mathematics
Math and Maritime Place-Based Learning – M2BPL Re-thinks Math Workshop
Math and Maritime Place-Based Learning
Rig up the mast, batten down the hatch and come sail away with the educators at the Blue Heron School in Port Townsend, Washington as they embark on their exciting project: Math and Maritime Place-Based Learning – M²PBL. The district’s Maritime Discovery Schools Initiative (MDSI), implemented in 2014, is guiding their transformation by encouraging teachers to change instructional pedagogy, increase student engagement, and experience connections between classrooms and business partners. This proposal develops 30 teachers over three years.
What exactly is the Math and Maritime Place-Based Learning – M2PBL?
Research has shown these educators that students benefit highly from using a Math Workshop (MW) model.
When executed successfully, MW models support a culture of underlying beliefs:
- all students are capable of quality thinking;
- participation through hands-on activities and discourse builds student thinking;
and - through true engagement, all young minds can make real sense of mathematics.
An engaging environment is also the premise for Project Based Learning (PBL), where students use 21st century skills to learn collaboratively while working on projects to benefit themselves and others. The M²PBL proposed a structure for K-8 teachers to collaborate and design sense-making math environments tailor made for their students.
Through deepening knowledge of the Common Core State Standards in Mathematics (CCSSM) – particularly in Number and Operations, Measurement, and Geometry – teacher teams (K-2, 3-5, 6-8) focused on:
1) Number Talks (NT), a workshop element where students apply and verbally share strategies to solve and improve mental computations (number fluency),
and
2) PBL projects to apply students’ growing math strategies and conceptual knowledge. The MDSI promotes community partnerships between the school district and maritime-related industries.
As exciting as this is for the teachers, when the students get involved it brings it to another level. The educators are partnering with Port Townsend Sails, a local business specializing in “quality sails for traditional and modern rigs.” Teachers, students, and employees will collaborate to explore authentic mathematics on-site in the sail loft. There, and in classrooms, student mathematicians will count and measure to possibly build boats, design sails, and and/or navigate!
What were the goals for M²PBL?
They had two primary goals to accomplish in year one. They wanted answers to the following questions:
- How do Number Talks increase the quality of students’ number fluency?
- Does authentic application of number fluency deepen student learning in project-based mathematics?
Eleven teachers initially met for professional learning in an elementary group and an intermediate group; each grade level met for two full days (early fall and mid-winter).
Those teachers recorded 10 half-day visits into classrooms (using a substitute) which totaled to around 15-20 visits arranged during planning times and/or with colleagues to “step out” for a short period to observe. One teacher also requested a grade level team observation one morning, so three teachers not technically a part of the grant this year joined in on observations of Number Talks. This was a productive way to share knowledge around fluency outside of the core group. Teacher texts, classroom fluency instructional materials, and PBL supplies were purchased. Items included: student journals, chart paper/markers, wood (for boats), bird feeders, bird ID texts, meter tapes, weights, calculators (specifically for order of operations), and math manipulatives for Family Math Night (dice, spinners, etc.). There, two classes taught fluency activities to parent/students, and the activities went home for continued learning. In-kind donations included dowels (masts), sail cloth (from PT Sails), sand paper/wood pieces for sanding blocks from the high school shop. Volunteer support was received from parents (chaperones), the Schooner Martha captain and family, the Northwest Maritime Center/Wooden Boat Foundation shop personnel, Carol Hasse and crew of Port Townsend Sails, the PT High School STEM/maritime students, and parents to help first graders drill boats for the mast and to tack sails to masts.
What were some of the challenges?
As we can see, they’ve been busy this year. But like all new project ideas, they are not without challenges. The biggest challenge was the collaborative work that required teachers to be out of their classrooms. One participant asked that her grade level team be able to collaborate around classroom observations, and that was accomplished. It’s also been more difficult than anticipated to get teachers to keep up with data collection. But they are already coming up with ideas on how to improve next year. Things like: 1) Supporting a full day of professional learning around math fluency/PBL for any teacher not involved in year one who volunteers (sub time/materials stipend); 2) Supporting grade level teams to collaborate around math fluency through collegial visits/observations (sub time); 3) And finally, approaching Port Townsend Rigging Company as an additional maritime partner to help expand and grow the program for years to come.
All in all, it’s an exciting project to see come together. We’re all waiting with bated breath for this ship to come back to harbor with tales of their next success.
Learn more
- Project-Based Learning: Students actively investigate solutions to complex, long-term challenges, often in groups
- Problem-Based Learning in Mathematics: ERIC Digest
- Maritime Discovery Schools Initiative
- Maritime Discovery update: Students helping salmon
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The Workshop Model: Focus on Communication Grows Math Expertise
In the age of the Internet, where we (kids especially) spend the much of our free time behind a screen, real interpersonal skills are at a premium. Being able to succinctly articulate your ideas is one of the greatest skills one can develop. It’s these skills that are an unintended benefit of The Workshop Model, a project funded by McCarthey Dressman Education Foundation designed primarily to help educators at Poudre High School more effectively communicate math concepts to their students. In turn, those students have practiced actively communicating with one another about how to best solve math problems. The result? Everyone learns an essential skill and everyone wins.
Maximizing learning for conceptual knowledge
The Workshop Model uses conceptual teaching (described by NCTM’s Guiding Principles for Mathematics Curriculum and Assessment, 2009) as a framework for teaching in a way that “emphasizes depth over breadth” and conceptual understanding over factual knowledge. Lessons are organized as workshops including independent and peer workshop time (see Education Week’s Minimize Lecture, Maximize Learning, 2012). According to the project proposal the Workshop Model is conceptual teaching where students engage in mathematics in three key ways:
- by solving specifically designed problems
- collaborating with their peers to discuss their problem-solving
- presenting their solutions to one another in a “math expert” type role
But before that even happens, the teachers collaborate to come up with lesson plans that foster critical thinking and reasoning from their students.
Incorporating Teacher Collaboration
With all the time constraints already placed on educators, collaborative lesson planning may seem like a tall order. While it is a lot of upfront work, the dividends (which continue to pay off) make up for the time spent. Here’s how this collaboration was organized.
- 2012-2013: Aligning Curriculum The educators at Poudre High School developed a team of Algebra I teachers to collaborate on eight units together. With each unit, the teachers created “a backwards map that included the standards, the formative assessments, right down to the specific problems students tackled to demonstrate their understanding.“
- 2013-2014: Incorporating Peer Observation For the next school year, teachers moved on to Geometry, spending eight full days to plan an additional eight units. The days were split between teacher development (lesson planning, addressing concerns, and sample tasks for students) and peer observation wherein one teacher would teach a class while the others observed and then gave constructive feedback.
The collaborative opportunities were so successful that another professional development session was scheduled in August so those teachers could improve upon their lesson plans.
Expanding Efforts
In the interests of covering all their mathematical bases, they are opting to use this years funding to put together a program for Algebra II while also continuing investing in the educators they have already worked with. This enables them to both grow the program and improve upon the pre-existing structures, but it doesn’t stop there.
In order to improve the standards of the whole district, all lesson plans were scanned and uploaded to district servers for all educators in the area to take advantage of. In addition to that, teachers from other schools are invited to take part and learn from the educators already in the program. This way those teachers can take what they’ve learned and implement it in their own schools.
How can you use this model?
The Workshop Model is very flexible and can be used to teach any subject. The major cost comes from allocating days to prepare the lesson plans for the year along with any ancillary materials dictated by the specific need of the subjects and the units contained therein. At the very least, this model should encourage more educators to collaborate and learn from one another, even if this specific model isn’t officially implemented at their school. When teachers collaborate, it is clear: no one person has all the answers, but those answers aren’t far away if you are willing to work together.
Further reading
- Concept Rich Mathematics Instruction (Ben-Hur, ASCD, 2006)
- Math Workshop: Using Developmental Grouping to Differentiate Instruction (Scholastic, 2010)
- Minimize Lecture, Maximize Learning: The Workshop Model (Education World, 2012)
- The Workshop Model for Differentiated Instruction (Aaron Allen, Teaching Channel)
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Teachers Solve Problems in Collaboration to Improve Mathematics Instruction in Project RENEW
We talk a lot about how isolating it can be to be a teacher, but nowhere is that more apparent than in small, rural districts. The teachers there are often the only instructor for a single subject. This is especially difficult for such an important and variable subject as mathematics. As Phillips and Hughes explain:
“Too often, teachers do not have sufficient opportunities to work together to examine work and structure interventions within their classrooms.
As the new standards are implemented, we must ensure that teachers are not left alone to figure out how best to teach to them.
The standards are an opportunity for greater collaboration, fresher thinking, and a rearticulation of shared goals for teachers and students.
By collaborating with each other and with instructional specialists through cycles of examining student work, creating hypotheses about how to implement common-core-aligned lessons, implementing them, and making adjustments in their practice in real time, teachers can find the best ways to help their students reach these higher expectations while still maintaining individual styles and flexibility.” (2012, Education Week)
With multiple levels and subjects within it, math is a daunting subject to teach. But that’s what the educators at West Elementary School in Manhattan, Kansas plan to do.
What is Project RENEW?
Project RENEW emphasizes the development of deeper content knowledge among teachers, as well as pedagogical knowledge aligned with a standards-based approach to content teaching. By building a cadre of elite math educators, the teachers at West Elementary School aim to create an easily adoptable model to improve math scores within their district and beyond.
What are the project goals?
With the adoption of a much more rigorous set of standards, Common Core Standards for Mathematics (CCSSM), the teachers at West Elementary realized that they must rethink how they teach mathematics. So, they came up with the following goals:
- Increase student achievement in mathematics for ALL students in grades K-12.
- Strengthen the content and pedagogical knowledge of K-12 teachers.
- Increase the implementation of CCSS-based mathematics instruction and curriculum in K-12 classrooms.
- Strengthen and expand existing leadership opportunities for teachers in mathematics to enhance collaboration to address the needs of K-12 schools, especially in small rural school districts.
The project proposed that by completing goals two through four (strengthening teachers, instruction and math leadership) that goal one (improved student achievement in math) would follow shortly after.
How did this project strengthen teaching in mathematics?
Project participants attended a summer math academy to develop CCSSM aligned curriculum and tasks. This academy helped the group understand their current practice and focus on ways to improve it.
First, teachers were pre-tested on their mathematical knowledge in relation to how they would implement mathematical practices in the classroom and had to submit an “action plan related to these practices and instructional strategies used for implementation.”
Next, they were observed during instruction and given feedback during professional development sessions.
In addition to this, teachers in smaller districts nearby that do not have funding for professional development and/or resources were contacted by the teachers from Project RENEW. Together, they were able to share resources and provide professional development for these small districts. Funds provided by McCarthey Dressman Education Foundation were also used to purchase new materials for the academy, so they were able to box up their “used” standards-based textbooks, load them up in a truck and delivered them to four different districts in the area.
How did this project impact the math instruction?
After a year of funding they’ve improved “by leaps and bounds and are ready to tackle the next steps” according to the project report.
The difference between the teacher Pre-Test and Post-Test was phenomenal. The average score starting out was a 2/7 correct responses and by the end that average had improved to 5/7. That’s 42.8% improvement in teacher knowledge of how to implement math instruction for CCSSM.
Teachers were also observed showing marked improvements on their in class instructional skills, particularly in the realm of “providing problem solving opportunities for their students, requiring productive struggle and discourse.”
To further extend the benefits of the program in their community, the teachers involved in the project were also responsible for disseminating what they learned in professional development sessions with the smaller districts.
What knowledge would they share with teachers exploring similar projects?
Like many of these ambitious projects one of the hurdles that must be overcome is the lack of resources. Even with the grant funding, they were unable to accommodate all the educators they would have liked to. The waitlist for additional involvement is long and shows no sign of letting up, much to the disappointment of those who know the project’s promise. In the future, they plan to video tape the lessons to help smaller districts to gain access to this valuable resource. This will be a focus in the year to come.
Also of note, the implementation of this program might encounter challenges operating on a larger scale due to the vast time requirements put on the educators and the stipends needed to cover their time. They hope that in the coming years that the texts, videos, and seminars resulting from this program will be able to be adapted for use by other districts and schools around the country.
Further Readings
- Report: Teacher Leadership Is Key to Common Core Success (2015, THE Journal)
- Teacher Leadership, Collaboration, and Common Core State Standards (2015, Learning First Alliance)
- Teacher Collaboration: Keys to Common Core Success (2014, AMLE)
- Teacher Collaboration: The Essential Common-Core Ingredient (2012, Education Week)
Additional Resources
- Mathematics Standards
- Common Core Standards Initiative
- Math Playground: Play with Math and Give your Brain a Workout
McCarthey Dressman Education Foundation 