Key lessons from research about project-based teaching and learning→

Anna Rosefsky Saavedra and Amie Rapaport, writing for Kappan:

"Our research has demonstrated that inquiry-based learning can be intellectually rigorous and cover a sufficient breadth of content and skills. Students learning through these approaches outperform comparison students on meaningful outcomes, including probability of high school graduation and AP scores."

They do a nice job summarizing implementation challenges inherent in project-based teaching and learning:

On the struggle of integrating PBL in traditional settings:

"In studies of PBL instruction that was not schoolwide, teachers struggled as the only adult in the building using the approach... For a student immersed in a traditional school, a PBL classroom can feel new, different, and unfamiliar."

On the tension between project depth and curriculum breadth:

"PBL requires students to spend a lot of time deeply exploring fewer content areas... This requirement can be in tension with the need to teach the breadth of content and skills in district and state learning standards."

On the financial and resource challenges of adopting PBL:

"Teaching PBL well requires materials and professional learning support that can be costly for schools and districts... These costs add up and can make transitioning to PBL a costly budget item for schools and districts that may already be strapped for cash."

They do an equally nice job of summarizing potential solutions and insights related to those challenges:

On the importance of patience and support for educators:

"Transitioning to effective implementation of PBL requires patience because pedagogical skills and culture take time to evolve... Educators, particularly those new to PBL, struggle."

On aligning PBL with standardized assessments:

"The IB Diploma Programme’s approach to assessment helps teachers overcome this barrier... students will have the choice on the exam to address questions related to those areas without being required to delve into others."

On leveraging open access resources and professional development:

"Many curriculum resources are open access... Even when the resources are free, professional learning workshops and coaches have costs, as does providing teachers with the time for extra course planning and professional learning community meetings."

They advocate for whole-school implementation of PBL as it addresses many of the challenges revealed in their research, such as the misalignment between different teaching methods and the need for a unified school culture that supports inquiry-based learning. They also emphasize the importance of district-level investment and support. This includes providing adequate resources, professional development for teachers, and the alignment of assessments with PBL methods to ensure that they measure the broad range of skills and knowledge that students gain.

The overarching message is that with support at both the school and district levels, the implementation of PBL can lead to transformative educational outcomes, fostering students who are not only academically successful but also adept at critical thinking, collaboration, and lifelong learning.

In my experience, that checks out and could easily be applied more broadly than to just PBL.

Decoding the Master Schedule: Analyzing Course Offerings, Choice, and Length to Uncover Educational Values

A school's master schedule speaks volumes about its priorities. It reveals how the school decides to allocate the time of students and staff and what it values most in education.

For example, a school that prioritizes test scores and academic achievement may require more instructional time for core academic subjects and less time for electives. Students who require additional support to improve their academic performance may get double the time in ELA or math. In contrast, a school that values a more "well-rounded" education may prioritize a wide variety of elective options for students to choose from, even for students who struggle academically.

Another way is to look at the type or length of courses offered. In schools that prioritize deeper learning and the development of essential skills, you will likely find courses with integrated curricula. They may offer courses like "GeoDesign," "Biolit," "American Studies," or "Civic Reasoning," with two teachers and more time for students to collaborate. In more traditional schools, courses will typically be of uniform length with titles aligned with specific graduation requirements like "English 9," "US History," or "Biology."

The number of choices offered to students at different grade levels can also reflect a school's priorities. A school that offers a lot of choices early in high school may have limited off-campus opportunities for students later in high school because students don't have as much flexibility in their schedule. A school that values off-campus opportunities may require a more rigid freshman schedule.

Schools that prioritize building a positive school culture or social-emotional learning may provide time in the master schedule for an advisory period to help facilitate restorative circles, mindfulness exercises, or workshops in conflict resolution. Schools without such a period prioritize academic class time and need to push into different subject areas for lessons on culture and social-emotional learning.

Master scheduling is an underappreciated art form. I urge administrators to review their master schedule with a team to ensure that it aligns with the school's values and goals for students. Promoting open dialogue and critical thinking is crucial during this process. If there is a discrepancy between the team's assessment and the school's priorities, changes should be made. The master schedule is a powerful tool to support the school's mission and vision for students. Don't be afraid to make adjustments that align with your school's values. Your students and community will thank you.

Math Dream Sequence A

​Here is my first shot at a dream sequence for high school math. It's truly a "dream" sequence: flaws, incomplete stories, and all. My point here is not to hit the nail on the head. I just hope to share an idea that math can be sequenced differently with a better result.

Here it goes:

​9th grade

All incoming high school students take the same math course integrating Algebra 1 and Geometry. If they were successful in Algebra 1 in middle school, great. They can take an "Honors Geometry" track embedded within regular Geometry and be leaders in the classroom by completing all problem extensions, helping others, etc.

Students in this integrated math course would receive two math credits and would have two math teachers, but there would be no difference between them. Both teachers would be responsible for both subjects and students would see them as equals.

The course would be 90–120 minutes long and would meet every day. Instruction would be 100% project- or problem-based. Students would be divided into periods by the previous year's academic performance to achieve a diverse group in every class. ​With two teachers and support from special education and counselors, learning would be differentiated for all learning styles and paces.

10th grade​

Learners who are successful in math during the 9th grade would ​move on to take an integrated Physics / Algebra 2 class. This course too would have an Honors track embedded within it. Extensions to problems would be required by these Honors students who would be expected to take a leadership role in the classroom.

This course would have two teachers: both certified in math and science. Again, students would not know who was who - both teachers would take responsibility for teaching both subjects. The class would be 90–120 minutes long and meet every day. Instruction would be 100% project- and problem-based. Learners at all levels would be in the same classroom for this course.

11th grade​

By the third year of high school, some students would be prepared (and will need) to take Pre-Calculus. ​Others may have struggled through their first two years of math and/or have educational plans that do not require them to learn much more advanced mathematics. Having already satisfied 3/4 of the MIchigan's requirements in mathematics, it's at this point that it makes sense for a few divergent paths to emerge in math sequencing.

1. Students in need of advanced mathematics understanding could take a stand-alone, hour-long, problem-based Pre-Calculus course or a more traditional semester-long Pre-Calculus and Calculus 1 course sequence at the community college.
   
2. Students not needing advanced mathematics who are interested in a service career could take an integrated Statistics & Social Science (Sociology/Psychology) course.
3. Students interested  in more hands-on technical career ​could earn their math credit through a program at the nearby Career and Technical Education Center.
   

12th grade

By creating divergent paths during the 11th grade, students' math options would become even more specific to their desired outcomes and ability during their fourth year of high school.

1. Students following a path of advanced mathematics could continue to take advanced courses at the community college.
   
2. ​Students following a service or health career path could earn credit through industry-specific math courses offered at the community college.
   
3. Students attending the Career Center would continue to earn their math credit through the programs offered there.​
4. Students choosing to change paths would be supported to do so according to their ability.​

Conclusions

To reiterate the point made in the first paragraph: this plan is not perfect. The cost of doubling up math in the freshmen year is substantial and would have to be offset in some way elsewhere in the school. The cost and quality of off-campus courses would also need to be considered.  

With that said, it gets students where they need to go without compromising classroom culture by splitting the most skilled math students from those who struggle.​ It creates math teaching teams who can support each other to truly differentiate. It provides ample time for students to complete challenging projects and problems. And, by providing two Michigan math requirements in the first year, it provides students the opportunity to re-take a course if they struggle and fall behind. It starts to get at some of the questions I was writing about last night.

I realize that there are a lot of points and assumptions that I'm making without specifically spelling them out. As a rule, that's probably going to be a theme in my writing. I simply don't have time to pull out every detail. The point is that I hope others will join in the conversation. Things will get spelled out in time. If you have questions, I encourage you to ask. 

Math Switch-a-roo

Lately, I've had trouble getting the sequence of high school math out of my head. For example, in Michigan, where I work and live, most students learn math as follows:

1. Algebra 1​
2. Geometry​
3. Algebra 2​
4. Pre-Calculus​
5. Calculus​

Following this sequence, the only ​way for a student to get to calculus while in high school is to take Algebra 1 in the 8th grade. Since not every student needs or will be successful in calculus, most students wait to take Algebra 1 until they get to high school.

In my district, a quarter to a third of students take Algebra 1 in the 8th grade. It's safe to say that most of these students are "good at school." What I mean is that they tend to watch their grades and have supportive families. Completing schoolwork comes somewhat naturally to them. Their being good at school is one of the reasons they get scheduled at a pace to complete calculus their senior year.

As a school administrator charged with the task of re-thinking teaching and learning, I have to question whether this practice is wise or necessary. Here are some of my questions:

1. What effect does being in a math class full of peers who are good at school have ​on your overall learning experience?
   
2. What effect does being in a math class absent any peers who are good at school have on your overall learning experience?​
3. ​What effect does putting all students who are good at school into one math class have on the rest of your courses or your school culture (especially in small schools)?​
   
4. What implicit messages are you sending students by separating them by ability in this way?​
5. What data and research exists to ​support separating students into ability groups in math?
   
6. What track record of success can schools who practice this method of scheduling math show to back up their practices?​
7. ​Who says that algebra should be split up like this? Is this best for learning?
   
8. Who says that any math should be separated at all? Should we integrate everything and teach logical chunks of math each year?​
9. Can 8th graders comprehend Algebra 1 deeply enough to change gears to Geometry for a full year before going back to Algebra 2?​
10. Might there be other ways to sequence and structure math to ​better serve our students' needs.​

I don't yet have answers to all of these questions, but I'm seeking them out. ​​​What I'm fairly certain of though is that math is sequenced the way it is ​because of tradition and status quo. We can change things if we have the will.

Last week we decided that all of our incoming 9th graders are going to take geometry. We're breaking the sequence to buy some time to think about algebra​, to integrate all learners in all classrooms (from special education to honors students), and to allow my 9th grade teacher to focus on one subject instead of two or three.

Next year, I'm not sure what we'll do. What I'd like to do is teach all algebra in one class with two teachers and twice the time. I doubt I'll have the numbers on my side to make that happen the way I want, but I have a year to think about it, to share my ideas with others, and to come up with a better solution.