Improving Mathematical Problem Solving

Based on extensive research, the Institute of Education Sciences (IES) has published a practice guide that provides five recommendations for improving students’ mathematical problem solving. This guide is geared toward teachers, math coaches, other educators, and curriculum developers who want to improve the mathematical problem solving of students.

The foundation for success in advanced mathematics is built on problem solving skills. Problem solving requires strong skills in reasoning, analysis, and argument construction, and the ability to apply innovative strategies to find a solution.

To help students become skilled problem solvers, teachers can:

• prepare problems to use in whole-class instruction
• provide explicit problem-solving instruction that teaches students to use visual representations, employ multiple strategies, and links mathematical concepts and notation to problems
• allow time to reflect and debrief on their strategies and solutions with classmates

While these skills should be taught at all levels, it's especially important to help students develop them as progress toward the more complex math concepts they will learn in high school.
Problem solving skills are essential for students as they progress through the entire mathematics curriculum. Students who develop proficiency in mathematical problem solving early are better prepared for advanced mathematics and other complex problem-solving tasks. Unfortunately, when compared with students in other countries, students in the U.S. are less prepared to solve mathematical problems.
Problem solving involves reasoning and analysis, argument construction, and the development of innovative strategies. These abilities are used not only in advanced mathematics topics — such as algebra, geometry and calculus—but also throughout the entire mathematics curriculum beginning in kindergarten, as well as in subjects such as science.
Pepper has released a new workshop focused on Improving Mathematical Problem Solving as part of it’s new Pepper Online Workshop (POW!) content. By taking this workshop you will explore strategies to help students become skilled problem solvers. Participants will be understand and take a deeper look at the three components involved in teaching problem solving to students.

You can check all of our new POW content by visiting the Courses and Workshops section on your dashboard.

Encouraging Girls in Math and Science

Although there is a general perception that men do better than women in math and science, researchers have found that the differences between women’s and men’s math- and science-related abilities and choices are much more subtle and complex than a simple “men are better than women in math and science." The Institute of Education Sciences (IES) has found that to encourage girls in math and science we need to:

• understand their beliefs about their abilities in these areas
• find a way to spark and maintain greater interest in these topics
• build skills that are related to other interest areas

Students’ choices to pursue careers in math and science reflect multiple influences that accumulate over time. In general, researchers have found that girls and women have less confidence in their math abilities than males do and that from early adolescence, girls show less interest in math or science careers. Women are less involved in career paths and post-secondary education in some areas of math and science than men. This pattern starts at school.The IES has identified practices that elementary, middle, and high school teachers can implement during instruction that they believe would increase the likelihood that girls and women will not prematurely decide that careers in math and science are not for them.

National Center for Education Research and the Institute of Education Sciences have published a Practice Guide, published on WestEd's website, that explores what can teachers do to encourage girls to choose career paths in math- and science-related fields. The report presents five research-based instructional and feedback strategies for teachers at all grade levels:

• Teach that abilities are expandable
• Provide prescriptive, informational feedback
• Show students female role models
• Spark curiosity
• Teach spatial skills

Pepper has released a new workshop focused on Strategies to Engage Girls in Math and Science as part of it’s new Pepper Online Workshop (POW!) content. By taking this workshop you will explore strategies for keeping girls engaged in courses of study related to Math and Science. Participants will be guided through the process of developing a plan for actively motivating and maintaining girl’s interest in Math and Science. You can check all of our new POW content by visiting the Courses and Workshops section on your dashboard.

Introducing Pepper Online Workshops (POW!)

POW! Are you ready to add some Pepper into your personalized, online learning plans?

PCG Education is introducing a new series of content collections - Pepper Online Workshops (POW!) – focusing on the hottest topics that educators are dealing with across the country. Our new workshop series is based on WestEd’s powerful collection of resources from their Doing What Works project featuring amazing videos, interactive planning tools, and other research-based materials.

In the spirit of keeping with Pepper’s core values, these online workshops – although much shorter – will remain true to our vision – to provide K-12 educators with high-quality, interactive, engaging, research-based and applicable to your school environment.  

Currently, users can find workshops focused on Universal Design for Learning (UDL) for Math, Science, and Language Arts. You can learn more about UDL by checking out a previous blog post, Making Learning Accessible for All: Universal Design for Learning.

Look for our new workshops this week focused on using Literature Circles in the classroom.

PCG Education will be releasing new POW content collections every week. To find these new workshops, visit your Pepper dashboard and click on the updated "Courses and Workshops" link.

Then, find the tile labeled "keep learning" to access our new Pepper Online Workshops.

Please visit us at PepperPD.com/courses to review the new online workshop series and sign-up today.

Teaching Math Modeling for Problem Solving

The National Science Foundation has funded a pilot program to help elementary teachers learn to teach Math Modeling to their students. Elementary students learn from the beginning using modeling and manipulatives. But this concept is something greater. According to a recent article in Education Week, this type of mathematical modeling “is something different and more complex: It's the process of taking an open-ended, multifaceted situation, often from life or the workplace, and using math to solve it.” In keeping with new standards, the goal is help students see the relevance and application of math to everyday life. The focus is on critical thinking and problem solving with the outcome being sometimes “messy” - meaning there may not be one definitive right answer. Students are being taught to work logically through a problem and develop a solution that can be justified. 

This pilot program, the IMMERSION project, is part of ongoing efforts to improve student proficiency and critical thinking in science, technology, engineering and mathematics (STEM), project leaders say. The project is designed to provide professional development to teachers from three different districts over three years. According to an article on the project website, “IMMERSION will help K–8 teachers incorporate modeling into their mathematics teaching by providing intensive professional development training during the summer, followed by support and collaboration during the school year as teachers begin to implement mathematical modeling activities in their classrooms—a practice that can have far-reaching effects on how students perceive and use mathematics. The study will focus on increasing the achievement of all students, including special education and advanced students, students with limited English proficiency and economically disadvantaged students.” This focus on differentiating instruction in addition to the math modeling will prepare these teachers to better meet the needs of all students.

You can find a wide variety of professional development options for Math in the Pepper Course Offerings. All of these courses focus on helping teachers teach math in a meaningful and engaging ways. You will also find courses focused on ELL and Special Education.

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STEM: Why it Matters

STEM is an education curriculum based on teaching students in four specific disciplines — science, technology, engineering and mathematics.  What makes STEM unique, however, is that rather than teach the four disciplines as separate subjects, STEM integrates them into a cohesive learning program with ties to real-world applications. According to the STEM Coalition, by 2020 there will be a demand for STEM professionals with over 1 million jobs in STEM-related fields.

STEM education is different from traditional math and science teaching in that is uses a blending learning approach. This approach shows students how science, math, engineering, and technology are central to everyday life and integrated into all that we do. According to an article from Live Science, “What is STEM education?”, the goal is to gain student interest in these fields so that they will want to pursue them as careers. STEM education begins in the elementary school with introductory courses and subject awareness. In middle school courses become more rigorous and students begin to explore career opportunities. By high school, students are focused on application and are exposed to career pathways and exploring post-secondary options.

According to the US Department of Education, “all young people should be prepared to think deeply and to think well so that they have the chance to become the innovators, educators, researchers, and leaders who can solve the most pressing challenges facing our nation and our world, both today and tomorrow.”

(US Dept. of ED)

Go to the Pepper Resource Library and visit STEM Builder for STEM curriculum resources. Be sure to check out all our Pepper course offerings.

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Mastering Math Language: Teaching English Language Learners

Pepper has just released 2 new ELL courses that make up a 2-course series on Mastering Language for College and Career Readiness, focusing on Elementary Mathematics. 

The first course in the series, Mastering Math Language: Reading and Speaking, is designed to help teachers teach students to read and speak the language of mathematics. In this course, participants will gather and analyze language samples that will show what students learn and what support they need in the elementary math classroom.

While part one of the series focused on reading and speaking the language of mathematics, the second course, Mastering Math Language: Conversations and Writing, builds on those concepts and places an emphasis on constructive conversations and writing in math. In this course, teachers will gain tools that will support formative assessment and instructional planning. Learners must complete the first course in the series before enrolling in this course.

These courses will enable teachers to collaborate with other educators and build professional relationships that result in an online community focused on improving students’ abilities to use rich academic language to learn and show learning of mathematical skills and concepts.

While the courses are intended specifically for those who teach English learners and students with disabilities, the content of the courses is equally applicable to teaching all students who are challenged by the academic uses of language in math instruction.

Click here to watch a video overview of the Mastering Math Language Courses.

These courses were developed by the Understanding Language Initiative at Stanford University.

Be sure to check out all our Pepper course offerings.

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Math Matters.

Math Matters.

For many students, math is hard. They don’t see the value or connection of solving pages of math problems to their everyday life. Will they ever need Algebra? As teachers of math, we see it’s importance. However, conveying that to our students can be challenging. Teaching a student to think creatively and to solve problems is one of the greatest gifts we can give them as a teacher. Karim Ani, former middle school teacher and math coach, founder of Mathalicious, talks about the importance of relating math to everyday life and making it relevant for today’s students in his recent Edutopia post, “Why Math?”. According to Ani, “Mathematics allows us to discuss important issues in a meaningful, constructive way. Why math? Because it allows us to be better citizens.”

EdWeek’s recent article, “What Two Schools are Doing About Teachers’ Math Anxiety”, states that retraining is the best way for teachers to feel comfortable teaching math according to new standards. 

Pepper offers a variety of math professional development courses designed by WestEd to sharpen your skills and help you relate math to your students, including “Conceptual Categories in High School”. 

Be sure to check them out here: Pepper Math Courses.

Inspiring Math Teacher Aims to Help Kids Graduate

From time to time, you read about truly inspirational teachers who have managed to help the toughest kids succeed. Rodney Carey is one of those amazing teachers. He teaches math in a windowless classroom in New Orleans to students ages 16-24--most of whom do not have a scholastic level above 5th grade. His ultimate goal is to help each of his students make it to graduation.

So, how does he do it? He's hard on his students, but he also does whatever it takes to encourage them. Before Carey was a teacher, he was a bail bondsman. Before that, he was a troubled kid himself. Seeing several young kids heading toward the unproductive road to jail time, he decided to become a teacher and make a real difference.

Check out Rodney Carey's inspiring story at NPR.com.

NEW COURSE AVAILABLE! Getting Started with Number and Operations in Base Ten

Our newest Pepper course focuses on the Number and Operations in Base Ten domain that spans kindergarten through fifth grade. Explore how the Number and Operations in Base Ten domain builds on Counting and Cardinality, connects to Operations and Algebraic Thinking, and creates a foundation for middle and high school mathematics. Identify strategies to support students with computational fluency, procedural fluency, and conceptual understanding. Learn More…

Click Here to view all courses in Pepper.  Simply Select “Sign up & Start Course” on any new course you would like to add to your dashboard. If you don’t have access at this time, please contact your District administrator or request access directly from the Pepper team.

Courses in Special Education and Argument Writing Coming Soon!

There is always something new to learn in Pepper.  Remember to take the PEP101 User’s Guide to Pepper Course to become familiar with Pepper and to help you be even more successful in your learning journey.

BRAND NEW! Check out these AMAZING Math courses that just hit PEPPER!

Two fantastic new middle school mathematics professional development courses are available in Pepper now. Take a look at the courses and their descriptions and get excited about the opportunities to be prepared and ready to work with your students as the new school year kicks into gear! Click on the course titles to learn even more about what you'll discover if you sign up!

Getting Started With Expressions and Equations (6-8)

Take a deep dive into the Expressions and Equations domain and the clusters of standards it includes at each grade level. Study the clusters of standards for each grade, work on math tasks related to each cluster, and learn more about the mathematics education research behind the CCSS.

Implementing Expressions and Equations (6-8).

Continue your journey into Expressions and Equations by understanding how to implement the domain effectively in your classroom. This course is designed to follow Getting Started with Expressions and Equations course.

Free Video Series--Geometry Instruction for K-8 Teachers!

If you have spare time this summer, take a look at the amazing, in-depth, comprehensive teacher resources from ANNENBERG LEARNER. The mission of the nonprofit organization is "To Advance Excellent Teaching in American Schools." The website is full of fantastic resources for all disciplines, and well worth a closer look.

Included in those resources are a number of in-depth video courses with supporting materials targeted to a variety of grade levels and subject areas. THIS VIDEO SERIES helps frame geometry, not only as a set of skills or objectives for your students to master, but also as a strategic method for problem solving in general. To follow the entire series, you should allow for the better part of a day. Begin with the first session, and then follow along with the prompts to move through the entire series.

Watch Math Coach Audra McPhillips Teach a Great Common Core Aligned Math Lesson!

Audra McPhillips is a math coach in Rhode Island. In this video for The Teaching Channel, she works with middle school students on understanding how functions operate. McPhillips believes that students in this age group can be engaged in grasping not only lessons and concepts, but also in seeing the way those connect with the standards themselves.

If you create a free account with The Teaching Channel, you'll be able to access all the supporting materials for this lesson--including the lesson plan. Stick around the website to check out a host of other great tutorials and videos.

Finding the Right Math Content for your Common Core Aligned Lessons!

The good news is that there are already thousands of great resources to be found online for math teachers who want to create fantastic lessons that are aligned to CCSS. The bad news is that there are thousands of great resources out there! How should you sort, sift, and dig through them all to find the resources and lesson ideas that are exactly right for your students and your classroom?

Check out ck12.org, a website run by the CK-12 Foundation, a non-profit committed to creating and aggregating top-quality STEM content. They have developed a Common Core Math Standards browsing tool that allows teachers to browse the standards and find aligned concepts, and then mine free, vetted resources to build out lesson plans for those concepts.

It may take a bit of practice to get comfortable with the tool, but it's a powerful resource that can help teachers find exactly the content they want to teach!

CLICK HERE TO TAKE A LOOK!

Over 300,000 Teacher-Created, Teacher-Vetted Resources--FREE!

Sharemylesson.com is a website that brings educators together to share their winning classroom and professional development resources with each other.

Intended to inspire and facilitate collaboration among teachers, this site includes an enormous number of Common Core-aligned lesson plans and resources, all of which you can access for free.

Searching can be a little bit of a challenge, but there are a few short, easy-to-follow tutorial videos on the homepage that will help you learn to navigate the site. And it's worth it! The site includes a Common Core hub, with news, information, updates, and forums to help you as prepare for the move to CCSS.

CHECK IT OUT HERE!

Digital Learning Activities and Educational Games -- Free!

As every teacher knows, not all educational games are created equal! Some have genuine value and can serve as wonderful reinforcements for student learning, or can expand student learning beyond the classroom. Yet how do you find educational games and digital learning activities that have been vetted and curated without spending hours of your own time testing them, or paying for memberships?

Check out this fantastic website: Powermylearning.org! It's a free digital learning platform with resources for teachers, students, and parents alike, and was developed by the well-respected national education nonprofit CFY. If you're looking for games, videos, interactives, and other digital resources to incorporate into your Common Core lesson plans for the classroom, then this is the website for you.

Each resource in Math and ELA is aligned directly to a Common Core standard. Plus, there are countless resources for science, social studies, the arts, technology and more. You'll need to create an account to access all the material on the site, but once you do, you'll be able to tap into hundreds of carefully-vetted, free digital resources.

Calling All Math Teachers—Upcoming Free Webinar on April 30th on Standards of Mathematical Practice!

Curious about the role of Standards of Mathematical Practice (SMPs) in Smarter Balanced Performance Assessments? Looking for more information about mathematics classroom practices on the ground? Look no further—and register for this free, 2-hour webinar led by Cathy Carroll of WestEd’s STEM program as she walks you through an overview of SMPs. The webinar will take place live on April 20, 2014, at 4 p.m. PST. Click here to register!

Can’t make it? Don’t worry—the webinar will be archived on the WestEd website for viewing anytime!