Evaluating Digital Math Tools in the Field

Many school districts have adopted digital tools to supplement or replace teacher-led instruction, usually based on the premise that these tools can provide more personalized or individualized experiences for students and at lower cost. Rigorously evaluating whether such initiatives promote better student outcomes in the field is difficult as most schools and teachers are unwilling to enforce rigorous study designs such as randomized control trials. We used study designs that were feasible in practice to assess whether two digital math tools, eSpark and IXL, were associated with improvements in 3rd – 6th grade student test scores in math. We also investigated the resource requirements and costs of implementing eSpark and IXL to assess whether these tools represent a valuable use of resources. We find that while IXL is substantially less costly to implement than eSpark, its use is not significantly associated with students’ math performance

Using a peer supervision model to implement recommendations of the NCTM standards in algebra classes in an urban school system.

The NCTM Standards have established new directions for math teaching and learning. The problem of implementation, particularly in urban school systems remains. This study focuses on an urban school system in Western Massachusetts. Of particular interest to the researcher is the lack of success of students in Algebra I. This particular course has traditionally been the pivotal course that determines if a student gets into and remains in the College Preparatory sequence. The fact that too many minority and women students are left out of these choices due to lack of mathematics preparation can be traced back to being left out of algebra in high school. What happened to these students? Why were they left out? Why is the failure rate nearly 45 percent in Algebra I in this public school system? Teachers working in the traditional classroom structure of the current school setting are isolated without opportunities to work in cooperation with other teachers. Without a process for sharing ideas and a method to support new teaching strategies, it will not be possible for the vision of the Standards to become a reality. The challenge for a supervisor is to bring the message of the Standards to the secondary mathematics teachers in an urban school system. This study develops and tests a supervision model, based on peer supervision, for the implementation of teaching strategies recommended in the Standards. The findings of this study show that peer supervision can help school systems bring new teaching strategies, like cooperative learning and hands-on activities, into its Algebra I classrooms

Technology-enhanced Personalised Learning: Untangling the Evidence

Technology-enhanced personalised learning is not yet common in Germany, which is why we have tasked scientists with summarising the current status of international research on the matter. This study demonstrates the great potential of technology in implementing effective personalised learning. Nevertheless, it has not been assessed yet whether the practical implementation actually works: Even in countries such as the U.S., which lead the way in using techology in classroom settings, hardly any evaluation studies have been done to prove the effectiveness of technology-enhanced personalised learning. In the light of the above, the authors make recommendations for actions to be taken in Germany to make best use of the potential of technology in providing individual support and guidance to students

Traditional vs. Blended: the Effect of Instruction Methods on Sixth Grade Pre-Algebra Students’ Performance and Perceptions

This study examined sixth grade students’ math performance under two models of instruction: traditional and blended. Blended instruction requires face-to-face learning with an instructor, but allows students to do a portion of the work independently online. Traditional instruction takes place with an instructor present at all times. One area of interest in this study was the level of procedural knowledge acquired under the two different models of instruction. Results from three different assessments indicated no significant difference between the two groups of students. An additional area of interest was students’ preferences in teaching strategies in math and approaches to learning. Results indicated that 85% of the blended students and 90% of the traditional students agreed they wanted to take ownership of their learning. All together, over 70% of the students felt that having the ability to work with the teacher one-on-one or in a small group was important. In addition, 78% of students felt it was important to work at varying paces. In order to keep up with the demands of a workforce that requires critical thinking, creativity, and collaboration, students have to be at the center of their learning journey and play an active role throughout the process. This requires breaking away from the traditional model of education where teachers are the sole transmitter of information and learning is confined to 42-minute time blocks Monday through Friday. Varying the way in which students access and learn content has the potential to transform educational landscapes in terms of quality and cost. The results from this study add to the research base on blended learning at the elementary level. It also includes implications for key stakeholders to consider as they think more broadly about instruction delivery methods

Investigating Learning in an Intelligent Tutoring System through Randomized Controlled Experiments

In the United States, many students are doing poorly on new high-stakes standards-based tests that are required by the No Child Left Behind Act of 2002. Teachers are expected to cover more material to address all of the topics covered in standardized tests, and instructional time is more precious than ever. Educators want to know that the interventions that they are using in their classrooms are effective for students of varying abilities. Many educational technologies rely on tutored problem solving, which requires students to work through problems step-by-step while the system provides hints and feedback, to improve student learning. Intelligent tutoring researchers, education scientists and cognitive scientists are interested in knowing whether tutored problem solving is effective and for whom. Intelligent tutoring systems have the ability to adapt to individual students but need to know what types of feedback to present to individual students for the best and most efficient learning results. This dissertation presents an evaluation of the ASSISTment System, an intelligent tutoring system for the domain of middle school mathematics. In general, students were found to learn when engaging in tutored problem solving in the ASSISTment System. Students using the ASSISTment System also learned more when compared to paper-and-pencil problem-solving. This dissertation puts together a series of randomized controlled studies to build a comprehensive theory about when different types of tutoring feedback are more appropriate in an intelligent tutoring system. Data from these studies were used to analyze whether interactive tutored problem solving in an intelligent tutoring system is more effective than less interactive methods of allowing students to solve problems. This dissertation is novel in that it presents a theory that designers of intelligent tutoring systems could use to better adapt their software to the needs of students. One of the interesting results showed is that the effectiveness of tutored problem solving in an intelligent tutoring system is dependent on the math proficiency of the students. Students with low math proficiency learned more when they engaged in interactive tutoring sessions where they worked on one step at a time, and students with high math proficiency learned more when they were given the whole solution at once. More interactive methods of tutoring take more time versus less interactive methods. The data showed that it is worth the extra time it takes for students with low math proficiency. The main contribution of this dissertation is the development of a comprehensive theory of when educational technologies should use tutored problem solving to help students learn compared to other feedback mechanisms such as hints on demand, worked out solutions, worked examples and educational web pages

Inside the Flip: A Look at Teacher Motivations and Activities in Flipped Classrooms

In the educational setting of the 21st Century and with requirements imposed on schools through state and federal mandates such as the Every Student Succeeds Act, teachers are looking for ways bring additional higher level activities and collaboration into their classrooms. These requirements along with increased educational technologies in schools have many teachers exploring the flipped classroom model of instruction. In a flipped classroom, educators flip direct classroom instruction and traditional homework or practice. Students might watch a lecture video at home covering a concept at home and then apply the concept to problems in class with the aid of the teacher or engage in collaborative application with their classmates. After almost two decades of teachers implementing this model and research, little of that research exists at grade levels 6-12, the grade range in which the majority of flipped classroom instructors report that they teach. Additionally, much of the research conducted at those levels involves either student perceptions of the model or the impact course grades. This study looked inside the flipped classrooms of seven middle and high school teachers from a variety of subject areas including mathematics, science, Spanish, and social studies. Data for the study were collected through interviews, lesson plans and materials, as well as through a classroom observation of each teacher in order to gain a rounded picture of what educational activities were taking place inside of flipped classrooms. Furthermore, this study sought to look at the teachers’ motivations for using the model and to see if more activities were taking place in their classrooms

Blending Learning: The Evolution of Online and Face-to-Face Education from 20082015

In 2008, iNACOL produced a series of papers documenting promising practices identified throughout the field of K–12 online learning. Since then, we have witnessed a tremendous acceleration of transformative policy and practice driving personalized learning in the K–12 education space. State, district, school, and classroom leaders recognize that the ultimate potential for blended and online learning lies in the opportunity to transform the education system and enable higher levels of learning through competency-based approaches.iNACOL's core work adds significant value to the field by providing a powerful practitioner voice in policy advocacy, communications, and in the creation of resources and best practices to enable transformational change in K–12 education.We worked with leaders throughout the field to update these resources for a new generation of pioneers working towards the creation of student-centered learning environments.This refreshed series, Promising Practices in Blended and Online Learning, explores some of the approaches developed by practitioners and policymakers in response to key issues in K–12 education, including:Blended Learning: The Evolution of Online and Face-to-Face Education from 2008-2015;Using Blended and Online Learning for Credit Recovery and At-Risk Students;Oversight and Management of Blended and Online Programs: Ensuring Quality and Accountability; andFunding and Legislation for Blended and Online Education.Personalized learning environments provide the very best educational opportunities and personalized pathways for all students, with highly qualified teachers delivering world-class instruction using innovative digital resources and content. Through this series of white papers, we are pleased to share the promising practices in K–12 blended, online, and competency education transforming teaching and learning today

Improving mathematics in key stages two and three:evidence review

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document Improving Mathematics in Key Stages Two and Three (Education Endowment Foundation, 2017). There have been a number of recent narrative and systematic reviews of mathematics education examining how students learn and the implications for teaching (e.g., Anthony & Walshaw, 2009; Conway, 2005; Kilpatrick et al., 2001; Nunes et al., 2010). Although this review builds on these studies, this review has a different purpose and takes a different methodological approach to reviewing and synthesising the literature. The purpose of the review is to synthesise the best available international evidence regarding teaching mathematics to children between the ages of 9 and 14 and to address the question: what is the evidence regarding the effectiveness of different strategies for teaching mathematics? In addition to this broad research question, we were asked to address a set of more detailed topics developed by a group of teachers and related to aspects of pupil learning, pedagogy, the use of resources, the teaching of specific mathematical content, and pupil attitudes and motivation. Using these topics, we derived the 24 research questions that we address in this review. Our aim was to focus primarily on robust, causal evidence of impact, using experimental and quasi-experimental designs. However, there are a very large number of experimental studies relevant to this research question. Hence, rather than identifying and synthesising all these primary studies, we focused instead on working with existing meta-analyses and systematic reviews. This approach has the advantage that we can draw on the findings of a very extensive set of original studies that have already been screened for research quality and undergone some synthesis. Using a systematic literature search strategy, we identified 66 relevant meta-analyses, which synthesise the findings of more than 3000 original studies. However, whilst this corpus of literature is very extensive, there were nevertheless significant gaps. For example, the evidence concerning the teaching of specific mathematical content and topics was limited. In order to address gaps in the meta-analytic literature, we supplemented our main dataset with 22 systematic reviews identified through the same systematic search strategy

Using web pages to enhance communication and learning in the math classroom

The purpose of this document is to review the incorporation of technology into a math classroom. With technology becoming more a part of our growing society it is important for teachers and students to stay up with the times

Symbolic Manipulators Affect Mathematical Mindsets

Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely offer a convenient way to perform the computations students would have otherwise wanted to do by hand. This paper presents examples from the work of upper level physics majors where Mathematica plays an active role in focusing and sustaining their thought around calculation. These students still engage in powerful mathematical reasoning while they calculate but struggle because of the narrowed breadth of their thinking. Their reasoning is drawn into local attractors where they look to calculation schemes to resolve questions instead of, for example, mapping the mathematics to the physical system at hand. We model the influence of Mathematica as an integral part of the constant feedback that occurs in how students frame, and hence focus, their work