations of their secondary students’ math abilities with the entry of problems that require flexibility of mind and strong problem-solving skills, there is a realization that teaching students procedures and rules without fostering a deep understanding of the structures and systems which these algorithms help to navigate is actually not preparing our students to be critical problem solvers.

Pictorial Models to Develop Conceptual Understanding

At the elementary math nights, the main part of the program focused on having parents and guardians work through common pictorial models being used at the K-5 levels. Participants rotated through stations dedicated to solving math problems through tape diagrams, array and area models, number bonds and ten-frames, and manipulatives to understand place value. The experience is intended to clarify for parents how these models support student understanding of various math concepts. As often happens when students encounter these models for the first time, light bulbs started to go off for adults when they started to recognize how their own mathematical understanding may or may not be based in a strong conceptual foundation.

One example of this is when parents were asked to use a tape diagram to help them understand how to solve the following 1st grade math problem from EngageNY:

Lucy has 5 pencils. Kim has 7 pencils. How many more pencils does Kim have than Lucy?

Over the course of the evening, parents quickly subtracted to find the answer. When asked how they knew to subtract, many of them struggled with a response. When it comes to elementary problems such as this, it is easy for us as adults to forget how we develop the ability to decode stories such as this into arithmetic problems. This is where models such as tape diagrams are useful in providing a visual reference for students as they develop skills to determine the best, most efficient approach to solve problems.

By providing a means for students to see a physical representation of the abstract problem, models such as these provide a scaffold for students as they transition between the concrete and abstract. Further, the integration of mathematical models incorporates at least 2 of the Mathematical Practice standards, furthering our young people’s development of critical and problem-solving skills: 4) Model[ing] with mathematics and 7) Look[ing] for and mak[ing] use of structure. Exposing parents to these modeling approaches, and providing them the experience and language to discuss these mathematical explorations with their children, is just one way that we can support students and their families in building mathematical understanding.

Collaboration to Build Mathematical Meaning and Understanding

At the secondary level, we have seen shifts in instruction towards more student-centered lessons, which often include moves towards increased collaborative learning. In order for students to be productively engaged with classmates, these transitions require problems which are usually open-ended, with multiple solutions and/or means of arriving at the solutions. These 2 basic shifts in content and student interactions require and develop another two of the 8 Mathematical Practices: 3) Construct a viable argument and critique the reasoning of others and 1) Make sense of problems and persevere in solving them.

Given how many of us learned mathematics (taking notes on examples provided by a teacher and then given a handful of problems that allowed us to implement that day’s learning or formula), the groupwork approach to learning and doing mathematics may seem strange. In an era where information and colleagues are at our fingertips, it is essential that we develop students’ abilities to think outside of the proverbial box in conjunction with others. Today’s business leaders are asking for nothing less.

And for those who worry that having students work collaboratively on mathematics reduces their access to rigorous content and skills, here is a great video (with links to others) that demonstrates the high quality of mathematical learning and understanding that can happen. Productive math conversations certainly do not happen by accident, and require ample preparation, but the rewards in terms of student learning are well worth the effort.

Moving Forward

Keeping families in the loop and involved in students’ education should not be limited to single events or to those occasions when major changes are happening in the education landscape. In order to continue the conversation, we encourage districts to continue communicating via language-accessible Parent Engagement nights and newsletters. Additional resources to provide context and language for parents seeking to communicate with their children and schools around math instruction include:

• GreatKids Milestones: videos of students demonstrating grade-level standards (only K-5 currently, with 6-12 coming soon)
• Parent Roadmaps to CCSS-Mathematics: brochures listing standards for each grade-level plus 3-year snapshots to show progression of standards (currently K-8, English and Spanish)
• PTA CCSS Guide to CCSS: Four-page overviews (English and Spanish) of grade-level standards in ELA and Mathematics (K-High School)

Keep the conversations happening, and let us know how they go!

by Celine Liu, Math Specialist

Aiding a Confused Parent with Arrays

Found on Twitter with the caption: “kids can't learn 6x8= 48 anymore its now 6x8=(5+1)x8 Why the confusing work”

Dear Confused Parent,

The picture you posted comes from a Powerpoint made by EngageNY to help teachers teach Grade 3, Module 3, Lesson 10.  Lesson 10’s objective is to “use the distributive property as a strategy to multiply and divide.”  So the question “How does topic C use the array model to move learning forward?”  is for teachers to consider as they think about the lesson.  The answer EngageNY gives is: “The array model helps students understand division as both a quantity divided into equal groups, as well as an unknown factor problem.”  Which provides important background, but does not directly answer your question.  

To get back to the first part of your statement, “kids can't learn 6x8 = 48 anymore.”  In fact, the Common Core State Standards state that by the end of third grade students should “know from memory all products of two one-digit numbers.”  So they can and should learn 6x8 = 48.  At the same time, they are learning why 6x8 = 48 and how to figure out that 6x8 = 48.   

That finally leads us to your question, “Why the confusing work?”  The answer boils down to two main reasons, 1) the distributive property and 2) helping students figure out why 6x8 is 48, based in facts they already know and might be able to do in their head.  The distributive property states that a(b+c) = ab + ac.  The property is important for understanding elementary ideas such as how multiplication and addition are related

5 x 3 = 5(1+1+1) = 5 + 5 + 5

to secondary concepts such as multiplying binomials

(x + 4)(x - 5) = x(x - 5) + 4(x - 5) = x2 - 5x + 4x - 20 = x2 - x - 20.  

In the problem you posted, students can break up the array of 48 dots into 
(5 + 1)8 = 5 x 8 + 1 x 8 or 6(5 + 3) = 6 x 5 + 6 x 3 to show that they both equal the same number of dots.  

This is also a strategy for figuring out 6x8 = 48 if students have forgotten the fact.  They may know 6x5 is 30 and 6x3 is 18 and can add to find 48.  Similarly, they may know 5x8 is 40 and 1x8 is 8 which together make 48 again.  An important part of the Common Core is building fluency through practice and conceptual understanding.  So by the end of third grade they should know 
6x8 = 48, but if they don't we should make sure they have the tools to figure it out.

I hope this makes you feel less confused,

Jim Town - Mathematics Specialist at ACOE Core Learning

Need more Common Core Math help?  Visit our Common Core Math Help page and get your answers today! 

Common Core English Language Arts Standards: Tips for Parents

Schools throughout the country are working to improve teaching and learning so all children will graduate high school with the 21st century skills they need to be successful in college, their careers and beyond! In English Language Arts (ELA), there are several changes that parents should be aware of. Students will, in addition to stories and literature, be required to read more non-fiction to learn important facts and background knowledge in subjects like history, art and science. They will need to read more challenging texts more closely and will be asked the kinds of questions where they will need to go back to the text to find answers. Students will need to learn how to make strong arguments and support their views using evidence from diverse viewpoints.

These changes outlined in the ELA Common Core Standards aim to prepare students for college and careers by:

• Increasing the quality and amount of reading and writing students are doing on a wide range of subjects – you should see your student reading more closely about current events in news articles for example in addition to text books and novels and writing more frequently
• Teaching students to work in teams to collaborate on tasks by listening to each other – you could see your student participating in teams tackling word games or preparing debates
• Teaching students to make strong arguments both in writing and while speaking – you will see your student back up what they say with lots of evidence from text and not just from their opinion.
• Teaching students to be independent readers and writers – you will see your student learn how to tackle difficult text and write clearly by themselves

Strategies parents can do to support ELA Common Core success: 

1.  Talk to your child's teacher about how you can best support your child during the transition to the ELA Common Core.
2. Get to know your child’s interests and choose books and magazines about those topics. Don’t worry if all they want to read about is cats for a couple of months or if they tire of a subject and move on. Find the zone that’s right for your child. Reading should not be a chore.
3. Read to your child often – even just the sports section or in a language other than English. 
4. Answer questions by asking more questions whenever possible. Ask your child what they think the answer could be. Help them give reasons for their choices. 
5. For the reluctant reader, ask them to replace the name of an animal or character in a story with a familiar name from your child’s life, a pet or friend will do. 
6. Encourage your child to write letters or emails to relatives and friends describing their day or a recent celebration or event. 
7. For older children, talk about the news together. Pick one story in the news, read it together, and discuss with your child what it means. 
8. Visit the campus of a local college with your teen. Have them write about what he or she expects from college. 
9. Visit a local museum together. Take time to closely observe the details of the paintings or exhibits and talk about what you see there. Have your child draw and write about what you saw and experienced.

For more information for parents on Common Core for each grade level visit: 
PTA Parent Guides to Common Core