By Patricia Ruiz Pati Ruiz is a doctoral student in Learning Technologies at Pepperdine University. She has worked as a teacher (Spanish and Computer Science), Director of Learning Technology, and is the incoming Dean of Studies at Convent of the Sacred Heart in New York City. As a teacher studying the learning sciences in graduate school, I understood constructivist practices in theory, but I often wondered what constructivism looked like in action. Taking a constructivist perspective, Windschitl (2002) describes learning as an act of both individual interpretation and negotiation with others, where knowledge is the collection of what is constructed individually and collectively. In classrooms, a constructivist or open approach should support learners in actively constructing their own knowledge, but what does that really look like? How much time does it take? What are the challenges? I spoke with some teachers to learn more about how they support an open approach to learning in their classrooms. This post will focus on the strategies of a middle and high school math teacher I interviewed. Future posts will focus on the work of high school Spanish and English teachers. Math Classroom Example: Christine Trying a New Curriculum Christine DeHaven is in her fifth year teaching middle and high school math. In her Honors Algebra 1 class at Pacific Ridge School, she always taught in a very guided or instructivist approach. For example, if the topic was lines, she would first lecture about lines, then work out one example in front of the class, and then students would do some problems on their own in class. For homework, students would complete more problems that progressed in difficulty. The class would then move on to the next topic. Christine noticed that students were just memorizing steps instead of problem solving, so she decided she needed to change her teaching approach. Christine had learned about a new curriculum that allowed the students to learn through conferences and visits to other schools, including The Bishop’s School, Deerfield Academy, and Phillips Exeter Academy (where the curriculum was developed). Christine and a colleague decided to swap their traditional directinstruction approach for a problembased approach. Christine had seen the new curriculum in action, and felt that it could work at her school, too. Still, she modified the curriculum slightly for her students. Sometimes the transition to a new approach needs to be done gently. Here is what Christine’s curriculum looks like now. First, students are assigned 810 homework problems per night. The goal for students is that they attempt all of the problems before class. When they arrive to class the next day, students pick a problem to solve on the board. Multiple students may put up the same problem, and everyone contributes at least one problem. After all of the problems are on the board, groups of students go to the board to present one problem at a time. If there are multiple solutions to the same problem, Christine leads a discussion about which solution is more efficient. With this new method, Christine finds that her students have more ownership of what they are learning. They apply problem solving skills to the homework and construct their own understandings through their solutions and conversations about their solutions. When they present their work and discuss the various solutions, students gain a better understanding of the concepts because they have to make a case for or against a certain way of solving a problem. Christine also encourages students’ use of graphing as a method to solve the homework problems. Students use tools like the Desmos Graphing Calculator to see a visual representation of the problem. In this way, Christine guides students to look at problems in three different ways: numerically, algebraically, and visually. Parent education and administrator support has played an important role in the ease of adopting her new curriculum. While Christine initially received some negative feedback about her approach from parents, she felt well supported by her school administrators who are able to point concerned parents towards research and articles about the success of this approach. Open house became an opportunity for Christine to educate concerned parentsshe even encouraged them to work with their children to solve the daily homework problems. Christine still attempts to engage parents by encouraging them to follow along on the course website. Many do, and often share stories of working on problems with their children. While parents were initially skeptical, many now tell Christine how much they appreciate the new approach and they have fun helping their children with their math homework. In the beginning, Christine also got negative feedback from students. But  for the most part  they have come around now that they have more practice with the approach. Something else that has helped students adjust is that the homework problems they are solving are very realistic; students can relate to them. For example, one problem, which aims to help students understand how dangerous glancing at a phone is when driving, asks students to compute how far they would drive down the highway in the time it took them to read or respond to a text message. Many of Christine’s students are learning to drive or have friends who are, so problems like these are relevant and engaging to them. (Please don’t text and drive!) Though challenging, Christine persisted in adopting the open curriculum because she felt that it was the best approach for her students. She thinks that students have a better understanding of the concepts they have covered. For example, they understand how to factor a polynomial and aren’t just guessing and checking. She reports they are able to prove why the square root of 2 is irrational. They also have a better sense of how a graph relates to algebra, and they persist in solving problems. When solving homework problems, students don’t always know the math theories or strategies they are using, but they are developing algorithms and figuring out problems as they go. These are essential skills for mathematics. Additionally, when students don’t solve a problem the first time, they are willing to try again and again. In this way, they are developing a growth mindset and starting to see the payoffs. This approach has been more time consuming for Christine. It’s the first time she’s seen many of these problems on the homework, so she needs to solve them all in multiple ways before going to class. She needs to think like her students and try to anticipate the problems they’ll have and the misconceptions they might bring to a problem. This means she really needs to know the content she’s teaching. It’s more prep time before class, especially in the first year, but this way she knows how to guide discussions and ask the right questions. Christine uses her expertise to help students gain a deeper understanding and make connections to content they have seen before. She’s not lecturing as much anymore, but she remains the content area expert. This idea leads to something that might be a struggle for some. It is described by Harland (2003) like this: “When students arrived at a position where they could function well together and drive the enquiry forward, they seldom asked for help, and the teaching team no longer had their old roles and familiar student contact. Paradoxically, we felt some sense of loss at this stage and concluded that a lot of pleasure in teaching had gone…” For Christine, though, she simply sees her role as a teacher changing. She is now more of a facilitator who ensures that students hit certain key points. She guides students in thinking more deeply by helping them ask questions instead of giving them answers. Her connection with students is now stronger, in her opinion. Preparing for class is more involved and timeconsuming and her role in the classroom is smaller. But for Christine, that’s okay. What excites her about teaching is helping students discover the math that she loves, and she’s doing that. If you’re interested in learning more about open approaches to Mathematics education, Christine recommended the Exeter Mathematics Institute and the Mathematics Visionary Project. We would love to hear what you think and the questions you might have for Christine or other teachers. Harland, T. (2003). Vygotsky's zone of proximal development and problembased learning: Linking a theoretical concept with practice through action research. Teaching in higher education, 8(2), 263272. Windschitl, M. (2002). Framing constructivism in practice as the negotiation of dilemmas: An analysis of the conceptual, pedagogical, cultural, and political challenges facing teachers. Review of educational research, 72(2), 131175.
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By Judi Fusco
Today, for something completely different, I include snippets from conversations with Katie Hong, an administrator in a large school district in a schoolwide Title 1 middle school. Katie is also a doctoral student pursuing her Ed.D. in the Pepperdine EDLT program. One of the first things Katie told me was how Keith Sawyer got it right when he said, “Many teachers spend their entire careers mastering the skills required to manage an instructionist classroom, and they understandably have trouble envisioning a different kind of school” (Sawyer, 2014 p. 3). Teachers are told to implement Common Core Standards with studentdriven learning, emphasizing collaboration, but they have not been equipped to implement or facilitate constructivist methods in their classroom. Another issue compounding the problem is administrators. Administrators often evaluate teachers based on the instructionist view. As they evaluate, they convey to the teacher how they want to see traditional classroom practices. When Katie was a young teacher, she did studentdriven, collaborative lessons; she had one on Mesopotamia where the students were working together exploring the role of irrigation and how it impacted the growth of civilization. Her principal walked in to evaluate her and was a little miffed because the class wasn’t quiet. He told her he’d come back when she was “teaching,” as he couldn’t do an evaluation on her with her students so offtask. Administrators have huge power over teachers, and teachers often continue to focus on the traditional classroom practices because they want to please their administrator, receive an effective evaluation, and be viewed as an effective teacher by their colleagues. Administrators aren’t completely to blame. as there aren’t good evaluation instruments or tools to help them evaluate constructivist methods or classes doing cooperative learning. Also, many administrators lack sufficient knowledge about studentdriven methods and collaboration. As Katie and I have continued talking, she has made many observations that have stayed with me. She spoke about how an ideal teacher evaluation should involve much more time than it’s given. Often there’s only time for one classroom visit with a pre and post meeting, but it would be better to have visits on a continuous basis throughout the year. She told me that she, as an administrator, would like to observe teachers facilitating studentdriven lessons, but teachers often don’t use studentdriven lessons on days she’s evaluating them unless she specifically asks them to in their premeeting. She also wishes she could have tools to help her understand what is happening more quickly when she walks into a classroom where students are collaborating. When there are a lot of groups, it can be hard to understand and evaluate what is occurring. And the forms she has to use for evaluation often involve a lot of answering of questions that may not capture the most important details. For her own research, she’s interested in thinking about how to help administrators evaluate a constructivist classroom effectively. She said, “I want to see the interaction with the students and teacher and how the teacher facilitatesthat would be my ideal observation. I learn so much more when I talk to the students. I want to see if they can synthesize material and apply it. I know the teacher knows the material. I don’t need to see them lecture. I want to observe what the students have learned and understand.” Thanks for the important perspective, Katie. We’ll have more of your thoughts on studentdriven learning in another post, soon. Administrators and teachers, what are your thoughts about teacher evaluations and studentdriven learning? What do you need to be successful? If you teach teachers, do you talk with them about the topics covered in this blog post? Cyberlearning researchers, can we help Katie with some new tools for evaluation of studentdriven collaboration? Sawyer, R.K. (2014) Introduction: The new science of learning. In: Sawyer R. K. (ed.) Cambridge handbook of the learning sciences. Second edition. Cambridge University Press, New York: 118. By Judi Fusco As I promised in the previous post, here’s a look at Tesha SenguptaIrving and Noel Enyedy’s 2015 article. In this post, I want to take a closer look at one study that shows the kind of work learning scientists do in classrooms with teachers. Some teachers (and principals, parents, and others) question whether studentdriven (open) pedagogies work for students; they worry if students are on their own, they might waste valuable instructional minutes, especially in math classes. However, by exploring data, discussing and debating, and constructing their own understanding, students in an studentdriven, open instructional approach achieve the instructional goals of the course as well as students in a teacherled (guided or instructivist) approach. In addition, and importantly, students seem to enjoy learning mathematics more when taught with an open or constructivist approach versus a guided approach. In their article, SenguptaIrving and Enyedy (2015) discuss how important enjoyment is in learning, and why and how a studentdriven instructional approach helps them learn. In the study, students' test performance was the same for both the teacherled and studentdriven approaches. So why don't we just stick with teacherled techniques? Why do we want to switch to more studentdriven approaches? SenguptaIrving and Enyedy, and many other learning scientists, don't think it’s enough to create mathematically proficient students without helping them develop an interest (or even love) for the subject that the studentdriven approach helps create. Learning without enjoyment seems like a lost opportunity that may prevent students from doing well in the future. The authors think if students learn and enjoy subjects, those students might want to go further in the subject and take more classes. Using Learning Science as the Foundation to Build Practical Classroom Practices So what did the students in the studentdriven condition do while learning? On their own, the students started with a discussion to explore the data, tried to understand the problem, and debated the approach or solution with peers. They also experimented and during their discussion “invented” an understanding, in this case, of statistics. They (hopefully) invent what the teacher would have told them during a lecture. While it may seem inefficient to let students invent, because, after all, we could just tell them what they need to know, but the discussion and inventing engages them, helps them enjoy the subject, and strengthens their learning. After they have gained some understanding on their own in their discussion, the teacher has a discussion with the students and helps them learn formal terms. Exploring first contrasts to what students do in the the instructivist or guided condition where the teacher tells them the formal terms, a great deal of information about the problem, what the important concepts are, and the approaches they should take in solving the problem. In the guided condition, students are not given an opportunity to explore informally. For a long time, learning scientists have known that “telling” students after they have the opportunity to explore and develop their own understanding is more effective than telling them before they have had that opportunity (Schwartz & Bransford, 1998). SenguptaIrving and Enyedy employ this learning science principle and find that students do well and seem to enjoy the lesson more. One other issue that is sometimes discussed about studentdriven approaches is whether students are offtask when on their own. It is true, studentdriven classrooms are usually noisier than instructivist ones, but that’s because there is learning occurring—in my experience, I have found that learning is a slightly noisy phenomenon. The researchers looked at offtask behavior in the two instructional approaches in the study and there wasn't a difference. They found more instances of offtask behavior in the teacherled condition than in the studentdriven condition and approximately the same number of minutes of offtask behaviors in the two conditions. I think it’s important to note that the teacher in this research reported that she was more comfortable with the teacherled approach. Because of that, the teacher may not have used an open approach very often, and her students may not have been as familiar with an open approachyet there was no extra offtask behavior. To alleviate concerns that studentdriven approaches require more time to work, both instructional approaches used the same amount of time for the lesson. I want to go back to the issue of enjoyment. If, after a lesson, students don’t want to think about it any more—because it’s boring, one of the terms the students in the teacherled condition used to describe the lesson—then we probably have not done the best we can for the students. Sure, if we tell students about something, we’ve gotten through the lesson and are able to cross that topic off the list. But shouldn’t learning be something more than just an item on a checklist? What if learning was enjoyable and students left wanting more? Learn the same amount, in the same amount of time, with very little offtask behavior, and enjoy it = winwinwinwin. And, add the bonus that enjoyment can potentially help students in their future work and motivate them to continue their studies. I'd make time for that in my classroom. I'd love to know what you think about the article and their findings. In future posts, we'll talk about how to o studentdriven approaches and hear from teachers who have some good tips. I'd also love to hear how you teach and what you've seen or experienced in your classroom. Below you can read more details of the study. SenguptaIrving, T., & Enyedy, N. (2015). Why engaging in mathematical practices may explain stronger outcomes in affect and engagement: Comparing studentdriven with highly guided inquiry. Journal of the Learning Sciences, 24(4), 550592, DOI: 10.1080/10508406.2014.928214. Schwartz, D. L., & Bransford, J. D. (1998). A time for telling. Cognition and instruction, 16(4), 4755223. Details of the study
In the study, one 5th grade classroom teacher taught two sets of students the same mathematics topic, for the same amount of time, using two different approaches: open (studentdriven; 27 students) and guided (instructivist; 25 students). The teacher was more comfortable with the guided approach, but had learned how to facilitate the open method and taught one class of students that way. The data collected included written assessments of the student’s work (a test), a survey inquiring about the students' affect during the lessons, and video of the 5 hours of class time devoted to the topic for each instructional approach. The researchers report three main findings based on the analysis of this data:

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