Improving Math Learners’ Conceptual Understanding with Technology
Introduction
As educators, we have become increasingly aware of the trend of technology use in the classroom. Due to recent current events, like the COVID-19 pandemic, we have now entered into an age in which a lack of technology makes it challenging, if not impossible, to successfully teach. We must aim to make conscious choices about technology in education. “When schools cram computers into traditional classrooms, at best they sustain or only slightly improve the way they already teach and run the schools” (Horn & Staker, 2018, p. 79). We must ask: How should we improve our teaching practices and implement technology use to allow for the best student learning outcomes?
Blended learning is a great way to integrate technology into the classroom and allow students to have access to learning that was nonexistent without our current technology (Horn & Staker, 2018). Online learning is one of the “fastest scaling… of any innovation in K-12 education” (Patrick, 2011). We must improve our teachers’ ability to meet the needs of each individual student and allow students to develop the necessary skills to succeed and grow. While many people mistake online learning or learning with technology as blended learning, we must specify requirements for learning to be truly “blended”. It is important to note that blended learning requires student learning to occur “at least in part in a supervised brick-and-mortar location away from home” and has a minimal requirement of student control, whether it is in regard to timing, placement, the path, or the pace in which students learn (Horn & Staker, 2018, p. 34-35).
To be successful with blended learning, we must start by providing student choice in learning with technology, modifying our school culture, and cultivating an effective professional development program. Recently, many schools have turned to the idea of online learning, and some schools have even shown great success educating with a blended-learning model (Horn & Staker, 2018, p.80). Such successes of the blended learning opportunity include improving the crux of mathematical thinking: students’ conceptual understanding (Setyaningrum & Jurnal Riset Pendidikan Matematika, 2018).
As a private Catholic school, St. Monica has been blessed with great resources. However, many special programs that are present in public schools are still not available to our students or teachers. One area in particular that is challenged by funding and staffing issues is their mathematics department. There are only two teachers to teach the 6th, 7th, and 8th grade mathematics course, in addition to teaching the honors version of each of the gradelevel’s math courses. Implementing a blended learning environment will allow nonconsumption opportunities in which students would not otherwise receive access.
If a school desires to improve student growth or give students access to opportunities or various courses they previously could not offer, blended learning is an appropriate remedy. Additionally, many schools will find that their finances can improve (Horn & Staker, 2018, p. 99). With students working at their own pace, students can also have the opportunity to receive personalized support for their different needs, even if they have learning disabilities or are English Language Learners. The format of blended learning also allows for students to revisit lessons as needed and easily access reminders of mathematical connections to models and various representations of mathematics concepts.
Mathematics Educators and School Culture
Creating Institutional Change
Horn & Staker (2015) explain how reshaping culture starts with one task at a time. It is never too late to improve processes and school priorities. Particularly in mathematics, schools have been feeling pressure to improve programs and try out new, innovative methods. We need teachers to implement new teaching practices and there are several ways to create real institutional change.
To improve teaching practices, we must carefully give leadership opportunities to teachers, create challenging yet manageable activities for students, support teachers in keeping up with the initiatives, and allow teachers to help find new solutions (Arnett et al., 2018). It is important that we do not make the innovation appear to be reinventing or transforming teaching, but rather improving practices (Horn & Staker, 2018). The way we have teachers view the innovation is just as valuable as how we move forward with the plan.
We need to create an autonomous team that is able to plan, research, and develop ways for the blended learning program to be successful. It is unfortunate, but according to research by Horn & Staker (2018):
reluctance to use autonomous teams is largely to blame for how hard it is to find schools that have converted traditional classrooms into flexible, student-centered learning studios in which the students genuinely control the pace of their learning. (p. 129)
Making the change to blended learning requires the leaders to be intentional with taking risks. In order to have success, we must be strategic regarding our organization before blended learning begins in the classroom.
Success is catalyzed by hardworking, focused, and dedicated leaders in schools and is essential to successful technology use and buy-in for our innovation plan (Brooks, et al., 2015). Thankfully, much change has already occurred over the past year and usage of a Learning Management System (LMS) has been implemented across the school. It is extremely helpful how teachers are already aware of Google Classroom basics. Research has shown that students are preferring courses with an online learning environment option (Brooks, et al., 2015). With blended learning, students will be able to participate in student-paced lessons through online learning. Not only do students want to use technology, but using technology with blended learning models also allows teachers to improve their practices and provide more focused support to each individual student. Our students want to use technology. Not only do they want to use technology, but using technology with blended learning models allows teachers to improve their practices and provide more focused support to each individual student.
Growth Mindset Benefits
For teachers to feel comfortable trying new things, we need to address the mindset of the culture at school. Developing a growth mindset can be done by teaching students about neuroplasticity and the way the brain develops (Robinson, 2017). Speaking kindly to ourselves deeply affects the way we feel about what we are doing in the classroom. It is valuable to ensure we are practicing positive self-talk and paying attention to the language used while communicating the importance of the process of learning rather than only correct answers (Robinson, 2017).
In both teaching practices and student learning, it is important to use and display various types of data so that teachers and students can reflect and set growth-oriented goals (Robinson, 2017). Developing a growth mindset in the classroom, particularly in the mathematics classroom, is essential for empowering teachers and students of mathematics.
Teacher Action: Professional Development and Planning
Effectively Creating Blended Learning Environments
We do not want to fall victim to developing an affinity for eye-catching and trendy technology. In contrast, we need to approach technology with the knowledge that purchasing computers has proven to show little change regarding how teachers deliver instruction and student learning, as it only raises costs and takes resources from other priorities at the school (Horn & Staker, 2018, p. 96 ).
In order for us to see a change, we must act. It is evident the purchases of Chromebooks and iPads have not resulted in a truly blended classroom. In fact, despite investing in expensive technology, the factory-style classroom is still present in schools today and many devices are used simply for substitution of paper. Assisting faculty in strategically incorporating pedagogically appropriate usage of technology in their teaching can support a culture of positive student interaction through engagement and an improved sense of connectedness (Brooks, et al., 2015).
Creating a Culture of Change
In order for the plan to come to fruition, teachers need to learn how to utilize blended learning and must be allowed to fail. “Teachers who are experimenting with bold new approaches to teaching and learning need to know up-front that it is okay if they have an initial dip in progress before they see improvement” (Arnett, et al., 2018). Developing a growth mindset is essential to any plan’s success. In order to provide teachers with the professional development necessary for implementing blended learning in the classroom, we must determine what is good quality professional development.
It is important to note how teachings provided during professional development should be done in ways that are similar to good teaching practices for students. Desmione (2011) explains how professional development needs to be organized by content area and there must be opportunities for active learning. Providing coherence during professional development is necessary, and so is providing a minimal twenty hours of professional development every semester (Desmione, 2011). Noting a recommended number of hours emphasizes how both teachers and students should be learning throughout each and every semester.
Professional development opportunities should exist to target entire grade levels, specific subject areas, and entire schools (Desmione, 2011). Therefore, it is valuable to create professional development sessions that support those specific audiences. Although teachers constantly utilize good teaching practices during lessons for students, good teaching practices are sometimes overlooked when people create professional development. Just like students, teachers all have different prior knowledge and various abilities and skills. Professional development instructors must keep this in mind while planning professional development lessons. To determine the effectiveness of professional development it is important to use observations, interviews, and surveys as measures (Desmione, 2011).
A valuable second purpose in providing professional development is to support teachers in feeling confident in the amount of support they will receive (Arnett, et al., 2018). In order to prevent stress or even anxiety, it is necessary to provide additional time for teachers to work together collaboratively to plan with colleagues (Arnett, et al., 2018). This can be done by allowing teachers to work with PLCs and giving teachers time in their schedules to plan.
Student Choice in Mathematics with Conceptual Understanding
Benefits of Choice in Learning
The U.S. Department of Education describes how research shows it is particularly effective when students individually pursue online learning that requires them to both self-monitor their understanding and reflect on learning (2010). We have to start by ensuring student learning is improved by providing student choice and supporting students in their development as self-paced and independent learners. Focusing on student choice will allow students to learn how to be lifelong learners. Blended learning allows the opportunity for students to learn in an individualized fashion (Stein & Graham, 2020). If one were to compare face-to-face learning, with learning done entirely online, blended learning would prove more successful than either (Stein & Graham, 2020). In fact, the preference students have for online work conveniently supports blended learning (Brooks, et al., 2015).
Conceptual Understanding: A Necessity for Mathematics Education
It has been argued that since blended learning allows students to move at their own pace through a lesson, teachers are no longer able to provide the necessary support to students to promote conceptual mathematics understanding. It has also been argued that instead, blended learning provides an education that can only embody a surface-level understanding in mathematics. One can define conceptual understanding of mathematics as developing the knowledge which requires a deep and thorough understanding of foundational concepts and underlying concepts which allow the concepts to be solved by algorithms (Setyaningrum & Jurnal Riset Pendidikan Matematika, 2018).
The opportunities for student choice in the enriched virtual blended learning format actually allow for the improvement of conceptual mathematics understandings (Setyaningrum & Jurnal Riset Pendidikan Matematika, 2018). A study that was conducted with 127 grade 8 students in Indonesia determined that “blended learning is better than conventional teaching methods in terms of improving students’ conceptual understanding in mathematics lessons” (Setyaningrum & Jurnal Riset Pendidikan Matematika, 2018). With features provided in an online Learning Management Systems (LMS), students can easily go back and rewatch a video explaining how the algorithm connects to the concept they are learning. In the classroom without technology, a teacher would have to independently explain this each time to a student. Unfortunately, it is highly improbable teachers would have the time to stop the whole group lesson and reteach, but in a blended learning environment this would be feasible.
Benefits of Blended Learning Immediate Feedback
In fact, the immediate feedback that can be provided through the blended learning environment is paramount in promoting conceptual understanding (Brosvic, Epstein, Cook, & Dihoff, 2005). When one spends time thinking about it, it makes perfect sense. “Students who receive immediate feedback perform better than those who had delayed feedback or those who did not receive any feedback (Brosvic, Epstein, Cook, & Dihoff, 2005). When students are on one-to-one devices, they are able to independently receive feedback regarding their understanding.
Authentic Learning Opportunities in Mathematics
Combating a Lack of Independent Motivation
While working in the classroom with students, it appears that many are not self-motivated and choose to sneak to games on websites in the middle of lessons. While promoting the development of a growth mindset in the math classroom may combat some of this, this behavior can be deterred in a blended learning setting. If we began using blended learning, allowed students to set goals to move at their own pace, and provided authentic learning experiences, we would see how students can develop the motivation and skills necessary to work individually.
By teaching students how to self-monitor, eventually students will be able to have autonomy over their learning and successfully participate in inquiry-based and project-based learning activities. The goal of teaching with student choice is to prepare students for being comfortable with self-paced learning using the station rotation model and eventually the disruptive model of individual rotation.
Importance of Teacher’s Role as Facilitator
Both the station rotation model and the individual rotation model require the teacher to become a facilitator. Altering the role of a teacher from presenter to facilitator can be challenging and it is common for teachers, especially in mathematics, to struggle with doing so effectively. Moving into the role of facilitator can be done by focusing on providing choice, allowing student ownership, and amplifying student voice through learning opportunities that are authentic (Harapnuik, et al., 2018, p. 24).
Teachers must begin releasing control. Researchers “[have] learned that authentic learning opportunities can all too easily become limited thematic projects that lose their effectiveness if you don’t give the learner the freedom to choose to do something that is authentic, to take full ownership, and use their voice” (Harapunik, et al., 2018, p. 11 ). If we do not become more comfortable with providing choice, students will continue to be disengaged with their learning. Providing student choice requires intentionality. Students need teachers to intentionally grow and challenge themselves so that they may be successful.
How to Be a Facilitator
Moving into the role of facilitator can be done by focusing on providing choice, allowing student ownership, and amplifying student voice through learning opportunities that are authentic (Harapnuik, et al., 2018, p. 24). Recently, Peter Liljedahl’s research has done an excellent job describing how to provide powerful authentic learning environments which promote student thinking due to teachers acting as facilitators (2020). The method suggests for the teacher to shift their role entirely to facilitator and provides a framework for doing so. Within the station rotation model, these activities could provide further conceptual understanding support.
If the blended learning model selected allowed for live, collaborative lessons either in person or online, Liljedahl’s methodology would provide excellent opportunities to allow teachers to be facilitators and students to take the initiative to think, collaborate, and solve the problems. With Liljedahl’s methodology, when students begin a topic they are assigned random groups of three to work in and are provided with engaging problems to solve on a vertical non-permanent surface (like hanging whiteboards) with one marker (2020). There were no peer-reviewed research articles posted regarding supporting middle-schooler’s conceptual understandings through specific practices within the blended learning models. In performing action research with use of the station rotation model, we can see if mathematical conceptual understanding is further supported by blended learning through Liljedahl’s methodologies.
Basis for Action Research
Setbacks of Blended Learning in the Middle School Research
There is little research that was found regarding middle school students specifically improving conceptual understanding in math through blended learning. It was indicated in one study that the middle school age-group particularly struggled with internet connection, challenges in comprehending learning materials or content, and challenges in managing their ability to focus and concentrate on materials (Setyaningrum & Jurnal Riset Pendidikan Matematika, 2018). Further research is necessary to determine how to specifically support focus and concentration in middle school students during blended learning.
Need for Research Regarding Facilitating Mathematics Learning
While research shows the importance of shifting the role of the teacher to facilitator in the mathematics classroom to promote students’ conceptual understanding, there is a lack of research specifically regarding how to do so with mathematics in the blended learning environment. Research has yet to answer the question: If a student is engaging with mathematical concepts while in a blended learning environment, how does a teacher act as a facilitator to provide effective collaborative activities that promote creativity, student choice and student voice so that students take ownership over their learning?
All of the research that was found had students utilizing blended learning to learn the same content as everyone else. The research does not include any independent, self-paced lessons or lessons in other blended learning environments. Without the possibility of a self-paced course, blended learning will never be truly “innovative”. Without ensuring students are learning how to think and have a conceptual mathematics understanding they can make connections to, will it be worth it?
Conclusion
As far as device-requirement goes, many schools are prepared for all the future holds. In an Educause Center for Analysis and Research study, they discovered that tablets are declining in popularity, importance, and utility because the functionality occurs in laptops and smartphones (2017). Thankfully, with the recent acquisition of Chromebooks we are well prepared with student access to technology for years to come. Research shows how “almost anything you can do to a student can contribute to their achievement, but the key is to do what is most effective” (Harapunuik, et al., 2018, p. 13). The 2017 research also found evidence to conclude that blended learning can be superior to both entirely face-to-face and fully online instructional methods (Brooks & Pomerantz, 2017). Not only can it prove useful across content areas, but particularly in students’ conceptual understandings of mathematics.
In order to be proactive rather than reactive in the future, beginning the use of blended learning in the classroom will prepare students to become independent and lifelong learners. COVID-19 has shown it is possible for a global pandemic to disrupt learning. If we use the disruptive innovation of blended learning, students will need support in developing the values and character-traits necessary for our students to become self-motivated and life-long learners that can withstand the struggles life may throw at us.
We cannot begin preparing our students for the future unless we step back and develop pedagogy focused on current research-based practices. We need to find specific methods that allow mathematics teachers to support conceptual understanding by changing their role to that of a facilitator for use during the station rotation model. Not only do students deserve the opportunity to become independent learners; they also deserve the opportunity to grow as mathematicians.
References
Arnett, T., Moesta, B., & Horn, M. (2018). The Teacher’s Quest for Progress: How school leaders can motivate instructional innovation. Christensen Institute. https://www.christenseninstitute.org/wp-content/uploads/2018/08/JTBD.pdf
Brooks, C., Dahlstrom, E., Grajek, S., & Reeves, J. ECAR Study of Undergraduate Students and Information Technology, 2015. EDUCAUSE Center for Analysis and Research. https://library.educause.edu/-/media/files/library/2015/8/ers1510ss.pdf?la=en
Brooks, D. Christopher, and Jeffrey Pomerantz. ECAR Study of Undergraduate Students and Information Technology, 2017. Research report. Louisville, CO: ECAR, October 2017. https://library.educause.edu/~/media/files/library/2017/10/studentitstudy2017.pdf
Brosvic, G., Epstein, M., Cook, M., & Dihoff, R. (2005). Efficacy of error for the correction of initially incorrect assumptions and of feedback for the affirmation of correct responding: Learning in the classroom. The Psychological Record, 55, 401-418.
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Harapnuik, D., Thibodeaux, T., Cummings, C. (2018). Choice, Ownership, and Voice through Authentic Learning. Creative Commons License.
Horn, M. & Staker, H. (2015). Blended: Using disruptive innovation to improve schools. Jossey-Bass.
Lawless, K., & Pellegrino, J. (2007). Professional Development in Integrating Technology into Teaching and Learning: Knowns, Unknowns, and Ways to Pursue Better Questions and Answers. Review of Educational Research, 77(4), 575-614. Retrieved October 23, 2020, from http://www.jstor.org/stable/4624911
Liljedahl, P. (2021). Building Thinking Classrooms in mathematics: 14 teaching practices for enhancing learning. Corwin.
Patrick, S. (2011). New Learning Models: The Evolution of Online Learning into Innovative K–12 Blended Programs. Educational Technology, 51(6), 19-26. Retrieved October 23, 2020, from http://www.jstor.org/stable/44429967
Robinson, C. (2017). Growth mindset in the classroom. Science Scope, 41(2), 18-21. Retrieved October 22, 2020, from http://www.jstor.org/stable/26387192
Stein, J., & Graham, C. R. (2020). Essentials for Blended Learning, 2nd Edition: A Standards-Based Guide (Essentials of Online Learning) (2nd ed.). Routledge.
U.S. Department of Education, Office of Planning, Evaluation, and Policy Development, Evaluation of evidence-based practices in online learning: A meta-analysis and review of online learning studies. (2010). Retrieved October 20, 2020 from https://www2.ed.gov/rschstat/eval/tech/evidence-based-practices/finalreport.pdf
Wahyu Setyaningrum, & Jurnal Riset Pendidikan Matematika. (2018). Blended Learning: Does it help students in understanding mathematical concepts? Jurnal Riset Pendidikan Matematika. https://doi-org.libproxy.lamar.edu/10.21831/jrpm.v5i2.21428
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