The National Science Foundation awards grant to study virtual worlds that afford knowledge integration

The Concord Consortium is proud to announce a new project funded by the National Science Foundation, “Towards virtual worlds that afford knowledge integration across project challenges and disciplines.” Principal Investigator Janet Kolodner and Co-PI Amy Pallant will explore how the design of project challenges and the contexts in which they are carried out can support knowledge integration, sustained engagement, and excitement. The goal is to learn how to foster knowledge integration across disciplines when learners encounter and revisit phenomena and processes across several challenges.

Aerial Geography and Air QualityIn this model, students explore the effect of wind direction and geography on air quality as they place up to four smokestacks in the model.

We envision an educational system where learners regularly engage in project-based education within and across disciplines, and in and out of school. We believe that, with such an educational approach, making connections across learning experiences should be possible in new and unexplored ways. If challenges are framed appropriately and their associated figured worlds (real and virtual) and scaffolding are designed to afford it, such education can help learners integrate the content and practices they are learning across projects and across disciplines. “Towards virtual worlds” will help move us towards this vision.

This one-year exploratory project focuses on the possibilities for knowledge integration when middle schoolers who have achieved water ecosystems challenges later attempt an air quality challenge. Some students will engage with EcoMUVE, where learners try to understand why the fish in a pond are dying, and others will engage with Living Together from Project-Based Inquiry Science (PBIS), where learners advise about regulations that should be put in place before a new industry is allowed to move into a town. A subset of these students will then encounter specially crafted air quality challenges based on High-Adventure Science activities and models. These, we hope, will evoke reminders of experiences during their water ecosystem work. We will examine what learners are reminded of, the richness of their memories, and the appeal for learners of applying what they are learning about air quality to better address the earlier water ecology challenge. Research will be carried out in Boston area schools.

Sideview Pollution Control Devices In this model, students explore the effects of installing pollution control devices, such as scrubbers and catalytic converters, on power plants and cars. Students monitor the level of primary pollutants (brown line) and secondary pollutants (orange line) in the model over time, via the graph.

The project will investigate:

  1. What conditions give rise to intense and sustained emotional engagement?
  2. What is remembered by learners when they have (enthusiastically) engaged with a challenge in a virtual figured world and reflected on it in ways appropriate to learning, and what seems to affect what is remembered?
  3. How does a challenge and/or virtual world need to be configured so that learners notice—while not being overwhelmed by—phenomena not central to the challenge but still important to making connections with content outside the challenge content?

Our exploration will help us understand more about the actual elements in the experiences of learners that lead to different emotional responses and the impacts of such responses on their memory making and desires.

Lessons we learn about conditions under which learners form rich memories and want to go back and improve their earlier solutions to challenges will form some of the foundations informing how to design virtual worlds and project challenges with affordances for supporting knowledge integration across projects and disciplines. Exemplar virtual worlds and associated project challenges will inform design principles for the design and use of a new virtual world genre — one with characteristics that anticipate cross-project and cross-discipline knowledge integration and ready learners for future connection making and knowledge deepening.

Simulating the Hadley Cell using Energy2D

Download the models
Although it is mostly used as an engineering tool, our Energy2D software can also be used to create simple Earth science simulations. This blog post shows some interesting results about the Hadley Cell.

The Hadley Cell is an atmospheric circulation that transports energy and moisture from the equator to higher latitudes in the northern and southern hemispheres. This circulation is intimately related to the trade winds, hurricanes, and the jet streams.

As a simple way to simulate zones of ocean that have different temperatures due to differences in solar heating, I added an array of constant-temperature objects at the bottom of the simulation window. The temperature gradually decreases from 30 °C in the middle to 15 °C at the edges. A rectangle, set to be at a constant temperature of -20 °C, is used to mimic the high, chilly part of the atmosphere. The viscosity of air is deliberately set to much higher than reality to suppress the wild fluctuations for a somehow averaged effect. The results show a stable flow pattern that looks like a cross section of the Hadley Cell, as is shown in the first image of this post.

When I increased the buoyant force of the air, an oscillatory pattern was produced. The system swings between two states shown in the second and third images, indicating a periodic reinforcement of hot rising air from the adjacent areas to the center (which is supposed to represent the equator).

Of course, I can't guarantee that the results produced by Energy2D are what happen in nature. Geophysical modeling is an extremely complicated business with numerous factors that are not considered in this simple model. Yet, Energy2D shows something interesting: the fluctuations of wind speeds seem to suggest that, even without considering the seasonal changes, this nonlinear model already exhibits some kind of periodicity. We know that it is all kinds of periodicity in Mother Nature that help to sustain life on the Earth.

Simulating geometric thermal bridges using Energy2D

Fig. 1: IR image of a wall junction (inside) by Stefan Mayer
One of the mysterious things that causes people to scratch their heads when they see an infrared picture of a room is that the junctions such as edges and corners formed by two exterior walls (or floors and roofs) often appear to be colder in the winter than other parts of the walls, as is shown in Figure 1. This is, I hear you saying, caused by an air gap between two walls. But not that simple! While a leaking gap can certainly do it, the effect is there even without a gap. Better insulation only makes the junctions less cold.

Fig. 2: An Energy2D simulation of thermal bridge corners.
A typical explanation of this phenomenon is that, because the exterior surface of a junction (where the heat is lost to the outside) is greater than its interior surface (where the heat is gained from the inside), the junction ends up losing thermal energy in the winter more quickly than a straight part of the walls, causing it to be colder. The temperature difference is immediately revealed by a very sensitive IR camera. Such a junction is commonly called a geometric thermal bridge, which is different from material thermal bridge that is caused by the presence of a more conductive piece in a building assembly such as a steel stud in a wall or a concrete floor of a balcony.

Fig. 3: IR image of a wall junction (outside) by Stefan Mayer
But the actual heat transfer process is much more complicated and confusing. While a wall junction does create a difference in the surface areas of the interior and exterior of the wall, it also forms a thicker area through which the heat must flow through (the area is thicker because it is in a diagonal direction). The increased thickness should impede the heat flow, right?

Fig. 4: An Energy2D simulation of a L-shaped wall.
Unclear about the outcome of these competing factors, I made some Energy2D simulations to see if they can help me. Figure 2 shows the first one that uses a block of object remaining at 20 °C to mimic a warm room and the surrounding environment of 0 °C, with a four-side wall in-between. Temperature sensors are placed at corners, as well as the middle point of a wall. The results show that the corners are indeed colder than other parts of the walls in a stable state. (Note that this simulation only involves heat diffusion, but adding radiation heat transfer should yield similar results.)

What about more complex shapes like an L-shaped wall that has both convex and concave junctions? Figure 3 shows the IR image of such a wall junction, taken from the outside of a house. In this image, interestingly enough, the convex edge appears to be colder, but the concave edge appears to be warmer!

The Energy2D simulation (Figure 4) shows a similar pattern like the IR image (Figure 3). The simulation results show that the temperature sensor placed near the concave edge outside the L-shape room does register a higher temperature than other sensors.

Now, the interesting question is, does the room lose more energy through a concave junction or a convex one? If we look at the IR image of the interior taken inside the house (Figure 1), we would probably say that the convex junction loses more energy. But if we look at the IR image of the exterior taken outside the house (Figure 3), we would probably say that the concave junction loses more energy.

Which statement is correct? I will leave that to you. You can download the Energy2D simulations from this link, play with them, and see if they help you figure out the answer. These simulations also include simulations of the reverse cases in which heat flows from the outside into the room (the summer condition).

Time series analysis tools in Visual Process Analytics: Cross correlation

Two time series and their cross-correlation functions
In a previous post, I showed you what autocorrelation function (ACF) is and how it can be used to detect temporal patterns in student data. The ACF is the correlation of a signal with itself. We are certainly interested in exploring the correlations among different signals.

The cross-correlation function (CCF) is a measure of similarity of two time series as a function of the lag of one relative to the other. The CCF can be imagined as a procedure of overlaying two series printed on transparency films and sliding them horizontally to find possible correlations. For this reason, it is also known as a "sliding dot product."

The upper graph in the figure to the right shows two time series from a student's engineering design process, representing about 45 minutes of her construction (white line) and analysis (green line) activities while trying to design an energy-efficient house with the goal to cut down the net energy consumption to zero. At first glance, you probably have no clue about what these lines represent and how they may be related.

But their CCFs reveal something that appears to be more outstanding. The lower graph shows two curves that peak at some points. I know you have a lot of questions at this point. Let me try to see if I can provide more explanations below.

Why are there two curves for depicting the correlation of two time series, say, A and B? This is because there is a difference between "A relative to B" and "B relative to A." Imagine that you print the series on two transparency films and slide one on top of the other. Which one is on the top matters. If you are looking for cause-effect relationships using the CCF, you can treat the antecedent time series as the cause and the subsequent time series as the effect.

What does a peak in the CCF mean, anyways? It guides you to where more interesting things may lie. In the figure of this post, the construction activities of this particular student were significantly followed by analysis activities about four times (two of them are within 10 minutes), but the analysis activities were significantly followed by construction activities only once (after 10 minutes).

Time series analysis tools in Visual Process Analytics: Autocorrelation

Autocorrelation reveals a three-minute periodicity
Digital learning tools such as computer games and CAD software emit a lot of temporal data about what students do when they are deeply engaged in the learning tools. Analyzing these data may shed light on whether students learned, what they learned, and how they learned. In many cases, however, these data look so messy that many people are skeptical about their meaning. As optimists, we believe that there are likely learning signals buried in these noisy data. We just need to use or invent some mathematical tricks to figure them out.

In Version 0.2 of our Visual Process Analytics (VPA), I added a few techniques that can be used to do time series analysis so that researchers can find ways to characterize a learning process from different perspectives. Before I show you these visual analysis tools, be aware that the purpose of these tools is to reveal the temporal trends of a given process so that we can better describe the behavior of the student at that time. Whether these traits are "good" or "bad" for learning likely depends on the context, which often necessitates the analysis of other co-variables.

Correlograms reveal similarity of two time series.
The first tool for time series analysis added to VPA is the autocorrelation function (ACF), a mathematical tool for finding repeating patterns obscured by noise in the data. The shape of the ACF graph, called the correlogram, is often more revealing than just looking at the shape of the raw time series graph. In the extreme case when the process is completely random (i.e., white noise), the ACF will be a Dirac delta function that peaks at zero time lag. In the extreme case when the process is completely sinusoidal, the ACF will be similar to a damped oscillatory cosine wave with a vanishing tail.

An interesting question relevant to learning science is whether the process is autoregressive (or under what conditions the process can be autoregressive). The quality of being autoregressive means that the current value of a variable is influenced by its previous values. This could be used to evaluate whether the student learned from the past experience -- in the case of engineering design, whether the student's design action was informed by previous actions. Learning becomes more predictable if the process is autoregressive (just to be careful, note that I am not saying that more predictable learning is necessarily better learning). Different autoregression models, denoted as AR(n) with n indicating the memory length, may be characterized by their ACFs. For example, the ACF of AR(2) decays more slowly than that of AR(1), as AR(2) depends on more previous points. (In practice, partial autocorrelation function, or PACF, is often used to detect the order of an AR model.)

The two figures in this post show that the ACF in action within VPA, revealing temporal periodicity and similarity in students' action data that are otherwise obscure. The upper graphs of the figures plot the original time series for comparison.

Visual Process Analytics (VPA) launched

Visual Process Analytics (VPA) is an online analytical processing (OLAP) program that we are developing for visualizing and analyzing student learning from complex, fine-grained process data collected by interactive learning software such as computer-aided design tools. We envision a future in which every classroom would be powered by informatics and infographics such as VPA to support day-to-day learning and teaching at a highly responsive level. In a future when every business person relies on visual analytics every day to stay in business, it would be a shame that teachers still have to read through tons of paper-based work from students to make instructional decisions. The research we are conducting with the support of the National Science Foundation is paving the road to a future that would provide the fair support for our educational systems that is somehow equivalent to business analytics and intelligence.

This is the mission of VPA. Today we are announcing the launch of this cyberinfrastructure. We decided that its first version number should be 0.1. This is just a way to indicate that the research and development on this software system will continue as a very long-term effort and what we have done is a very small step towards a very ambitious goal.

VPA is written in plain JavaScript/HTML/CSS. It should run within most browsers -- best on Chrome and Firefox -- but it looks and works like a typical desktop app. This means that while you are in the middle of mining the data, you can save what we call "the perspective" as a file onto your disk (or in the cloud) so that you can keep track of what you have done. Later, you can load the perspective back into VPA. Each perspective opens the datasets that you have worked on, with your latest settings and results. So if you are half way through your data mining, your work can be saved for further analyses.

So far Version 0.1 has seven analysis and visualization tools, each of which shows a unique aspect of the learning process with a unique type of interactive visualization. We admit that, compared with the daunting high dimension of complex learning, this is a tiny collection. But we will be adding more and more tools as we go. At this point, only one repository -- our own Energy3D process data -- is connected to VPA. But we expect to add more repositories in the future. Meanwhile, more computational tools will be added to support in-depth analyses of the data. This will require a tremendous effort in designing a smart user interface to support various computational tasks that researchers may be interested in defining.

Eventually, we hope that VPA will grow into a versatile platform of data analytics for cutting-edge educational research. As such, VPA represents a critically important step towards marrying learning science with data science and computational science.

The National Science Foundation funds large-scale applications of infrared cameras in schools

We are pleased to announce that the National Science Foundation has awarded the Concord Consortium, Next Step Living, and Virtual High School a grant of $1.2M to put innovative technologies such as infrared cameras into the hands of thousands of secondary students. This education-industry collaborative will create a technology-enhanced learning pathway from school to home and then to cognate careers, establishing thereby a data-rich testbed for developing and evaluating strategies for translating innovative technology experiences into consistent science learning and career awareness in different settings. While there have been studies on connecting science to everyday life or situating learning in professional scenarios to increase the relevance or authenticity of learning, the strategies of using industry-grade technologies to strengthen these connections have rarely been explored. In many cases, often due to the lack of experiences, resources, and curricular supports, industry technologies are simply used as showcases or demonstrations to give students a glimpse of how professionals use them to solve problems in the workplace.

Over the last few years, however, quite a number of industry technologies have become widely accessible to schools. For example, Autodesk has announced that their software products will be freely available to all students and teachers around the world. Another example is infrared cameras that I have been experimenting and blogging since 2010. Due to the continuous development of electronics and optics, what used to be a very expensive scientific instrument is now only a few hundred dollars, with the most affordable infrared camera falling below $200.

The funded project, called Next Step Learning, will be the largest-scale application of infrared camera in secondary schools -- in terms of the number of students that will be involved in the three-year project. We estimate that dozens of schools and thousands of students in Massachusetts will participate in this project. These students will use infrared cameras provided by the project to thermally inspect their own homes. The images in this blog post are some of the curious images I took in my own house using the FLIR ONE camera that is attached to an iPhone.

In the broader context, the Next Generation Science Standards (NGSS) envisions “three-dimensional learning” in which the learning of disciplinary core ideas and crosscutting concepts is integrated with science and engineering practices. A goal of the NGSS is to make science education more closely resemble the way scientists and engineers actually think and work. To accomplish this goal, an abundance of opportunities for students to practice science and engineering through solving authentic real-world problems will need to be created and researched. If these learning opportunities are meaningfully connected to current industry practices using industry-grade technologies, they can also increase students’ awareness of cognate careers, help them construct professional identities, and prepare them with knowledge and skills needed by employers, attaining thereby the goals of both science education and workforce development simultaneously. The Next Step Learning project will explore, test, and evaluate this strategy.

Twelve Energy3D designs by Cormac Paterson

Cormac Paterson, a 17-years old student from Arlington High School in Massachusetts, has created yet another set of beautiful architectural designs using our Energy3D CAD software. The variety of his designs can be used to gauge the versatility of the software. His work is helping us push the boundary of the software and imagine what may be possible with the system.

This is the second year Cormac has worked with us as a summer intern. We are constantly impressed by his perseverance in working with the limitations of the software and around problems, as well as his ingenuity in coming up with new solutions and ideas. Working with Cormac has inspired us on how to improve our software so that it can support more students to do this kind of creative design. Our objective in the long run is to develop our software into a CAD system that is appropriate for children and yet capable of supporting authentic engineering design. Cormac's work might be an encouraging sign that we may actually be very close to realizing this goal.

Cormac also designed a building surrounded by solar trees. Solar tree is a concept that blends art and solar energy technology in a sculptural expression. An image of this post shows the result of the solar energy gains of these "trees" using the improved computational engine for solar simulation in Energy3D. 

Seeing student learning with visual analytics

Technology allows us to record almost everything happening in the classroom. The fact that students' interactions with learning environments can be logged in every detail raises the interesting question about whether or not there is any significant meaning and value in those data and how we can make use of them to help students and teachers, as pointed out in a report sponsored by the U.S. Department of Education:
New technologies thus bring the potential of transforming education from a data-poor to a data-rich enterprise. Yet while an abundance of data is an advantage, it is not a solution. Data do not interpret themselves and are often confusing — but data can provide evidence for making sound decisions when thoughtfully analyzed.” — Expanding Evidence Approaches for Learning in a Digital World, Office of Educational Technology, U.S. Department of Education, 2013
A radar chart of design space exploration.
A histogram of action intensity.
Here we are not talking about just analyzing students' answers to some multiple-choice questions, or their scores in quizzes and tests, or their frequencies of logging into a learning management system. We are talking about something much more fundamental, something that runs deep in cognition and learning, such as how students conduct a scientific experiment, solve a problem, or design a product. As learning goes deeper in those directions, data produced by students grows bigger. It is by no means an easy task to analyze large volumes of learner data, which contain a lot of noisy elements that cast uncertainty to assessment. The validity of an assessment inference rests on  the strength of evidence. Evidence construction often relies on the search for relations, patterns, and trends in student data.With a lot of data, this mandates some sophisticated computation similar to cognitive computing.

Data gathered from highly open-ended inquiry and design activities, key to authentic science and engineering practices that we want students to learn, are often intensive and “messy.” Without analytic tools that can discern systematic learning from random walk, what is provided to researchers and teachers is nothing but a DRIP (“data rich, information poor”) problem.

A scatter plot of action timeline.
Recognizing the difficulty in analyzing the sheer volume of messy student data, we turned to visual analytics, a whole category of techniques extensively used in cutting-edge business intelligence systems such as software developed by SAS, IBM, and others. We see interactive, visual process analytics key to accelerating the analysis procedures so that researchers can adjust mining rules easily, view results rapidly, and identify patterns clearly. This kind of visual analytics optimally combines the computational power of the computer, the graphical user interface of the software, and the pattern recognition power of the brain to support complex data analyses in data-intensive educational research.

A digraph of action transition.
So far, I have written four interactive graphs and charts that can be used to study four different aspects of the design action data that we collected from our Energy3D CAD software. Recording several weeks of student work on complex engineering design challenges, these datasets are high-dimensional, meaning that it is improper to treat them from a single point of view. For each question we are interested in getting answers from student data, we usually need a different representation to capture the outstanding features specific to the question. In many cases, multiple representations are needed to address a question.

In the long run, our objective is to add as many graphic representations as possible as we move along in answering more and more research questions based on our datasets. Given time, this growing library of visual analytics would develop sufficient power to the point that it may also become useful for teachers to monitor their students' work and thereby conduct formative assessment. To guarantee that our visual analytics runs on all devices, this library is written in JavaScript/HTML/CSS. A number of touch gestures are also supported for users to use the library on a multi-touch screen. A neat feature of this library is that multiple graphs and charts can be grouped together so that when you are interacting with one of them, the linked ones also change at the same time. As the datasets are temporal in nature, you can also animate these graphs to reconstruct and track exactly what students do throughout.

The National Science Foundation funds SmartCAD—an intelligent learning system for engineering design

We are pleased to announce that the National Science Foundation has awarded the Concord Consortium, Purdue University, and the University of Virginia a $3 million, four-year collaborative project to conduct research and development on SmartCAD, an intelligent learning system that informs engineering design of students with automatic feedback generated using computational analysis of their work.

Engineering design is one of the most complex learning processes because it builds on top of multiple layers of inquiry, involves creating products that meet multiple criteria and constraints, and requires the orchestration of mathematical thinking, scientific reasoning, systems thinking, and sometimes, computational thinking. Teaching and learning engineering design becomes important as it is now officially part of the Next Generation Science Standards in the United States. These new standards mandate every student to learn and practice engineering design in every science subject at every level of K-12 education.
Figure 1

In typical engineering projects, students are challenged to construct an artifact that performs specified functions under constraints. What makes engineering design different from other design practices such as art design is that engineering design must be guided by scientific principles and the end products must operate predictably based on science. A common problem observed in students' engineering design activities is that their design work is insufficiently informed by science, resulting in the reduction of engineering design to drawing or crafting. To circumvent this problem, engineering design curricula often encourage students to learn or review the related science concepts and practices before they try to put the design elements together to construct a product. After students create a prototype, they then test and evaluate it using the governing scientific principles, which, in turn, gives them a chance to deepen their understanding of the scientific principles. This common approach of learning is illustrated in the upper image of Figure 1.

There is a problem in the common approach, however. Exploring the form-function relationship is a critical inquiry step to understanding the underlying science. To determine whether a change of form can result in a desired function, students have to build and test a physical prototype or rely on the opinions of an instructor. This creates a delay in getting feedback at the most critical stage of the learning process, slowing down the iterative cycle of design and cutting short the exploration in the design space. As a result of this delay, experimenting and evaluating "micro ideas"--very small stepwise ideas such as those that investigate a design parameter at a time--through building, revising, and testing physical prototypes becomes impractical in many cases. From the perspective of learning, however, it is often at this level of granularity that foundational science and engineering design ultimately meet.

Figure 2
All these problems can be addressed by supporting engineering design with a computer-aided design (CAD) platform that embeds powerful science simulations to provide formative feedback to students in a timely manner. Simulations based on solving fundamental equations in science such as Newton’s Laws model the real world accurately and connect many science concepts coherently. Such simulations can computationally generate objective feedback about a design, allowing students to rapidly test a design idea on a scientific basis. Such simulations also allow the connections between design elements and science concepts to be explicitly established through fine-grained feedback, supporting students to make informed design decisions for each design element one at a time, as illustrated by the lower image of Figure 1. These scientific simulations give the CAD software tremendous disciplinary intelligence and instructional power, transforming it into a SmartCAD system that is capable of guiding student design towards a more scientific end.

Despite these advantages, there are very few developmentally appropriate CAD software available to K-12 students—most CAD software used in industry not only are science “black boxes” to students, but also require a cumbersome tool chaining of pre-processors, solvers, and post-processors, making them extremely challenging to use in secondary education. The SmartCAD project will fill in this gap with key educational features centered on guiding student design with feedback composed from simulations. For example, science simulations can be used to analyze student design artifacts and compute their distances to specific goals to detect whether students are zeroing in towards those goals or going astray. The development of these features will also draw upon decades of research on formative assessments of complex learning.