This post is sponsored by Curriculum Associates.
There has been considerable discussion around Common Core math, as teachers and school leaders grapple with the best way to transition students to the new standards. Educator and math expert, Mark Ellis, details why students struggle and what schools can do to help all students achieve success.
Why are students struggling with many of the new Common Core math standards?
Pre-CCSS, students may have learned math skills and procedures but without a focus on the underlying meaning and sense-making. This makes it extremely difficult to apply those skills and procedures in unfamiliar situations and real-world contexts. The new standards are designed around progressions of concepts that inform procedural fluency, so if the foundational understanding is not in place, it makes it very difficult for students to progress successfully. When skills are built on a foundation of strong conceptual knowledge, students are more likely to use them more accurately and flexibly. In the 21st century, people rarely encounter neatly ordered problems to be solved with pre-determined rules (since these are routinely taken care of by computers) but rather must tackle complex situations that require reasoning, sense-making, and perseverance. So the new standards emphasize not only knowledge but also habits of doing mathematics so students can actually use math as a tool for understanding the world they are entering.
Which standards are proving to be the most challenging for students?
Based on data from i-Ready®, we know that the most challenging standards for elementary students relate to fractions, geometric measurement, and modeling. Students in the middle grades are struggling with geometric measurement as well as statistics.
Modeling includes taking a realistic situation and representing it mathematically to answer a question. Students often struggle with this if they have not developed the habit of making sense of a problem, identifying how it might be represented mathematically, and circling back to check whether their result is reasonable in the original context. Without this habit, students will try to map a familiar procedure to a word problem and obtain results that are nonsensical. However, if we teach students to reason and make sense of the context of a word problem and provide them with ways to generate meaningful mathematical representations (including visual models), they will be more successful at coming up with solutions that make sense.
It’s a similar issue for fractions. Students do not inherently understand fractions. We have to help them grasp foundational concepts and relationships so they understand what a fraction represents and can make sense of fraction operations. The new standards provide students with that experience. It starts very early with helping students understand the concept of fractions and what they look like, and then moves into giving fractions a numerical representation and using models to associate fractions with whole numbers. We can do this with a number line or fraction bar to show students, for instance, what one-fourth looks like both as a unit and as it relates to a whole.
How do teachers and students benefit from targeting the most challenging standards?
We often focus on how quickly teachers are getting through content. However, with the new standards, we need to reframe this focus to support the development of meaning so that learning happens, stays with students, and can be built upon as students progress throughout the year. The beginning of the school year should be about establishing a culture of learning that enables this. Investing time at the beginning of the year in helping students acquire habits for learning, such as how to talk to each other about math, share their thinking, and understand errors as part of the learning process, will help students take risks and develop mathematical understanding and interconnections. Once these habits are ingrained, it can accelerate the pace of learning, and teachers will not spend as much time re-teaching prior content. As students develop knowledge through these processes of reasoning and sense-making, they can reconstruct how to work through a procedure and recognize how new ideas connect to prior learning.
What are some practical strategies you can suggest for teachers as they tackle these challenging areas?
The first thing teachers need to do is to think about their own mathematical understanding and engage themselves as learners of the mathematics too. They need to understand the inherent logic to math before they can support students in recognizing it. Activities like book clubs, blogs, and Twitter groups that share ideas about teaching and learning math are just a few of the ways teachers can collaboratively grow as professionals. Teachers must also be open to the idea that they—and not just their students—are learning. In some cases, the students might actually contribute to a teacher’s deepening understanding of mathematical ideas.
Second, teachers should think about how they can design lessons that successfully engage all students in making connections between mathematics and their own identities. This includes drawing on students’ cultural and community knowledge—their interests, their community experiences, and their ways of communicating (including acknowledging their immersion in a digital world). Educators need to determine how they can use this knowledge to really engage and motivate students. When they do, educators will see students get excited about math.
What advice can you offer administrators as they lead their schools and districts through transition and in mastering the most challenging standards?
There is a belief, particularly in the U.S., that only certain people are good in math. Administrators and teachers need to ensure that every student knows he or she is capable of learning math and those who are struggling may just need targeted intervention. We need to instill in students a growth mindset—understanding that learning takes effort and through that effort, they will continue to improve.
In addition, administrators can provide support by organizing schedules that permit and promote collaboration, allowing professional development to be driven by listening to what teachers say they need to grow mathematically, and by leveraging the experience and expertise within their staff. For example, teachers may want to deepen their understanding of the learning progressions embedded in the new standards, such as how fraction knowledge builds coherently from grade 2 through grade 6 on a foundation of unitizing. Administrators must recognize the importance of such a request and support cross-grade collaboration among teachers.
It is also important to not get caught up in the idea of assessment as a summative endeavor. Rather, it should be viewed as a way of informing where we are along a journey and providing information to guide future instructional planning. It is unproductive to view the assessments in the spring as a “did we make it or not” proposition. Much like the progressions mentioned earlier, this is a multi-year process.
Learn more about the most challenging standards and get lessons that were 100% built from scratch to meet the rigor of the Common Core. Visit: www.ReadyCommonCore.com/MostChallengingMathStandards.
Mark Ellis is a National Board Certified Teacher and professor of education at California State University at Fullerton. He is an author of Curriculum Associates’ Ready® Mathematics program.