Instructional Features
Most computer-based mathematics instruction programs offer a limited, fixed set of problems. These systems also provide only minimal feedback, telling students little more than whether they answered the exercises correctly. With such systems, students are merely engaged in repetitive, one-size-fits-all practice, which is insufficient to promote learning. This is why most so-called “test-prep” programs do not, in fact, improve students’ performance on exams.
In contrast, Learning Conductor, developed through decades of educational research, is designed to help students achieve a deep, lasting understanding of mathematics. The program helps students recognize and begin to take charge of their own growth as mathematics learners.
Learning Conductor turns assessment into assessment-guided learning, by providing:
- Dynamic Problem Generation
- Worked-Example Solutions
- Representation-Rich Approach
- Real-time Reporting and Study Guidance
Dynamic Problem Generation
Learning Conductor’s problem generator gives students the amount and variety of problems they need to master the required mathematics curriculum. The system utilizes templates based on publicly released items for standardized exams, along with a sophisticated parameterization algorithm that generates up to 100 problems from each template. This results in a very large pool of items, allowing Learning Conductor to produce a different set of standards-aligned exercises every time the student uses the program. The streams of exercises can be customized to address individual students’ current levels of proficiency, as well as particular mathematical content areas or standards.
Worked-Example Solutions
For every exercise created by the problem generator, Learning Conductor provides a step-by-step, “worked-example” solution. Students receive the solution immediately after submitting the answer to the exercise. Research has repeatedly shown that such immediate, detailed feedback helps students recognize and correct misconceptions and faulty strategies before they become ingrained in long-term memory. Over time, worked-example solutions help students take charge of their own growth as mathematics learners, increasing both their confidence and their proficiency.
Image 1 Caption: In this screenshot, the worked-example solution for the problem is shown in conjunction with the correct answer. The solution is provided in discrete steps, with each step showing the strategy and computations needed to solve the problem.
In cases where the problem includes a representation, that representation is used as part of the worked-out solution. The representation is geometrically correct, and presented in such as way as to help the student envision the steps and strategies needed to solve the problem.
This example shows students how to apply their knowledge of standard-area calculations to irregularly shaped figures composed of rectangles. Thus, the worked-example solution goes far beyond right / wrong scoring, helping students recognize and apply their existing knowledge to more complex problems.
Representation-Rich Approach
Learning Conductor’s exercises and worked-example solutions include a diverse array of explanatory text, diagrams, models, pictures, charts, graphs, tables, symbols, and equations. This representation-rich approach has been proven especially effective in helping novice and linguistically diverse students. For this approach to work, representations must be geometrically correct so that students can better visualize the problem—which is not always the case with other online instructional systems.
Learning Conductor has the unique capability to dynamically generate geometric representations according to the specifics of each problem. Whenever new problem sets are generated, each problem’s representation also changes, showing dimensions that are geometrically accurate.
Image 2 Caption: In the screenshot from Learning Conductor, below, each line dimension is correct relative to the other dimensions, and all the portrayed dimensions are accurate with respect to each other. This allows students not only to see the problem precisely, but to better understand the mathematical concepts underlying it.
Real-time Reporting and Study Guidance
Learning Conductor’s relational database generates an array of student performance reports on demand. These detailed reports, in easily readable formats, allow students, parents, and / or their teachers to continuously monitor and respond to their performance on the exercises.
In addition to helping students understand their strengths and weaknesses within the standards-based curriculum, Learning Conductor’s reports are also designed to help students evaluate their readiness for standardized exams. Because Learning Conductor’s exercises are “clones” of publicly released items from these exams, this performance data gives a highly accurate snapshot of students’ levels of preparedness, and guides them to concentrate on areas of weakness.
The example below shows a student’s readiness to take the California High School Exit Exam (CAHSEE) in mathematics. Note that Learning Conductor holds students to a higher performance standard (75% correct answers needed to pass) than the CAHSEE exam itself does (only 55% correct to pass).
Based on a student’s readiness status, Learning Conductor activates navigation buttons, leading them through Readiness Tests to assess strengths and weaknesses and then through Practice Sessions to focus on the areas where extra work is needed. Topics in which students have shown proficiency are not recommended for study, allowing students to spend their time more efficiently as they prepare for the exam.
