Posts Tagged ‘Instructional Coaches’

Observing Best Practices in a Mathematics Classroom

Wednesday, May 18th, 2016

AUTHOR: Virginia Keasler, Secondary Math Specialist

Walking into a math classroom, an observer of the lesson may view many modes of instruction. The list may include:

  • Teacher shows students step by step problem solving and expects students to do problems in the way they are instructed
  • Students sitting quietly in rows
  • Students rotating around stations exploring challenging problems
  • Students are working on a problem together in groups, some individually, not necessarily doing exactly the same thing
  • Students engaged in critical thinking
  • A few students working at the board while others watch
  • Students who have completed their work and are waiting for the next problem
  • Teacher asking probing questions about the way students are attempting to answer questions

Generally you may see one or both of the two prevalent approaches to mathematics instruction. In the more traditional approach of instruction, skills-based, teachers may focus on how to solve the problem, show that problem solving strategy, and then require the students to quickly repeat that strategy. This method focuses on developing computational skills.

In concepts-based instruction, teachers have students solve a problem in a way that makes sense to them and then explain how they solved their problem. This method helps students be aware that there is more than one way to solve a problem.

You may be trying to decide what is the best way, but most researchers (e.g., Grouws, 2004) agree that both approaches are important, that teachers should strive for procedural fluency that is grounded in conceptual understanding.

There are three critical components to effective mathematics instruction (Shellard & Moyer, 2002):

  • Teaching for conceptual understanding
  • Developing procedural literacy
  • Promoting strategic competence through meaningful problem-solving investigations.

In an effective classroom an observer may see the teacher

  • Accepting students solutions to challenging problem which includes their explanation how they found their solution and the reason they chose to try their method.
  • Posing interesting questions to students to spur their interest in the problem.
  • Encouraging students to see that problems are challenging and that you sometimes have to search more than one method to find the answer.  
  • Instilling the belief that the goal of answering the question is attainable and worthwhile and can even be “cool”.  

In an effective classroom an observer may see the student

  • Solving the problem themselves and not just “mimicking” the procedure shown to them by others.
  • Challenging themselves to investigate a meaningful question.
  • Sharing their ideas with each other and as a group
  • Using various ways to show their work
  • Conducting an experiment by analysing data and coming to a conclusion
  • Are using calculators where appropriate
  • Using manipulatives to engage in problem solving to help form a concrete understanding of the concept where needed.

The National Center for Educational Achievement (NCEA, 2009) examined higher performing schools in five states (California, Florida, Massachusetts, Michigan, and Texas) and determined that in terms of instructional strategies, higher performing middle and high schools use mathematical instructional strategies that include classroom activities which:

  • Have a high level of student engagement
  • Demand higher-order thinking
  • Follow an inquiry-based model of instruction – including a combination of cooperative learning, direct instruction, labs or hands-on investigations, and manipulatives
  • Connect to students’ prior knowledge to make meaningful real-world applications
  • Integrate literacy activities into the courses – including content-based reading strategies and academic vocabulary development

Additionally, NCEA researchers found that it was important for teachers to create classrooms that foster an environment where students “feel safe trying to answer questions, make presentations, and do experiments, even if they make a mistake” (p. 24).

In summary, while both methods are important, teachers must reach students where they are and in the method that works best for each of their students.  While procedural learning is important to learn math facts and algorithms, students still need to be challenged, allowed to learn by exploring, and encouraged to keep trying knowing that math is meaningful and a huge part of the environment around us everyday.

References

The Education Alliance. (2006). Closing the Achievement Gap: Best Practices in Teaching Mathematics. Charleston, WV: The Education Alliance.

Grouws, D. (2004). “Chapter 7: Mathematics.” In Cawelti, G, ed., Handbook of Research on Improving Student Achievement. Arlington, VA: Educational Research Service.

National Center for Educational Achievement. (2009). Core Practices in Math and Science: An Investigation of Consistently Higher Performing Schools in Five States.  Austin, TX: National Center for Educational Achievement.

Shellard, E. & Moyer, P.S. (2002). What Principals Need to Know about Teaching Math. Alexandria, VA: National Association of Elementary School Principals and Education Research Service.

Be the Learner

Monday, December 7th, 2015

AUTHOR: Laura Lee D. Stroud, Elementary English Language Arts Specialist

Superintendents expect principals to learn. Principals expect teachers to learn. Teachers expect students to learn. The field of education sets high standards for our children but do we hold ourselves as educators to the same standard? How often do we engage as learners outside of the classroom ourselves? We want students to ask questions, seek the answers, problem solve and ask more questions, pursue learning; but are we doing the same? Are we pushing ourselves beyond what is comfortable, beyond what we know?

Whether you are a principal, an academic coach, specialist, parent, or all of the above—you are a teacher. And someone is learning from you. Watching you to see if you practice what you preach. Watching to see if you are engaging in the types of literate activities you have assigned to them. Stellar leaders, whether classroom teacher leaders or superintendent leaders, are learners. They are stellar because they spend time learning through reading, writing, and discussing their profession in order to be better at their craft. They are stellar because they are action researchers who reflect on their practice. Stellar because they adjust instruction to fit the needs of their learners.

In this day and age, there are shifts in pedagogy that require our attention. Our students have vast amounts of information at their fingertips but need us to structure the environment for collaboration, discussion, critical thinking and relating with their peers in academic discourse. Our learners are different than the learners we were. No longer is it valuable for them to answer our questions and forget theirs. Our world is different. Technology is redefining the way text is processed. So we must do what we can to stay on top of the changes, zone in on our students’ instructional needs, and adjust our instruction to maximize their learning.

With encouragement from Ghandi, I would like to empower educators with this phrase: be the learner you want your students to be. There should be an expectation that educators and students alike continue to push themselves to become the best they can be.

Time, or the lack thereof, is often used as an excuse for limited learning and growing as professionals. Professional development opportunities on a district level often tend to provide one-size fits all learning. On the other hand, each of us is aware of our individual needs as learners. We know where our understandings are solid and in which areas we require growth. We have the ability to tailor make a menu of professional learning for ourselves.  But where to go from there?  How do we get the necessary information to meet our individual needs?

Personal Learning Networks (PLNs) are groups of educators dedicated to supporting each other in achieving learning goals. So create yours. Ask yourself: where is an opportunity for growth in my practice? And then research, try new ideas, read, write and blog, ask others, take risks, reflect. Just as Ronnie Burt, a participant in the Twitterverse expressed, “…I realised that developing a Personal Learning Network is an empowering, transformational process, which fundamentally transforms your professional learning and teaching approach. And my experience is hardly unique…”

Just like our students, we may need a little inspiration to work harder. Here are a few things you can do to get started:

  1. Find fresh texts for your students to read and discuss based upon their interests. Share the outcomes along with the text with your colleagues. Follow this link to Tcher’s Voice, a blog from TeachingChannel.org that incluldes a wonderful annotated list of sites to find such texts.
  2. Contribute to our profession through writing a blog and reading others. To discover a great way to begin blogging follow this link to Slice of Life Writing Challenge.
  3. Participate in a twitter chat. Need help to understand how to participate? Look at this Edublog site for all you need to get started: Step 3: Participate in Twitter Chats and then click here find a twitter chat relevant to you.
  4. Or, last but not least, read a trade book on literacy practice. Need a suggestion? For elementary practitioners, Jennifer Serravallo’s Reading Strategies Book has teachers raving about the accessible, “implement tommorow” content and format. Although Serravallo’s latest work has strategies for beginning readers, it is appropriate for all levels because of the complexity of comprehension strategies it includes. All grade level teachers can find ways to help their readers slow down and notice author’s purpose through Reading Nonfiction: Notice & Note Stances, Signposts, and Strategies by Kylene Beers and Bob Probst.

Once you have engaged in one or more of these suggestions, share what you have learned and ask others about their new understandings. Decide what you want to put into action in your practice.  Be a risk-taker and be prepared to reflect on and learn from your mistakes. And repeat. In this way, educators continue to refine and improve our craft.  So, what kind of learner are you going to be?

References

  1. Burt. (2014, September 23). Step 1: What is a PLN? [Web log comment]. Retrieved from http://teacherchallenge.edublogs.org/pln-challenge-1-what-the-heck-is-a-pln/

Math with Mary!

Friday, August 24th, 2012

Author: Mary Headley – Elementary Math Specialist

The introduction of new math concepts can be described using three stages:

I. Concrete (the “doing” stage) – This stage involves both teacher and student modeling.

II. Pictorial (the “seeing” stage) – This stage transitions the concrete model into a representational level such as  drawing pictures or using dots or tallies, etc.

III. Abstract (the “symbolic” stage) – This stage uses numbers and mathematical symbols.

Using concrete models is the first step in building the meaning behind mathematical concepts.  These models include a variety of math manipulatives, measuring tools, and other objects that students can handle during a lesson. Research-based studies show that students who use concrete materials develop more precise and more comprehensive mental representations, often show more motivation and on-task behavior, understand mathematical ideas and better apply these ideas to life situations.  (Harrison & Harrison, 1986; Suydam & Higgins, 1977)

Pictorial representations help teachers provide the perfect bridge between concrete representations and abstract algorithms. Pictorial representations include drawings, diagrams, charts and graphs that are drawn by the student or provided for the students to read and interpret. Pictured relationships show visual representations of the concrete manipulatives and help students visualize the mathematical operations. It is imperative that teachers explain how the pictorial examples relate to the concrete examples.

“Up the Hill” Manipulatives stmichaelschool.us

Connecting the dots between the concrete, pictorial, and abstract is the glue that cements the learning for students. This connection provides the understanding that students need to demonstrate a problem or operation using symbolic representations such as numbers. The meaning of symbols and numbers must be rooted in experiences with real objects (concrete) and pictorial representations. Otherwise the symbolic operations (abstract) become rote repetitions of memorized procedures with no understanding.

The gradual movement from concrete to pictorial to abstract benefits all students and helps to prevent the frustration that some students feel when instructed only with abstract processes and procedures.

Perhaps this article has caused you to think about exploring multiple ways to teach math.  Would you like to observe and experience the conceptual development of content? Do you want to give students multiple strategies for success? Would it help you to see how manipulatives can be used to build the meaning behind math concepts?

If the answer to these questions is yes, you may be interested in Math with Mary, an online resource tool that offers professional learning modules designed to build teacher content knowledge and teacher confidence with the use of manipulatives. These modules are hosted by Mary Headley, Education Specialist for K-5 Mathematics at Education Service Center Region XIII, and will walk participants through the use of a specific manipulative which will allow students to explore and develop a variety of math concepts. Using the strategies presented, students will be able to visualize the math while engaging in strategies that build conceptual understanding.

The first course module, Math with Mary: Multiplication with Base Ten Blocks (FA1224478), is appropriate for grades 3-6 and is currently available on E-Campus. This course lays the foundation for understanding multiplication of 2 digit numbers and beyond. Student expectations related to Number and Operations emphasize the use of concrete models and visual representation of numbers and operations. The Multiplication with Base Ten Blocks course supports student expectations outlined in the TEKS and will help teachers build the bridge between concrete models, pictorial representations and the abstract multiplication algorithm. (2 hours CE credit)

 

Sources

Harrison , M., & Harrison, B., “Developing Numeration Concepts and Skills,”  Arithmetic Teacher 33 (1986): 1–21.

Suydam, M. N.; & J. L. Higgins,  Activity-based Learning in Elementary School Mathematics: Recommendations from Research. Columbus, OH: ERIC Center for Science, Mathematics, and Environmental Education, 1977.