by Jesse Diachuk
Jesse Diachuk is an Albertan educator who has spent his nine-year teaching career in the Edmonton Catholic School District, the latter eight at Monsignor Fee Otterson Elementary/Junior High School. He teaches predominately junior high mathematics and is in the process of completing his Masters of Education in Educational Studies at the University of Alberta, where his graduate research has been focused on student perceptions of mathematics. His interest in mathematics education led to his involvement in the NORCAN Project, an international partnership between Canada and Norway centred on promoting equitable mathematics learning experiences for all students.
The purpose of this basic qualitative research was to explore junior high students’ perceptions of mathematics learning experiences. To facilitate this research, four eighth grade students from one school in an urban central Albertan school district were interviewed to unveil the challenges associated with learning mathematics, strategies and supports that increase chances of success, and the impact of assessment in the classroom. One-on-one interviews, ranging from 17-25 minutes in length were utilized. These interviews were open-ended, semi-structured, and conducted from a constructivist theoretical frame.
The data analysis process involved transcribing, analyzing, and interpreting qualitative data attained in the interviews. Raw data from interview transcripts was sorted into a number of open codes, whittled down via axial coding, and finally sorted into the emerging themes presented in this paper.
The research question guiding this inquiry was: What are the perceptions of four Albertan junior high students about their mathematics learning experiences? To support this key question, I utilized the following sub-questions: (a) What challenges exist for junior high mathematics students? (b) What learning techniques increase the likelihood of success in junior high mathematics? (c) How are students supported in their junior high mathematics learning experiences? (d) How do students describe assessment practices that improve mathematics’ learning experiences?
Upon completion of data collection and analysis, four main themes emerged from the central phenomenon of student perceptions of mathematics learning experiences: (a) barriers to student success in mathematics, (b) learning supports that increase likelihood of student success, (c) factors affecting student engagement in mathematics, and (d) impact of assessment on mathematics experiences.
After analyzing the participant data, it became evident that barriers to student success could be sorted into four sub-categories.
Barrier #1: The Content. All four participants indicated that curricular content served as an inhibitor to success in mathematics. Both Participant 3 (P3), who pointed out that success in previous grades impacts success in future mathematics, and Participant 4 (P4) referred to the sequential aspect of mathematics as being a potential barrier. As P4 stated, “If you don’t understand the first part, you’re not going to understand the rest of the unit.” Participant 2 (P2) lamented her inability to understand some curricular content, even with repeated explanations from the teacher, while Participant 1 (P1) and P3 pointed out the content-related barriers associated with problem solving question formats, which can undoubtedly be a struggle for struggling readers and English language learners. Taken together, the participants’ perceptions of content as a barrier illuminate the important role learning supports play in increasing the likelihood of student success in maths.
Barrier #2: The Teacher. Participants zeroed in on many teacher-centred barriers to student learning. Both P3 and P4 acknowledged having difficulty when the teacher provides either too little or simply a lack of explanation of content, with P3 elaborating that some teachers “don’t explain” and others “talk too fast.” P1, P2, and P3 reported that different teaching methods impact student understanding. P1 expressed confusion when the teacher is “teaching one way, but you actually know the other way” and queries, “If the teacher recommends one [method], but we get the other one, what should we do?”
This sentiment was echoed by P3, who belaboured the problem of learning one method at home, then being expected to use a different method at school. P2 admitted to struggling when one teacher “used to write all around the classroom” and “all over the board.” The first three participants also emphasized their frustration when teachers struggle to explain something properly. The participant views support the notion that, aligned with inquiry-based, student-centred mathematical pedagogy, teachers must embrace different styles and methods of both teaching and learning to better accommodate all learners.
P1 highlighted the issue of poorly established teacher-student relationships, disclosing that she was “not really comfortable” with her teacher, conceding, “Even if I have questions, I won’t ask.” P2 noted that access to the teacher can be a barrier to student success because “there are a lot of people in our class, so the teacher can’t focus on us individually” and that sometimes “everyone needs help with different things, so the teacher gets kind of confused.” Taken together, these accounts demonstrate how instrumental it is for teachers to build relationships with their students and make themselves readily available as learning supports.
Barrier #3: Peers. Participants named several barriers to mathematical success, both in collaborative work situations and project-based learning (PBL) settings. P3 remarked that working with people who are at different levels of understanding can “bump you down and make you feel different,” while P2 stated that, in group situations, “if it’s a concept I don’t get, it’s going to be tough for me.” She elaborated, “If I’m with people I’m uncomfortable with, I won’t share my ideas. I would just do everything that they say.” P1 raised issues related to differing ideas about the direction of projects, working in confined spaces, and forwarded that noise was a problem when everyone talked and planned at the same time in PBL environments.
Two of the four participants conveyed hesitance about depending on other people to complete their work effectively with P4 claiming, “If they do something wrong and I’ve done all my work, it’s all their fault.” P3 and P4 clarified that they both prefer independent work to PBL, citing differing personalities, levels, speeds, and quality of work, as well as issues connected to meeting outside of class time. Teachers can address these concerns by allowing students to choose with whom they work, by employing flexible project timelines, and by coaching students on group dynamics and productivity.
Barrier #4: The Classroom. Participants identified numerous classroom-based barriers to optimal mathematics learning. P3 and P4 cited noise and distractions as factors preventing them from focusing on their work. Lack of time to respond to teacher questions was seen as a barrier by P1, who asserted that it “doesn’t give people that many chances to answer questions,” and P2, who reported that it “brings me down [when] I’m trying to figure out the answer and they already said [it].” P3, who took three years of math in French before pivoting outright to English classes, and P2 discussed communication as a barrier to learning. P2 sat beside three people who routinely spoke a different language and struggled because she “focused less on math and more on trying to figure out what they were trying to say.”
All four participants discussed the downside of technology in the classroom, referring to its distractive nature as a barrier to student learning. Participants explained that students routinely “sneak onto YouTube” or other websites and “lie, saying their doing their work.” As summarized by P4, “It’s hard to keep a junior high school student focused on the task at hand.” It would behoove teachers to be aware of the distractive elements that serve as barriers to students and mitigate the effect of these detrimental classroom factors.
During data analysis, a myriad of factors were identified that support student learning in mathematics. Within this theme, five sub-categories emerged.
Support #1: The Teacher. All four participants spoke of the importance of having a strong teacher who is willing to help students, explains material effectively, and allows multiple methods to finding answers. Three of the four participants insisted on the importance of communicating directly and sharing work progress with the teacher. Teacher-student relationships also directly impact student success, and teachers seen as “encouraging,” “nice,” and “understanding” are deemed more approachable and supportive. P2 and P3 denoted the importance of teachers being accommodating to students’ individual needs and differentiating learning in their classrooms.
Support #2: Peers. One of the most discussed topics across all four interviews was that of peer support. All four students communicated regularly and believed strongly that peer support was essential to their success in the classroom. P1 stated that working with peers makes learning math “more fun and easy,” a sentiment echoed by each of the other three participants, who also explained that, in this manner, students can share methods and ideas.
All participants made it known that they enjoy supporting classmates as much as seeking help of their own. The collaborative nature of math classrooms, according to P4, leads to a situation where students are “all very supportive of each other and help each other learn what we need.” P3 specified that sometimes she would ask what the right answer is and work backwards to learn how to find it, while other times she would ask other students, “Which way are you doing it?”
In PBL situations, three of the four participants pointed out that group work can involve idea sharing and helps fill in knowledge gaps for each group member. Participants unanimously agreed that peer support was extremely important to finding success in math. Teachers should be ever cognizant of the benefits of peer support and should continually promote healthy collaboration in the classroom.
Support #3: Personal Strategies. Three of the four participants disclosed personal strategies that they employ to help them achieve success in mathematics. Each described practice and completing assigned work as important to achieving success in math. P1 and P3 both referred to their personal learning styles as visual-spatial. P1 stated, “If I do hands-on stuff, I understand it better.” P3 seconded this sentiment and continued, “I have to visually see the pictures.” P1 talked of how supportive it can be to her learning to explore different methods before selecting the one that works best for her.
Support #4: External Supports. Both P1 and P2 disclosed that they spent some time with a tutor outside school, which helped support their mathematical understanding, while P3 noted regular time working with parents as helpful, expressing that “she [her mom] can explain it in a smaller way.” Additionally, P3 spoke of private classes she attended in prior years to augment her learning.
Support #5: Technology. All participants confirmed that technology was present in their classrooms and that, despite the aforementioned barriers it can present, there are ways technology can support student learning in mathematics. P1 and P2 pointed to the academic benefit of YouTube, because many mathematics help videos are available to help explain concepts when other support is not available. P1 and P4 explained that websites such as Mathletics and MathAntics are strong learning supports, both for extra practice and video tutorials. P2 offered that her math class uses Google Classroom and that the teacher posts notes and support materials for the students. When it comes time to work collaboratively, P3 said computers could be helpful “if we’re working on a project.” All participants indicated that it would be helpful if teachers could figure out a way to ensure students are responsible when using technology, but did not seem confident it would happen.
Participants were eager to detail the factors that affected student engagement in mathematics learning. Due to the nature of the responses, I arranged this emerging theme into two sections: (a) engagement and (b) disengagement.
Student Engagement. Participants mentioned an array of factors that increased student engagement in mathematics. Pl explained that her teacher tells students “there are no right and wrong answers” and noted that this process-based approach makes it “nice to participate.” All four participants discussed the fact that mathematical content can be fun and engaging. P1 and P2 both enjoy “learning new things,” and P2 spoke of the sequential aspect of math, claiming that students get to “build on what [they] learned about last year.” P4 indicated that he “enjoys the challenge and the subject matter.”
An interesting revelation by P3 is that she won’t raise her hand, but shows engagement to her teacher by “mouthing the answer to herself instead of [saying] it out loud.” Another indicator of student engagement, suggested by both P1 and P2, was attention-seeking behavior such as engaging in class talks and going in front of the class to explain concepts to peers. P2 explained that doing this “shows the teacher that I care.” Three of the four participants stated that students engage in and are motivated by math because of success experienced. P1 exclaimed, “When people get it, they’re really noisy because they’re confident.” Based on participant perceptions, teachers would be wise to facilitate student exploration of curricular content, provide opportunities for meaningful class discussion, and celebrate student learning breakthroughs and successes.
Student Disengagement. Three participants cited the mood in the classroom as contributing to their disengagement from math. P1 clarified that, “if it’s too quiet, it gives you a vibe that no one gets it,” which “brings you down.” For all four participants, content emerged as a source of disengagement for a range of reasons. P4 stated that it was sometimes “too easy” and “boring,” while P1 and P2 claimed to disengage when faced with an utter lack of understanding. For P1, P2, and P3, feelings associated with math anxiety were also an impetus for disengagement. All three conveyed a sense of fear associated with providing wrong answers in front of other people. Two of three participants added that they disengaged when people got answers too fast around them and chose not to be supportive. Classroom distractions served as a source of disengagement for all four participants. P4, who claimed to have a high success rate in mathematics, asserted that “it’s very hard for [him] to concentrate” when classroom pacing is too slow. He stated, “I usually end up talking because I get too bored.” It is essential that teachers become attuned to the factors contributing to disengagement and work to ensure that classroom practices afford all students the unimpeded opportunity to learn.
Participants were asked what kinds of assessment practices enhance their mathematics learning and help them to experience success in the mathematics classroom. P1 and P4 both expressed the importance of teachers providing review packages for students. The first three participants claimed to have no aversion to testing, but felt somewhat apprehensive about concepts that were not well understood. P3 suggested that she preferred assignments and bookwork to projects and exams, stating that she “prefers not to work with other people” and fears “not understanding on a test” because one misunderstood concept can “hurt my whole...test.” P4 said he favoured test-writing to other assessments because he wants to “just get down to the material rather than spending forever on a whole bunch of tiny projects.” P1 suggested that, with regard to group work, teachers should consider “marking just one person, not the whole group” because, “if the group does badly, you get the mark, too.” Participants did not seem overly concerned with the type of assessments they were provided by a teacher, instead choosing to focus more on the ways they could support themselves in day-to-day mathematics learning to prepare for those assessments, a notion that was reflected by the significantly lower number of codes in this theme.
As evidenced by these findings, student perspectives are a valuable source of information for informing teacher practices and should be central in conversations of pedagogy. Based on my research findings, I propose the following six suggestions for teacher action:
Suggestion One: Teachers should be aware of content, teacher, peer, and classroom related barriers that prevent students from reaching their full learning potential.
Suggestion Two: Teachers should maximize the availability of learning supports in their classrooms, so that students are best equipped to overcome barriers to learning.
Suggestion Three: Teachers should build healthy, supportive relationships with students in order to nurture the development of trust and care, which serve as the foundation of optimal learning environments.
Suggestion Four: Teachers should encourage regular, meaningful collaboration between students, including project-based learning, and promote the benefits of peer support.
Suggestion Five: Teachers should be aware of classroom dynamics, including the notion of productive noise, helpful and harmful student interactions, and the positive and negative impact of technology, to ensure students are placed in positions that will enhance their chances of success.
Suggestion Six: Teachers should adopt a process, rather than product-based approach to mathematics that celebrates mistakes as part of the learning process and embraces the idea of productive struggle. Using a process-centred approach will help reduce the effects of math anxiety and limit likelihood of student disengagement.
This paper reviewed four themes that emerged surrounding the central phenomenon of students’ perceptions of mathematics learning experiences: (a) barriers to student success in mathematics, (b) learning supports that increase likelihood of student success, (c) factors affecting student engagement in mathematics, and (d) the impact of assessment on mathematics experiences. Findings suggest that students are attuned to the intricacies of their mathematics’ learning experiences. As such, it is evident that student voice warrants regular consideration when discussing pedagogical advances in and beyond the mathematics classroom. Although they seem to be less inclined to weigh in on assessment practices, students are acutely aware of barriers preventing them from achieving success, well versed in seeking ways to support and augment their learning, and cognizant of the factors affecting their engagement in mathematics.
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