In today's current educational landscape, "redesign" is the key buzzword in developmental math. Several states are embarking on across-the-board projects to change their programs. The common approach involves the emporium model with modularization. The premise is that the prealgebra/beginning algebra/intermediate algebra curriculum is thought of as one large sequence instead of individual courses. Schools divide the content in various ways (units, weeks, chapters, etc.) and often call those pieces "modules." They then develop a way for students to start either at the beginning and move quickly out of the content they know or place in the sequence based on a test. Either way, a self paced approach to completing the remaining content is usually taken. Students watch videos, read the book or use workbooks, and work homework problems in an online homework system. Tests are taken at the end of each module. In theory, students can move through content quickly. Lectures are often not included but some schools incorporate weekly one-hour sessions for problem solving purposes.
Having used self paced approaches (unsuccessfully and then successfully) for 10 years and helping schools who are using them, I'm familiar with the emporium model. It has a new name but the approach has existed for decades. It's improved, certainly, with current online homework systems.
Some students will thrive and love this approach to math education. The ones that are close to being at college level and are motivated can do especially well. Students who have seen the content before, need a brush up on missing items, and who are not that far from the finish line are best suited for the approach.
Likewise, some instructors love moving around a lab full of students, answering questions that vary wildly. The challenge in being prepared for hundreds of topics interests them and they enjoy not preparing lectures. It can be a refreshing change of pace from the typical classroom environment.
The issue is that it is not the right approach for everyone, especially students who have large gaps in understanding and/or place very low in the developmental math sequence. It is also not attractive to many faculty. Since faculty support and buy-in are critical to a redesign's success, that matters. Schools and states can impose mandates but if the faculty don't believe in them, they will wait out the administration until the movement passes and revert to their prior techniques.
These statements will incur disagreement. The emporium model is controversial so heated discussions come along for the ride. I've been told by some of its advocates that everyone responds well, some take longer than others, but it works for all. And I disagree. First, because I've seen it firsthand and heard from many around the country. But for another perspective, consider this:
This summer my children have 3 full months off from school, longer than they ever have had due to school construction. We always do math, reading, and writing throughout the summer but this year I feel it especially important to have a deliberate approach since they're away from school so long. We have workbooks and library time but we've also added the Khan Academy to our repertoire. I thought, "they will love this! It's interactive. There's videos when you need help. The practice sets are like a video game. They earn points. They can move as fast or as slow as they want. This is awesome!"
Except it didn't turn out to be that way at all.
They liked it initially but the novelty wore off. Also, they didn't want to watch a video about a new topic. They wanted me to explain a new topic and us talk back and forth as they had questions.
It was a nice addition, something different, and something they liked on occasion. But they did not want it to be their bread and butter. I asked them both (aged 7 and 11) if they could imagine only learning math by working in a program like the Khan Academy with a teacher answering questions. They both looked at me like I had grown a third eye. "But what about the teacher? Don't they get to teach?" They don't equate teaching with answering questions from someone else's explanation. And maybe it is teaching to some but many think otherwise.
Reading that, you may think, "but they're children. These are adults who are in a completely different place in their mathematics education." Are they really in that different of a place?
I see students constantly who know so little about math that their understanding is like that of a child. Years of rules and varied approaches has left them insecure and confused with little natural curiosity or confidence. I often think how great it would be to start them over and let them explore math, ask the questions they have, work with more manipulatives, and build their confidence with their understanding. Sure, use worksheets and computers and books but that's not enough. The human element is needed to create it, direct it, and solidify it. I don't mean lecture needs to be there 100% but a person needs to be a part of the equation, working with students to build their understanding. People, tools, computers, and paper need to exist but with balance.
Ask students when they remember loving math (and most will) and they will nearly always say elementary school. Ask them when they stopped liking it and many will say 4th or 5th grade. The change came when the subject stopped being physical and meaningful and started becoming procedures and rules. Both are necessary but when we emphasize only one aspect to the subject, we often lose students.
One of my main problems with an emporium approach across the board is that it works under the assumption that our subject is just a stack of skills to be learned and that our curriculum is fine. The problem just lies with the speed or delivery of it. Also, when used across the board, it works on the assumption that one solution is right for everyone. In the age we live in of choice and options, it can be infuriating to students to lose that entirely.
So where do Statway and Quantway come into this?
Both pathways strive to look at the curriculum and how we teach it, changing that experience from primarily lecture on skills to some direct instruction but more time problem solving with students. There is deliberate design of activities to create engagement of students with one another. Can you get engagement with emporium models? Yes, if you accept the idea that engagement is two students discussing how to work through an exercise. That's fine but I want to see more than that. I want to see them also discussing problems (not just exercises) and mathematics in a larger sense.
The pathways can be a cost effective addition to a department. They also accelerate the timeline for students. So they offer solutions to some key, common problems in developmental math programs.
Lest you think I believe the pathways to be the solution to all of our ails, I don't. I don't think there's any singular approach that will fix the problem for everyone and even if it there is one, I don't profess to have it. The problem is just too big and too complex for that to be the case. A myriad of approaches is necessary to solve the myriad of issues.
The pathways are an excellent addition to a department to serve students with specific goals, specifically the ones who are not headed toward a STEM direction. Emporium models are excellent for those students who are headed to STEM areas but are close to college level, motivated, and just need a little time. For the students who aren't in either category, a well designed curriculum using instructional principles from research on developmental students can work to serve them as well. We've seen that in our school's redesign. We get 65-70% of students to pass nearly all our developmental math classes. The sections are not self paced; most live in a classroom. A few are computer assisted with about 70% of the class time on direct instruction the remainder spent with students on computers and the teacher helping. We have many options, offerings, and solutions to help solve the problems we have. Most work well, some are still being massaged. If you want to read and hear more about our redesign, click here.
My point is that I don't believe there is a quick fix to this issue of developmental math education and my antennae go up when I hear someone professing there is one. The latest ideas for innovation (emporium, pathways) can live together in harmony as just a few pieces of a much larger redesign puzzle. Schools have multiple options for making change based on their funding and their culture. One size need not fit all.
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