This section describes the findings from my research study. It is divided into three parts, beginning with a chronological retelling of how I implemented the stations. Part II is a description of what the stations looked like in my classroom, and Part III includes a discussion of the major themes that presented themselves in my work.
Part I: Chronology and Description of Stations
When I think back to a little over a year ago and my first attempt at setting up stations in my classroom, I often cringe as I remember how difficult it was. It is important to point out that the challenges I faced had little to do with philosophy. I had chosen to implement stations then for the same reasons I wanted to do so again this year: I believed that they were an effective way to differentiate instruction. In other words, I thought that stations sounded like a manageable way to address the wide range of interests and abilities found in my class and give my students the different kinds of experiences they needed to develop as mathematicians. The key word here is manageable. That is where the system broke down, and where I needed to make changes if I were going to be able to sustain the practice long enough to conduct a research study this year.
After introducing last year’s students to each of the seven stations described in my Introduction (Teacher Town, Center City, Media Mall, Project Place, Quiz Corner, Practice Plaza, and Problem Park), I worked on the final touches of the organizational system that was going to help me keep track of everything. First, we had the Stations Summary, a simple spreadsheet printed with the students’ names onto which I would write the date and the stations each student visited. We also had the Stations Board, an extra-large magnetic pocket chart affixed to my white board that held index cards with the station names and student names on them. Its purpose was to inform the students of what station they would be going to that day. Then there was the Daily Memo, a piece of paper fashioned to look like a clipboard onto which I would write student names, materials needed, and the day’s assignment for each student. The Daily Memos were color coded to match the magnetic pockets and tubs holding each station’s exit cards and station materials, respectively. Finally, we had the exit cards themselves, also color coded to match the station. The color coding was done to ensure that the students could easily find all of their materials, but admittedly it had just as much to do with my desire to make the stations look nice, too.
Sounds good, right? Like a well-thought out, “practically runs itself!” kind of classroom structure? In reality, nothing could be further from the truth. In my quest to be ultra-organized, I had also ended up with a system that was ultra-dependent on me to make it work. I updated the Stations Summary. I chose every station the students would visit, every time. I wrote the Daily Memos detailing what each of the 40 kids should do that day. I moved the index cards on the Stations Board to show the kids where to go. I made the color coded copies. After just a few rounds of this, I was exhausted, and I quickly began to dread stations days. It took me hours to do all of these tasks, and the worst part was that despite all of this planning, something always went wrong anyway (e.g. we ran out of exit cards, a website didn’t work, the tasks were too easy or too hard, kids were absent, materials went missing, etc.). I had spent so much time getting the students excited about the stations that I felt I couldn’t just abandon the idea, nor did I want to let all of my hard work go to waste. I also was hesitant to completely start from scratch with a new organizational system since I had already trained the kids in how to use this one. In addition, I wasn’t exactly sure how to make it better. Caught between a rock and a hard place, I resigned myself to just continuing what I was already doing and making small adjustments along the way. By the end of the school year, I couldn’t wait to shelve the whole thing until I could figure out what to do with it next year.
For better or for worse, it has been part of my nature as an educator to abandon things that haven’t worked well in the classroom and to quickly move on. This can be a good thing when a lesson is tanking and I can turn it into something better on the spot. On the other hand, it’s not such a good thing when I move on without taking the time to reflect on what went wrong and to learn from my mistakes. Considering the somewhat disastrous experience I’d had with my first attempt at stations, I wanted nothing more than to walk away from the whole thing and file stations under “never again” in my teacher toolbox. However, just as the mess was unfolding, I was in the process of becoming more and more committed to using stations as the focal point of my action research. As we approached the summer vacation, my choices became clear: I could either choose a new action research question and forgo most or all of the research work I’d done up until that point, or I could bite the bullet and give stations another try the next year. After much thought, I decided I wanted another chance to make the stations work in my classroom, and after developing a clear understanding of what I didn’t want to have happen in the next go-around, I did just that.
…and moving forward
Armed with the knowledge gained from a challenging semester-long trial of learning stations, an action research question, and the promise of a fresh start, one might think I was ready to just jump right into using stations this year. Wrong! Making the necessary adjustments to my existing system proved to be as great of an obstacle as the stations’ initial set up. I knew I needed to change my stations, but I wasn’t sure what to change or how to change them, and this ultimately led to inaction. The first few weeks of the new school year flew by with no stations. Eventually, I knew I had to do something and fast, or else I’d end up with no research data for my project. Enter Halloween.
Yes, it wasn’t until the end of October that I began my first attempt at stations during the new school year. In reality, it was more like "Stations Lite" because it certainly did not reflect what I thought my stations would look like on a regular basis. These stations were an assortment of activities focused on different math concepts, and were tied together with a holiday theme. They were not a series of activities on a single math topic or concept as I envisioned my stations to be. Also, the students rotated through all of the stations in an hour, with no establishment of routines and expectations ahead of time. It was truly just a "let's give it a whirl" kind of thing, which fortunately allowed me to investigate some of the management issues I’d been concerned about (e.g. traffic flow, exit cards, groupings, materials management, engagement, kids doing different tasks at the same time, etc.). The stations included Jack-o-Lantern Combinations, which involved finding out how many unique pumpkin faces could be made from a variety of different mouths, noses, and sets of eyes. Then there was an Estimation Station where students guessed the amount of seeds inside of a pumpkin. Another station was Pumpkin Belts, in which the students had to estimate and cut a piece of string that would fit perfectly around the pumpkin's midsection. Finally, we had Candy Corn Probability. At this station, the students reached into a bag fifteen times that contained a predetermined amount of three different types of candy corn. As they drew each piece of candy from the bag, they recorded the frequency of each type of candy corn, predicted how many of each type was in the bag, and then looked in the bag to compare their predictions to what was actually inside.
At the end of the session I had each student fill out an exit card about their experience. Overall, most students seemed to enjoy the stations. In response to the question, “What was your overall enjoyment level of today's stations?” one student chose "I did not enjoy any of them," (Amy)12 students chose "I enjoyed some of them,"and 20 students chose "I enjoyed all of them." I was discouraged that Amy didn't enjoy any of the stations, though I was not entirely surprised. She was one of the top two math-phobic students I had this year. However, I also noted her response to another exit card question, "Do you think we should use math stations more often in class? Why or why not?" She wrote, "Yes, because they are more active than worksheets." At that point, my hope was that future successful experiences at the stations would turn things around for her. Katie, another student who was easily frustrated and often expressed negative feelings toward math, found success early on at the Pumpkin Belts station and remained excited throughout the rest of the session. This was reflected in her overwhelmingly positive responses to all of the exit card questions, more positive than I would have normally expected from her.
When asked the question, “Do you think we should use stations more often in class? Why or why not?” 24 out of 26 students agreed that they would like to do stations again, with the most frequently cited reason being that the stations were fun. The response that intrigued me the most, however, did not mention fun as a main reason to revisit stations. Sonia wrote: “I do [think we should use stations more often] because it gives you a choice of what you want to do, and more things to do when you are done.” Interestingly, Sonia had addressed ideas about student choice and differentiation in her answer, two areas that eventually became the crux of my action research project.
Beyond building the students’ interest in learning stations, I noticed other positive results from this trial period as well. One benefit was that the stations significantly reduced off-task behaviors. My top six behavior-management-issue students were active and engaged for almost the entire session. Four of them reported on their exit cards that they liked some of the stations, and two students said they liked all of them. Another nice outcome was that the students had a lot of choices that day (who to work with, where to work, what order to do the activities in) and the session still ran smoothly, which was a huge relief. Last year I micromanaged everything and it was exhausting and ineffective. This year I wanted to release a lot of the responsibility to the kids but I wasn’t sure if they would make appropriate choices. The outcomes from this preliminary stations experience helped decrease my anxiety in that area. Finally, despite the fact that the students had never done exit cards before, I was pleased at how much useful information I was able to glean from them, and how well they seemed to reflect they students' true feelings and experiences. This definitely reinforced my plans to use them as a data collection method for my action research.
Despite the relative success I’d had with my Halloween stations, I still wasn’t ready to make stations a permanent part of my instructional plans. The main reason was not at all ambiguous to me; I was still scared to try again after my lousy experience with stations from the previous year. Eventually though, I found the courage to try again, and as a result my perspectives on teaching have changed dramatically.
Finally jumping in
It wasn’t one particular thing that finally motivated me to start doing stations this year, but rather the culmination of many factors. Time was slipping away and I needed to start collecting data to analyze and reflect upon in my action research journal entries. I’d also had some thought-provoking conversations with other educators, including a math coach who’d said to me “If you’re waiting for things to be perfect, you’re going to be waiting for a long time.” Listening to some of my GSE classmates talk about their research also reminded me that you never really know how things are going to go until you try, and as one classmate so eloquently put it, “Missteps are part of the journey.” I kept all of these ideas in the back of mind when I finally decided I was ready to jump in.
The first order of business was to look at my previous station offerings and make any needed adjustments before designing the organizational system to accompany them. I decided to ditch the cutesy station names and the color coding, both of which had taken up considerable amounts of preparation time without contributing to the students’ learning. I also decided to scale down the number of stations from seven to six knowing that I could always add new ones later if needed. I took out the computer station to eliminate the possibilities of technical difficulties and off-task behavior, both problems I’d encountered with the computers the previous year. Next, I removed a station that focused exclusively on solving word problems, for two reasons. First, I knew we’d be doing a lot of problem-solving on our non-stations days, and second, matching the students up with appropriately challenging problems they could do independently had been extraordinarily difficult the year before. Teacher Town and Project Place had also been only mildly successful and were swapped out as well. That left me with six stations: Math Quiz Game Show, Math Art, Fact Practice, Math Games, File Folder Activities, and Math Magazine (descriptions of and discussions about each of these stations can be found in Part II of my Findings).
Once I knew what the stations were going to be, I was able to move forward with making adjustments to the organizational system that had nearly prevented me from ever attempting stations again. I devised a simple litmus test (a question, really) to help me determine whether I was on the right track with the changes I was making. The question was: could the stations run smoothly with minimal preparation and without me present? If the answer to both parts of the question was yes, I had achieved my goal, a complete turnaround from the mistakes of the previous year. If the answer to either part was no, there was still more tinkering to be done. I kept running though various scenarios in my mind and applying the test, and it wasn’t until I had really thought long and hard for several days about how to make the system better that I came up with a viable solution: student choice.
As mentioned above, the Halloween stations experience was a positive one, and the structure of those stations had included a great deal of student choice. I began to wonder if those same choice elements could be integrated into our regular math stations to help alleviate some of the management challenges I had encountered last year. After reading that “choice opportunities are also an easy and time-saving strategy for designing and facilitating multiple tasks in your classroom,” (Heacox, 2009, p. 71) I began to consider the types of choice I could offer and their potential outcomes. If I allowed the students to choose what stations they went to, I would no longer have to agonize over assigning 40 students to stations, determining exactly what each student would do there, and writing instructions for those tasks. If I let the students choose their own work spaces, I wouldn’t need to worry so much about managing the flow of student traffic, since they would naturally choose an area that was comfortable for them and appropriate to the task they selected. Giving students the opportunity to move between stations when they wanted to would significantly reduce their time spent in stations that were too easy, too difficult, or uninteresting to them. In theory, this would lead to greater engagement, more meaningful use of instructional time, and natural differentiation. The last choice element was the one I was most hesitant about: allowing students to choose whether to work alone or with a partner, and if they chose the latter, allowing them to choose with whom they worked. While I looked forward to no longer having to analyze the complex classroom social dynamics each week to form station groups like I had done the previous year, I had visions of goofing around and wasted time dancing in my head.
Ultimately, I decided to push these concerns away in favor of taking s risk. After all, I thought to myself, I could always make adjustments or add restrictions later on if needed. Despite any misgivings, my desire to reinvent the stations into something better than the first incarnation drove me to commit to implementing all of these choice elements at once to simply see what would happen. It definitely required a leap of faith to shift so much of the control to my students, but at that point it was a leap I was ready to make.
Part II: A Day in the Life
Before discussing my thematic findings, I believe it is important to provide a clearer picture of each station and what the whole endeavor really looked like in my classroom. The “Day in the Life” vignette written in italics below accurately describes some the people, places, and events I witnessed during stations time, though not all of these observations actually occurred on the same day. My commentary is interspersed throughout the vignette.
On stations days, we began by gathering as a whole group in the rug area up near the front of the room. The stations pocket chart was posted and contained the names of all six stations, but did not yet contain the names of the students. I started by asking a simple question: “Who is interested in going to Math Quiz Game Show today?” A flurry of hands shot into the air and the procedure known as “Status of the Class” officially began.
Math Quiz Game Show is a commercial product I purchased from Lakeshore Learning Store’s online site (www.lakeshorelearning.com). It’s a Jeopardy-style quiz game targeted toward grades four through six. It came with its own pocket chart, 200 question cards, 11 category cards, and extra cards printed with sayings like “Double Points” and “Risk Any Amount.” Last year when I bought the game, I sorted all of the cards by category and difficulty to custom-build five levels of the game (Game A is the easiest; Game E is the most difficult). Within each game, I also sorted the questions in each category from easiest to hardest to correspond with point values from 100 points to 250 points. I marked each question card with a colored sticker to help keep track of which game level the card belonged to and its point value. It was an enormous up-front time investment, but I believe the work paid off because the game has been very low-maintenance ever since. To update this station, all I needed to do was swap out the cards every once in awhile and we had a whole new game! For management purposes, I limited this station to four students, and because it was so popular, I often resorted to drawing names randomly to decide who got to go there each day. The students were allowed to choose how they played the game (in teams, with a rotating host, with or without points, with or without a time limit, etc.) so the game was a little different with each new group of students.
After “picking sticks” to decide who got to go to Math Quiz Game Show first, I removed the name cards for the rest of the students from the top row of the pocket chart and shuffled them. It was time to determine to which stations everyone else would be traveling. I drew a name randomly from the stack. “Matthew, where are you heading today?” He responded with enthusiasm, “Math Magazine!” and eyed the new issue I had just added to the cardboard magazine holder where the magazines were kept.
The materials for the Math Magazine station came from a year-long subscription to Scholastic’s DynaMath (www.scholastic.com), a monthly student magazine for grades three to six focused on problem-solving and real-world connections to mathematics. Each issue featured high-interest stories and pictures accompanied by word problems, puzzles, or multiple choice questions. To minimize cost and maximize student access to the materials, I purchased ten copies of each issue and slid the pages into plastic sheet protectors so the students could write on them with a dry-erase marker and erase their answers without damaging the pages. I also included copies of the answer key with each issue so the students could check their work on the spot.
As I continued to go through the name cards and check in with each student, I was not at all surprised to learn that both Mark and Andrew had selected Math Games for the day’s station work. The two boys were best friends and often chose to work together during stations time. I heard them whispering to each other about which game they would play; Andrew wanted to play Target, a multiplication game introduced several weeks prior, while Mark pushed for Wipeout, a newly-added fractions game. They decided to start with the latter.
The Math Games station encompassed a variety of activities, and its offerings grew throughout the year as new units of study were introduced. Most of the games were originally taught to all of the students as a whole-class lesson, and were then added to the station’s repertoire. Ideas for the games came from articles, books, and curriculum guides. At the midpoint of my study, there were three games offered at the Math Games station: Target (a partner game focused on multiplying with multiples of ten to get a total sum closest to the target number), Tic Tac Toe Product (a game similar to Connect Four focused on practicing basic multiplication tables and identifying factors), and Leftovers (a division game in which students divided a pile of colored tiles into groups and scored points based on the number of leftover tiles). As the second half of the year progressed, new games like Cover Up, Uncover, and Wipeout (all fractions games) were introduced and added to the selection at the Math Games station.
On that particular day, Fact Practice was one of the more popular station choices. I assumed that several of the students would continue playing the game they had invented, which involved “buzzing in” and being recognized by the “host” before giving the correct answer to a multiplication fact. This hunch was verified when Antonio ran up to grab the flashcards after his name was called. “Wait!” I cried. “It’s almost time to start, but not yet. Have a seat.” He smiled and sat back down, eagerly awaiting his opportunity to get started on the game.
Like Math Games, the Fact Practice station offered a variety of options. In this case, the activities were focused on helping the students develop recall of their basic multiplication facts. One option the students had was using a tool called a Wrap-Up (www.learningwrapups.com), which was a set of plastic “keys” with a string attached that allowed students to practice a specific multiplication fact family and self-check their answers. The students could also use pre-printed flashcards (like Antonio and his friends did for their quiz game), take paper-based quizzes with the option of timing themselves, or review a personal set of flashcards made by parent volunteers. The personal set of cards was made for each student using index cards and metal rings and contained only the multiplication facts that the student had personally identified as ones he or she had not yet mastered. For some kids, the set contained just a handful of cards, while other kids’ sets contained a few dozen cards or more.
As we completed our “Status of the Class” check-in, I noticed that File Folder Activities was empty and that two students (including Amy) had selected Math Art. The girls were immersed in a long-term project they had come up with on their own and had been visiting this station frequently. As I released the kids to their work, the pair picked up right where they left off without skipping a beat.
There are plenty of resources available to teachers who want to integrate portable learning centers into their math curriculum, and although I wasn’t planning to make these a focal point of the stations, I believed they would be a worthwhile option for kids who liked completing worksheets. I used books such as Take It to Your Seat Math Centers (www.evan-moor.com) as the primary sources for the File Folder Activities station. These books contained all of the directions, playing pieces, black line masters, recording sheets, game boards, etc. needed for the activities; all I needed to provide was the three-pronged paper folder to hold these items (I laminated the folders and playing pieces to make them more durable). Altogether I had over 20 different activities addressing multiple areas of mathematics typically taught in grades two through six, and about 10 of the folders were available to the students at any given time.
The Math Art station originated out of an assignment that integrated math, writing, and art and was based on a children’s book I’d read to the class. I was looking for a way to give a group of students extra time to finish the assignment, and thought to myself, “Why not design a station to address this need?” I believed that having a Math Art station would be the perfect way to give students additional class time to work on this and future unfinished assignments without holding back everyone else who was done and ready to move on. In terms of meeting this objective, Math Art actually worked quite well, but on the other hand, this station was empty most of the time because there was nothing specific for the students to “do” there. Eventually, a few creatively-minded students came up with the idea of designing their own book of illustrated math word problems, and this task became a relatively popular Math Art activity. Other student-generated ideas that came from this station included reading math-related books and creating math-related games.
I stood back to take in the scene that was unfolding before me. Students were settling into the day’s work all around the room. Some were at desks, others were on beanbags, and still others had taken up residence on our classroom couch. The room buzzed with noise, but for the most part it was “productive noise” emerging from the various tasks happening around the room. Out of the corner of my eye, I saw a six-sided die fly into the air, which led me to take a quick walk across the room to remind a few students about proper rolling procedures while playing their game.
While I’d love to be able to say that all classroom management issues disappeared during stations work, the reality is that not all of the students responded appropriately to such a large amount of freedom. There were a few who consistently needed reminders about behavior expectations (such as the proper way to roll dice) and a good deal of modeling to be able to use their time productively. I made sure to constantly circulate throughout the room to check in on progress and redirect as necessary.
After chatting with my “high-rollers,” I then moved on to a pair of students who were working on a Math Magazine page. “We’re confused about this page,” they said when I asked how things were going. I grabbed a small white board and a dry-erase marker and engaged them in an impromptu multiplication lesson that helped them successfully complete the problems on the page.
One of the many things I loved about this year’s stations arrangement was the frequency of “teachable moments” that occurred. In the scenario described above, I was able to address exactly what those students needed in real time and their motivation was built right into the moment. My ability to move throughout the room to different students paved the way for these moments to occur, and I consider them to be some of the best opportunities for meaningful differentiation I had all year long.
As I got up from the beanbag I’d been sitting on, the girls from Math Art ran over to me while excitedly waving around one of the word problems they’d been creating together. They asked me to review their work before they started coloring the illustrations.
A question that I often wrestled with when thinking about how my students worked in stations was, “How much math are they actually getting out of this experience?” When I reviewed the detailed drawings that accompanied the girls’ somewhat rudimentary word problem, and then thought about how much time they would likely spend coloring it, I cringed. A majority of the time they devoted to creating that math problem was probably not helping them become better mathematicians. On the other hand, they were so enthusiastic about their work. This situation and others like it reminded me of the fact that while learning content is a goal of instruction, for many educators (including myself), it is not the only goal of instruction. As I looked at Amy’s eyes all lit up with excitement and remembered how much she feared math class at the beginning of the year, suddenly the content itself became less important than allowing her to have this positive experience with math and to feel good about her work. I also knew that because I didn’t use stations every day, Amy and her classmates would have numerous other opportunities to interact with grade-level math content, and with that in mind I was able to embrace more of the academic and non-academic benefits stations had to offer.
With just five minutes left in our hour-long math block, I called for the students’ attention. “Time to clean-up!” I said over the din. “Please fill out your exit cards and station logs!” A flock of students rushed over to the magnetic pockets up front on the board to get the appropriate card for their station. Others took out their math folders and recorded the names of the stations they’d visited on their personal stations log. The flurry of activity seemed chaotic, but a closer look revealed that almost everyone was following the end-of-the day procedures rather efficiently.
It was important to me that the students be held accountable for the work they did during stations time, and exit cards were a teacher-and-student-friendly way to provide that accountability. The exit cards contained questions about progress, level of difficulty, enjoyment, and more depending on which station the card represented. The cards were not only tremendously useful as a source of data for my research, but also gave the students an opportunity to reflect on their learning and provide feedback. The station logs helped me look for patterns in the students’ choices and served as a reference during conversations about these choices. The combination of both the exit cards and the logs provided just the right amount of accountability and record-keeping to help me manage all that was going on without being overwhelmed by an enormous mountain of paper and information.
The materials were put away, the room was reset, and another round of stations had come to a close. As I scanned the room and prepared to dismiss the students to line up for their next class, Matthew raised his hand and I called on him. “Ms. Sam, can we do stations again soon?” he asked. Unlike last year, it was a request I looked forward to fulfilling. When I responded with a “yes,” Matthew’s grin was matched by one of my own.
Part II: Thematic Analysis
When I analyzed all of the data I had gathered throughout my action research study, four main themes emerged. The first theme is about student reactions to the different types of choice offered they encountered while working in math learning stations. The second theme is related to the actual activity choices they made during stations time. How stations impacted differentiation is the focus of theme three. The final theme examines the relationship between learning stations and mathematical dispositions. All four of these themes are discussed in detail in this section.
Theme 1: Students value choice and autonomy in mathematics learning stations
In January, a few weeks before the end of the first semester, I gave the students a mid-year survey to get their feedback on several areas related to their stations experience (to view the survey, see Appendix 4). One of these areas was student choice, the focus of my research question. I wanted to see what the students thought about the four different areas of choice they had during stations time: the space in which they worked, whether to work alone or in a partnership (and with whom to work), what station they went to, and when they got to move to a new station. The students gave each element of choice a rating of “Very Important,” “Somewhat Important,” or “Not Important” to them. They also wrote “Agree” or “Disagree” in response to statements about the choice elements.
When it came to choosing a work space, the students had a wide range of options. They could work at their own desk, someone else’s desk, on our classroom couch, on the carpet, with a “cozy item” (e.g. bean bag, pillow, etc.), laying down, standing, or sitting. On the survey, all of the students agreed with the statement “I like being able to choose my own work space,” although the degree to which this element of choice was important to them varied. Out of 35 students, nine said choosing their work space was “Very Important” to them, 23 said “Somewhat Important,” and three said it was “Not Important.” When compared to the other elements of choice discussed below, it is clear that making decisions about their physical learning environment was important to the students, but not as important as the elements more closely related to the station activities themselves.
Another element of choice the students were asked to evaluate was the degree to which being able to choose whether they worked alone or in a partnership (and with whom they worked) was important to them. Again, all of the students agreed that they liked having the choice, but compared to the first question about work space, this element of choice was of an overall higher priority to the students. Fifteen of the 34 students said that being able to choose their partners (or to work alone) was “Very Important” to them, about the same number of students (16) chose “Somewhat Important,” and only three students said that being able to make this choice was “Not Important” to them. Interestingly, two of the three students who selected “Not Important” were very shy and all three rarely initiated partnerships with other students; instead, they would typically wait to be asked by someone else or would choose to work alone. Since these three kids often did not take advantage of the opportunity to choose a partner during other academic activities, it made sense to me that this element of choice would be of lesser importance to them. Furthermore, I found it interesting that two of these three students had chosen “Not Important” on the work space question as well, which made me wonder if they generally preferred to not have to make these kinds of environmental decisions about their learning.
When it came to being able to choose which stations to go to, an overwhelming majority (25 out of 35 students) reported that this element of choice was “Very Important” to them, while another seven said “Somewhat Important,” and three chose “Not Important.” Of note is the fact that none of the three students who chose “Not Important” on this particular item were the same students who chose “Not Important” on the two previous questions. Two of the students who selected “Not Important” on this question often had a difficult time making choices in other academic areas (e.g. what books to read, what to write, what part of the homework to do first, etc.), and assigning a low importance to choosing their own stations seemed to be in keeping with this pattern.
The final choice element students were asked about on the survey was being able to choose to move to another station when they wanted to. When I used stations last year the students did not have this option. They were assigned to a station and were required to stay at that station for the entire block of time. This year, I had decided to lift this restriction and allow the students to move between stations as they pleased. I was surprised to see that not one student selected “Not Important” for this element. Their responses were split roughly equally between “Somewhat Important” (19 out of 35 responses) and “Very Important” (16 out of 35 students).
All of these results support the notion that most students value choice and enjoy taking control of their learning, although certain choices were more important to them than others. Based on this data, my students would have preferred to give up control over their physical work environment and social groupings than to give up control over their learning activities. This is a significant finding, as it suggests that the areas in which students are most often given choice (where and with whom to work) by their teachers are actually less important to them than the area in which students typically have the least amount of choice (what kind of work they do). Perhaps one way to increase motivation would be to turn this paradigm on its head and offer students more opportunities to make choices about the learning activities in which they participate. In fact, both Sousa (2008) and Heacox (2009) omit learning environment considerations from their respective discussions of student choice, suggesting an awareness of the relative unimportance of such choices compared to choices about content, process, and products.
Theme 2: Students prefer stations that offer variety, competition, and peer interaction
Something I discovered early on in my stations experiences from both last year and this year was that not all stations are created equal. Some stations were hits, some were duds, and many needed ongoing updates to maintain their appeal. On the same mid-year survey discussed above, the students were asked to evaluate their enjoyment of each of the six stations using a four-point scale. For each station, they could choose one of these four responses: “Don’t like it,” “Like it a little,” “Like it a lot,” or “It’s my favorite station.” The students were told to choose “It’s my favorite” for only one station. They were also instructed to cross out the names of any stations they had not visited. In this section, I divided the six stations into three groups based on their relative levels of enjoyment, examine the factors that contribute to the successfulness (or lack thereof) of a station, and discuss both the merits and challenges of each of the station offerings. Descriptions of each station can be found in Part II of my Findings.
The MVPs: Math Quiz Game Show and Math Games
Based on the survey results, Math Quiz Game Show was the most enjoyable station with 11 students naming it as their favorite station and another 10 students reporting that they “Like it a lot.” When asked in another survey question why Math Quiz Game Show was their favorite station, many students mentioned that it was fun. Some also hinted at the competitive and collaborative aspects of the game as seen in the quotes below:
“You’re asked questions and it’s fun to guess for the answer.” –James
“It’s fun because you can get math points.” –Chance
“I like math quiz game show because people can work together and it’s a great way to see me and other people as a learner.” –Sonia
The last student quoted, Sonia, also discussed her preference for this station when interviewed in person. The interview took place while she and her partner were at the Math Quiz Game Show station, and both students mentioned that not being able to go to this station all the time contributed to their overall enjoyment of it. For these and other students, it may have been that basic principles of supply-and-demand were at work here; limiting access to this station was increasing its desirability. In addition, the game offered variety in terms of content, structure, and peer interactions, which kept it fresh and exciting.
Although the Math Quiz Game Show station was popular, it presented some unique challenges. In terms of management, I never quite figured out a good way to deal logistically with a game not being finished within the allotted time, or the best course of action when players disagreed on issues related to the game format. In terms of learning outcomes, I worried about that fact that not all of the content on the cards was relevant to the students’ current level of understanding and appropriately challenging for all, and I was unsure about how to assess what the students are learning. Nevertheless, it seemed like there was more real math work than guessing going on and I liked the exposure the students were getting to other areas of math, not just the topics we were focusing on in class at the time.
The other top station pick according to the mid-year survey was Math Games. Like Math Quiz Game Show, 11 students chose Math Games as their favorite station, in addition to another eight students who said they “Like it a lot.” This was not a surprise considering that most students ranked math games as their most preferred math activity over centers, homework, projects, worksheets, and tests/quizzes on the beginning-of-the-year survey.
The “fun” factor of Math Games was once again the most frequently cited reason for this station’s popularity, but a number of students also offered additional reasons for why this station was their favorite. Two students mentioned the “variety of stuff to do” and ability to “choose what games you want to play,” while two others referred to how the Math Games station integrated fun and learning. A particularly social student remarked, “It’s fun to play games with your friends, especially math games.” For all of these students, the engagement level was high, and the games addressed something that was important to each of them, whether it was choice, a high-interest way to learn, or social interaction. From the teacher perspective, Math Games was a great way to offer repeated exposure to math concepts and a low-maintenance extension of what we had already been doing in class. Some of the games even generated a written record for me to review at a later time which was nice for assessment purposes. Overall, this felt like a station that could withstand the test of time and in practice it turned out to do just that.
The Middle of the Pack: Fact Practice and Math Magazine
As our stations were just beginning to get underway, I thought that Fact Practice would be among the least popular stations simply because practicing multiplication facts is inherently less engaging than, say, playing a math game. However, Fact Practice actually remained quite popular throughout the year and ended up being the second most frequently visited station overall. Many students chose to take out their personal flash card sets and quiz each other in partnerships, or flip through the cards on their own. Another group of students devised a way to use the pre-printed flash cards to play a quiz-show style game in which participants earned points for answering quickly and accurately. Still others were drawn to the novelty of the multiplication Wrap-Ups tool.
I was truly amazed by the innovation I witnessed at this station. The students were taking a task that could often be somewhat dry and using the flexibility of the stations and their own creativity to make it fun for themselves. It was also great to see some of the kids who really needed the basic fact practice choosing to visit this station. Some students seemed interested in coming to Fact Practice because the flash cards were “theirs” (the facts they had personally selected to work on) and as a result the practice time was more meaningful. Having pre-printed practice quizzes available also allowed students to set and work toward personal fluency goals and build confidence. Another plus of this station was that it could easily accommodate many different learning environments; the cards, quizzes, and Wrap-Ups could go anywhere, and many configurations of kids were possible. Overall, three students considered Fact Practice their favorite station, eight students said they liked it a lot, and an additional 13 students reported that they liked it a little. Two of the students who chose “It’s my favorite station” were students who frequently chose to practice their facts in a quiz show format, which mirrored the popularity of games found in some of the other stations.
The other station that experienced a moderate level of success in terms of student enjoyment was Math Magazine. Three students named this station as their favorite, and six selected the “Like it a lot” rating. At the time of the mid-year survey, just over one-third of the students (13 out of 34) said they hadn’t tried the Math Magazine station, a number almost identical to the number of students who didn’t like it or liked it a little (one student and 11 students, respectively). Despite these mixed results, Math Magazine attracted some devoted followers who looked forward to checking out what each new issue had to offer. The magazines offered a novel application of math and appealed to a wide variety of students, particularly the more advanced learners (Grace, one of my top math students, stated that Math Magazine was her favorite station because “it really makes you think”) and the kids who loved to read, possibly because it integrated something they enjoyed (reading), with something that was more challenging for them (math). The contextual applications of mathematics were highly engaging for many of the students, including Katie, who said that she liked this station because she was able to “look through a mag., read cool stories, and do doable math.” From a teacher standpoint, it was great that in addition to being easy to manage, the subscription was inexpensive and provided multiple issues that could be reused the following year. Having multiple copies of each issue also provided flexibility in student configuration, as it allowed students to work in partners and was also a nice option for kids who wanted to work alone.
The Bottom Tier: File Folder Activities and Math Art
Out of the six stations I implemented during my action research study, File Folder Activities and Math Art were the least popular. Each of these stations had only three students name it as their favorite station or as one they liked a lot. Thirteen students liked File Folder Activities only a little or not all, and three students felt the same way about Math Art. Perhaps the most noteworthy statistic, however, was that a whopping 28 out of 34 students had never tried the Math Art station, and 16 had never visited File Folder Activities. Why had so few students taken part in these stations? I believe the answer is revealed upon closer examination of their structure.
Although there were many potential benefits to the File Folder Activities station, including the ability to provide targeted practice on specific topics, a tangible record of student work available to me for review, and materials that were highly portable and reusable, in reality the File Folder Activities fell short of their potential. On our mid-year survey, one of the more advanced students wrote, “I don’t like folder activities because they are too easy for me and I just find them boring.” Another student wrote, “I don’t get folder activities because it doesn’t make sense to me,” alluding to a lack of clarity in the directions and uncertainty about what he was expected to do at that station. Upon closer inspection, I did find many of the centers to be somewhat simplistic and/or containing unclear directions, so both of these student comments seemed justified. In hindsight, I could have done more to make File Folder Activities a more meaningful part of our stations line-up. I could have re-written or explained the directions more clearly, explicitly taught the students how to use the centers, or offered activities that appealed to a wider range of readiness levels. I did not put much energy into this particular station, and this was reflected in its poor reception by the students.
The sixth and final station was Math Art. As mentioned above, nearly three-fourths of all the students had never been to this station even once at the time of the mid-year survey. Among the few students who had been to Math Art, three students said they “Like it a little,” one chose “Like it a lot,” and two selected that it was their favorite station. For these latter two students (mentioned in Part II as the girls who had come up with the idea of creating a book of their own math problems), Math Art ultimately became their favorite not because of the station’s original design, but because they had seized an opportunity to mold it into a place where they could engage in work that was meaningful to them. Despite Math Art’s overall lackluster showing, the fact that it helped facilitate a positive math experience for this pair of students was enough to make it worthwhile in my opinion.
Theme 3: Differentiation efforts are more manageable for the teacher and more meaningful for the students
One of my main goals for this action research study was to examine how the choices students made during stations time impacted differentiation of math instruction. Carol Ann Tomlinson (2008), a well-known authority on differentiation, writes that “armed with assessment information and other knowledge about a student- the teacher should adapt teaching plans to attend to learner readiness, interest, and preferred modes of learning" (p. 27). After conducting a variety of assessments, both formal and informal, I knew that my students were diverse in all three of these domains, particularly readiness. To address these differences, Tomlinson (2000) outlines four distinct areas in which one can differentiate instruction: differentiation of content, differentiation of process, differentiation of product, and differentiation of learning environment. The impact of learning station choices in these different areas of differentiation, and in terms of the student considerations mentioned above, are discussed in this section.
The Big Four of Differentiation: Content. Process, Product, and Learning Environment
Content is the information that students are to learn, and content can be differentiated to accommodate different student readiness levels. Stations were a great way for my students to work on “just right” content challenges. They could skip tasks that were too difficult for them at that particular point in time (such as certain pages in the Math Magazine, or the higher point questions at Math Quiz Game Show) but were still exposed to higher level math concepts. During my study, I was happy to see that the students rarely chose tasks that were too easy or too hard, as such tasks would provide limited contributions to their mathematical development. Letting the students manage their own interactions with the content (within a certain range of options) was such a pleasant change for me compared to last year when I was trying to assign or match every child to each and every activity, problem, and appropriate difficulty level. That was a tremendous amount of work and there were several instances in which I was not successful in matching the students with content at their readiness level, resulting in negative outcomes like frustration or boredom. Putting the power of choice into the hands of the students was able to change those outcomes for the better.
Differentiation of process was one of the areas where stations were most effective. The station activities allowed students to engage in a variety of learning modalities that included processes such as reading, problem-solving, working collaboratively, expressing creativity, practicing basic skills, and more. The students were able to choose the tasks that were appealing and comfortable to them, which led to a higher level of engagement and more on-task behavior. Another positive outcome from giving students choices about their learning processes was that some of the “math anxious” students began to see math as more approachable and enjoyable (see Theme 4, below, for more on student attitudes and dispositions). In the beginning of the year, many of these students described math as boring or scary, and associated the words “math class” with test-taking or lecture. My hope was that working in math stations would open their eyes to all math can be, all the forms it can take, and its relevance to their lives. The enthusiasm and interest I observed throughout the year suggests that we were well on our way to meeting this goal.
Differentiation of product was another area that stations addressed, although to a lesser degree than the other areas mentioned in this section. Much of the work the students did in stations did not produce a tangible product, which was both good and bad. It was good in the sense that I didn’t have the students doing pencil-and-paper tasks just for the sake of producing a record of their activities (which can be especially overwhelming to struggling writers), and it was great that I didn’t have a stack of papers I felt obligated to look through. At the same time, a lack of tangible product was challenging because there was not always evidence of student learning or understanding to which I could refer after the activities ended. I tried to make up for this deficit by collecting data from the students via exit cards, surveys, journals, interviews, and observations, which did end up giving me a good sense of what the students were getting out of their station experiences. The idea that the students could still be learning even if they were not producing something for me to read or look at each and every time they engaged in stations work took me some time to fully comprehend and accept. In an age of standardized testing, it’s easy to forget that the learning taking place cannot always be captured by a written assessment.
Attending to students’ preferred working arrangements (in both the spatial and social senses) was one way of addressing differentiation of the learning environment. Based on the results from a beginning-of-the-year survey in which 33 out of 42 students selected “in partners” as a preferred working arrangement, I wanted to make sure that my stations allowed for that kind of collaboration. In the same survey, 23 of the students responded that they liked to work alone and 13 students marked “small groups” (the students were allowed to select all options that appealed to them). Surprisingly, I had nine kids mark “working alone” as their only preferred work arrangement, so I also made a mental note to ensure that I addressed their needs as well by not always making partner work the default arrangement. In Methods that Matter, Bizar and Daniels (1998) assert that learning stations should offer “some kind of interaction,” preferably opportunities for students to engage in group exploration and conversation. Giving students the choice to work in partnerships during station activities provided the venue for this kind of interaction, and it was an option that many of the students exercised on a regular basis.
In terms of the choices students made about their physical work environment, I observed just about every possibility imaginable over the course of my study. The students worked at desks, on the floor, on the couch, outside, and in corners. They worked while sitting, standing, or lying on their stomachs. They worked quietly, loudly, independently, in partners, and in groups. The one consistency was that they chose to work in all the ways that felt right to them. Except in a few instances, they were not viewing this as an opportunity to goof around or avoid work. In fact, off-task behavior reduced dramatically during stations time compared to some of the other lessons where student choice was limited to just choices about the learning environment. After making this observation I began to wonder if offering choice in one realm of differentiation is sufficient for a learning activity, or if the presence of all four of the components mentioned in this section is essential to the success of differentiated tasks. It’s a question I look forward to exploring in more detail as I grow as an educator.
How Choices During Station Time Address Student Differences in Readiness
Addressing differences in student readiness is closely connected to the content being taught. Developmentally, not all students are ready to take on the complexities of more challenging content all at the same time. Each student also brings with them different life experiences that further shape their readiness levels. As I observed the students and analyzed their exit card data over the course of the study, I found that they were very much in tune with what kinds of content and activities were too easy and too difficult for them, and made choices accordingly.
According to Tomlinson (2000), students performing around 80% accuracy learn more and feel better about themselves. I believe that most of the students were intuitively aware of their readiness for a task, and letting them choose what station to go to and when to move to another station was a logical extension of this self-awareness. Data from our mid-year survey supported this assertion. Six out of 34 students agreed with the statement “Most of the stations are too easy for me,” and just one student agreed with the statement “Most of the stations are too hard for me.” In other words, most students found that the stations offered tasks at a “just right” readiness level for them to choose from. The exit cards students filled out at the end of each stations session also provided student-reported data on how the stations addressed their readiness level. Again, students reported experiencing a “just right” level of difficulty most of the time, which is critical for minimizing boredom and frustration and for maximizing learning and increased mathematical confidence.
How Choices During Station Time Address Students’ Different Learning Profiles
Learning profile was another area in which my students differed as learners, and the stations were designed to address many of the multiple intelligences found in my classroom. I knew that my linguistically-minded kids might be excited about the Math Magazine station. My highly social kids were the ones constantly choosing to revisit Math Games. The auditory learners enjoyed having the Math Quiz Game Show questions read to them. Students who tended to be more analytical often visited the straightforward Fact Practice station. The opportunity for students to choose activities that matched their learning profile, as well as some activities that were perhaps little out of their comfort zone, was a terrific benefit of using the stations.
As an educator, it was critical for me to understand the different learning profiles of my students and design activities that addressed these differences, yet what we as teachers choose to present and how we choose to present it is often inherently biased toward our own learning profiles. What I would have found dull (e.g. Fact Practice) was highly enjoyable to some of my students, while my personal favorite (Math Quiz Game Show) was a station some kids consistently avoided. The need to expand our instructional offerings beyond our own personal preferences is captured in the quote below:
“When we catch fish, we bait the hook with what the fish likes, not what the fisherman likes” (Chapman & Gregory, 2007).
In the sea of the classroom, focusing only on what I (the fisherman) enjoyed would have been far less effective in getting the students (the fish) excited about mathematics than integrating what they liked to do. I believe it is important to offer opportunities and activities that we wouldn’t necessarily choose ourselves, because those activities might be just the right “hook” for getting our students excited about learning. As a result of analyzing the students’ station choices, I truly learned a lot about who they were as learners and discovered yet another reason why offering a variety of different activities and allowing students to make their own choices was a valuable teaching and learning strategy.
How Choices During Station Time Address Students’ Different Interests
It is human nature to enjoy and be engaged in what we are interested in. Higher interest in the task at hand leads to more engagement, which leads to more learning. Offering choices during math learning stations allowed the students to pick processes and learning environments that appealed to them in order to learn content and, in some cases, produce products of their learning. Two main pieces of quantitative data I collected during my study suggested that the learning stations in our classroom were addressing students’ interests. The first was from our mid-year survey, in which just three out of 34 students agreed with the statement “Stations are boring.” Interestingly, all three of the students who felt this way also agreed with the statement, “Most of the stations are too easy for me.” This suggests an important link between engagement and the level of challenge presented in a learning activity, an idea that was reinforced by the responses on student exit cards. For example, on an exit card for the File Folder activities station, a student wrote that the activities were too easy and she did not enjoy any of them. Conversely, the stations where students frequently reported experiencing a “just right” challenge (such as Math Games, Math Magazine, and Math Quiz Game Show) were some of the most visited stations and received higher enjoyability ratings on the mid-year survey\.
Overall, I witnessed the students making many “just right” choices for themselves in terms of content, process, and learning environment throughout the course of my action research study. They were choosing partners they worked well with, a comfortable physical environment, and activities that were appropriately challenging and held their interest. These choices not only helped to make their mathematical experience more enjoyable, but also helped me to manage the challenging task of differentiating for the variations among a diverse group of learners.
Theme 4: (Some) students’ dispositions toward math improve
Measuring and seeking to improve students’ perceptions of themselves as mathematicians over time supports the NCTM (2000) goals of helping students develop the non-intellectual aspects (e.g. confidence, persistence, and positive attitude) of problem-solving. I was definitely interested in finding out if the stations affected the students’ attitudes toward math, so I made sure to collect and analyze data about students’ mathematical dispositions over the course of the year. Overall, the results were rather mixed, but there were definitely some highlights worth mentioning here.
In the second week of school, I distributed a beginning-of-the year survey to all of the fourth graders. The first question on the survey was, “What sentence best describes you as a math student?” The results for this question were as follows:
Four students selected “I am a math expert.”
Twenty-four selected “I am pretty good at math.”
Ten chose “Math isn’t my best subject, but I’m getting better at it.”
Three picked “I don’t think I’m any good at math.”
Although most of the students expressed a fairly high level of confidence about their math skills, I was still concerned about the thirteen that doubted their abilities, particularly the three students that claimed they weren’t any good at math. At that moment, I made a mental commitment to do anything I could to help those students feel better about themselves as mathematicians, and hoped I could use stations to work toward meeting that goal.
Another method I used to get an initial glimpse of my students’ feelings toward math was asking them to reflect in their math journal. Within the first week of school, I asked the kids to write their very first math journal entry (in words or pictures to support my struggling writers) in response to the prompts "What do you picture when you hear the words 'math class'? and "How do the words 'math class' make you feel?" I originally wasn't going to use this piece of data in my research, but after thinking about it some more I realized that it could be a pretty revealing source of information and a tool that I could reuse later in the year to look for a shift in dispositions toward math.
When analyzing the data, I chose to focus primarily on the question “How do the words ‘math class’ make you feel?” As I reviewed the students’ initial responses to this question, I categorized them into three categories: positive comments, neutral comments, and negative comments. Positive comments expressed excitement, happiness, enthusiasm and/or other positive feelings toward math. Negative comments often expressed fear, boredom, or anxiety. There were two kinds of comments that I categorized as neutral: comments that did not express any emotion and comments that expressed both positive and negative emotions. Examples of all three types of comments can be seen below:
"It makes me feel excited!"
"It makes me feel good."
“Yes math. I can’t wait for something new. [I feel] excited, jumpy, filled up with joy.”
“It makes me feel excited. I love math!!!!”
“Happy because I like math. I think math is awesome.”
“I feel good. I think I’m pretty good at math and it’s fun. And I know I will get some answers wrong and some answers right.”
"It makes me feel like I'm a clock because numbers are math."
"Math makes me feel happy and bored at the same time. But I do think math is cool."
“Excited and scared and fun.”
“I feel excited and worried because I need to brush up on my fractions and decimals.”
"I feel scared and when I am in math class I can't think right." (L.G.)
"Scared and upset because I don't like math...and I think it’s kind of boring."
"It makes me feel enslaved."
"When I hear math class I do not want to go."
“Worried that I will mess up in front of the class.”
Source: Students’ beginning-of-the-year journal entries
Among those who responded to the journal prompt (25 students total), I counted nine positive comments (36 %), nine neutral comments (36 %), and seven negative comments (28 %). Not surprisingly, six out of the seven students who had written negative comments had also selected either “Math isn’t my best subject, but I’m getting better at it,” or “I don’t think I’m any good at math” when asked to describe themselves as a math student. As the semester went on, I made a point to do whatever I could to facilitate positive experiences for these seven students. I was eager to gather additional data at a later date to see if their feelings and attitudes had improved.
The opportunity for comparison arrived when I analyzed the data from our mid-year survey. I asked the students the same question (“How do the words 'math class' make you feel?") and again categorized their responses as positive, neutral, or negative comments. Out of the 33 responses, 14 comments were positive (42.4 %), ten comments were neutral (30.3 %), and nine comments were negative (27.2 %). While I was encouraged by the overall increase in the number of positive comments, I was also discouraged by the fact that so many kids still had negative feelings about math class. There was a silver lining, however. Among the 21 students who had responded to the same question on both the beginning-of-the-year journal entry AND the mid-year survey, five kids had written comments that were more positive at the mid-year point than at the beginning of the year, and another four students had maintained their positive feelings toward math. Unfortunately, about the same number of students wrote comments that were more negative at the mid-point (four students) or maintained their negative feelings (four students). To go back to the bright side, though, I was ecstatic to find that the two most math-phobic students in the entire fourth grade had written positive comments on the mid-year survey. Making a positive difference in just those two students’ mathematical dispositions may not seem like much, but to me it felt like a significant achievement that made every moment of hard-work, preparation, and attention to their needs well worth it.
When I thought about why there were still so many students that felt negatively about math class, I was unable to come up with anything conclusive, but I do have some ideas. One possibility is that having the same question presented twice prompted them to respond in a similar manner to how they responded in the beginning of the year, perhaps as a matter of convenience or a desire to be consistent. Another possibility is that the general nature of the question led them to focus on overall impressions from all of their previous mathematical experiences, instead of just this year’s experience as I had intended. Of course, it is also possible that the students truly did feel negatively about our math class, but my everyday observations of and conversations with the students suggested that this was not the case. Regardless of the students’ true motivations for responding in the ways they did, reviewing their responses was an important reminder to me that there was still work to be done in the area of improving their feelings towards math.
Despite the mixed results that came from analyzing the open-ended question discussed above, a different piece of data from the mid-year survey led me to believe that, overall, implementing stations into my classroom was indeed a good decision. In the final section of the survey, the students were asked to write either “A” for agree or “D” for disagree for a series of statements. Some of the statements had to do with choice elements or differentiation considerations, but three statements were of particular interest to me in terms of how the students benefited from the stations in general. The results were as follows:
- 30 out of 34 students (88.2 %) agreed with the statement, “Stations have made me a better math student.”
- 28 out of 34 students (82.4 %) agreed with the statement, “Stations have made me like math more.”
- 28 out of 34 students (82.4 %) agreed with the statement, “Stations are my favorite thing to do in math class.”
Based on this data, most students found the stations to be an effective strategy for improving both their mathematical skills and attitudes, and found it more enjoyable than any of the other activities and approaches they encountered in math class. While I was excited about the overwhelmingly positive results, the fact that there was even a single student that disagreed with the above statements reinforced my belief that a balanced mathematics curriculum offering a variety of approaches is critical for meeting the needs of a diverse group of students. There is no magic solution, no “one-size-fits-all” technique that supports all students all of the time. My action research taught me that using math stations can be beneficial, but to use it exclusively would be to deny some students the opportunity to learn math in a way that is more meaningful to them. This is not an acceptable outcome if we are to provide an equitable education for all of our students.
 While a more thorough discussion of this topic is beyond the scope of this thesis, Vygotsky’s work on the topic of Zone of Proximal Development is a recommended resource.