Final Draft IJWC Fall 2021 Issue 12.20.21


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International Journal of the Whole Child                                         
2021, VOL. 6, NO. 2          

                                                                       
Emerging Scholar 
“Productive Struggle” as an Effective Strategy in Elementary Math Classrooms 
 
Sara Dailya 
 
aMiddle Tennessee State University 
 
Sara Daily graduated from Middle Tennessee State University with her Bachelor's in Film and 
Video Production in 2016. She is currently earning her master’s degree at Middle Tennessee 
State University in Curriculum and Instruction with an emphasis on Elementary Education in the 
Initial Licensure Specialization. Her research interests focus on improving education for all 
elementary students.  
 
Abstract 
 
Productive Struggle refers to a strategy that gives students an opportunity to increase their 
background mathematical knowledge. Productive Struggle helps students connect key concepts, 
determine how and where an error occurs, and supports students in figuring out how to use their 
own thinking and reasoning skills to correct an error. Teaching without utilizing Productive 
Struggle instruction can lead to students being reluctant to work towards developing a deeper 
understanding of math concepts. Without a deeper understanding of mathematical concepts, 
students, who often do not perceive themselves as competent in math, may continue to find math 
difficult for them in the future. 
 
Introduction 
 
Productive Struggle (Murdoch et al., 2020) is an instructional strategy designed for teachers to 
help students use their own thinking and reasoning skills to solve math problems. The process 
helps students develop an improved understanding of conceptual math as well as to gain 
confidence in their abilities to solve problems.  
 
Productive Struggle instruction is not a concept that is easily implemented. It requires teachers to 
know the material well enough to determine where a student may go wrong in the process and 
then, know how to guide them to the correct solution without directly providing the answer. 
Productive Struggle, as a part of instruction, enables students to develop confidence in their 
abilities, become more willing to take risks, and grow in their understanding of the content. 
 
When students are building a new skill, it is not always comfortable for them. In addition, 
allowing students to struggle is typically not in most teachers’ comfort zone, which begs the 
question: What is to be gained from this uncomfortable and time-consuming method? 



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Productive Struggle Instruction 
 
Productive Struggle, as explained by Murdoch et al. (2020), is recognized both in policies and 
research as a signal of quality education. They believe Productive Struggle is an important and 
necessary strategy for teaching mathematics for conceptual understanding. Instruction in 
Productive Struggle can help students by teaching them how to problem-solve effectively. These 
skills will help students, not only in their current classroom, but throughout their educational 
time as well. 
 
Traditionally, a common method of instruction in mathematics involves teaching students a 
formula or pattern to follow. These instructional methods provide students with the correct 
answer in a timely manner, but unfortunately, do not teach students how to independently solve 
problems. This leads to other issues in both their future math classes and in real-life situations.  
 
Mathematics teaches students the important skills of how to problem solve and adapt in a variety 
of situations, not just get right answers. By only teaching formulas and not problem solving, 
teachers deny their students the opportunity to perceive themselves as competent at math; this 
perception undermines students’ potential to become a problem solver.  
 
Math problems are often tasks without clear solution paths. Effective teachers can provide their 
students with more than just a formula; rather, they can highlight the possibility of how students 
can solve problems by themselves in a variety of ways. The instructional method used to teach 
problem solving and help aid students in becoming more confident in their mathematic abilities 
is called Productive Struggle. Productive Struggle is an effective method for enhancing the 
process of mathematics teaching for the benefit of students. 
 
Productive Struggle Goals 
 
Productive Struggle instruction goals include students learning to think deeply, gaining 
understanding, and developing independent problem-solving skills (Amidon et al., 2020; Baker 
et al., 2020; Granberg, 2016). While students who develop their own methods may encounter 
more errors and take longer to solve the problems, they often score more positively on tests than 
students who use memorized procedures. Even if the students who created their own methods are 
incorrect, they are more likely to adapt their methods than their classmates who used memorized 
information (Granberg, 2016). By creating their own methods, students can create new pathways 
and develop connections to concepts previously taught in mathematics. Without assistance from 
teachers, this is much more difficult for students to accomplish if all they have previously 
learned to do is memorize how to solve a problem. 
 
As teachers, one of the most limited resources is time. Spending time doing something deemed 
unproductive is not a common practice. It is more likely that teachers will evaluate struggling 
students as doing something unproductive and provide those students with steps in how to solve 
the problem rather than allowing the students to develop the techniques themselves. There is a 
possibility when teaching problem-solving, that teachers will reduce it to following an algorithm 
rather than allowing the students to reason it out for themselves (Brousseau & Gibel, 2005). 



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Another problem may arise when teachers become unwilling to allow their students to fail, so 
they make the problem easier to solve, taking away the chance for the students to develop 
problem-solving skills (Brousseau & Gibel, 2005). Struggle takes time and is often not seen as 
worth the risk to a teacher not familiar with the benefits of Productive Struggle. 
 
However, teachers who use Productive Struggle are taking a risk. First, implementation of 
Productive Struggle requires teachers to truly know their content. Thorough knowledge of the 
subject matter increases teachers’ effectiveness in challenging and encouraging their students to 
engage in Productive Struggle (Murdoch et. al., 2020).  
 
Second, learners possess diverse background knowledge and require different strategies to 
challenge them. Because of this, unpredictable behaviors often occur as they struggle during 
learning events. Teaching Productive Struggle not only takes preparation and an in-depth 
knowledge of the content but also understanding of the individual students’ needs in order to be 
implemented effectively. 
 
Most research describing Productive Struggle regards secondary students struggling in 
mathematics (Baker et al., 2020; Granberg, 2016; Warshauer, 2015; Zeybek, 2016). Research 
describing implementation of Productive Struggle in elementary schools is limited. However, 
this approach is complementary to Constance Kamii’s (1982, 2000) constructivist understanding 
of how young children (ages birth to eight) develop logico-mathematical knowledge. Kamii 
(1982) asserts, “Relationships are created by the child from within, and not taught by someone 
else from the outside” (p. 29). She advises teachers to create an environment that encourages 
children to think and make their own decisions. Kamii (1982) explains that the teacher’s role is 
not simply correcting children’s answers, but rather figuring out how the child made the error, 
and then guiding the child’s “process of reasoning which is far better than correcting the answer” 
(p. 41). Similar to Productive Struggle, Kamii’s (2000) approach supports children developing 
their thinking skills, rather than memorizing rules, as this will enhance their understanding of 
math concepts as well as build their confidence.  
 
Lev Vygotsky’s theory, zone of proximal development, can be found in several Productive 
Struggle studies. Struggle involves students doing scaffolded tasks that are within the student’s 
understanding (Betts & Rosenberg, 2016; Vazquez et. al., 2020). Scaffolding allows the students 
to take steps towards the desired goal at a reasonable pace. These scaffolded tasks can lead to 
better memory of the material, a deeper understanding, and a chance to create more solutions to 
the same problem (Vazquez et. al., 2020). The key to Vygotsky’s theory is for teachers to 
maintain high expectations of their students. In a study by Ewing et al. (2019), English language 
learners were thought to not have mastered English and were provided with problems outside 
their zone of proximal development. These expectations only hurt the students and the teachers. 
By providing problems within the zone of proximal development, students can develop their 
mathematic skills without becoming overwhelmed. 
 
Brousseau’s theory of didactical situations in mathematics has been implemented in Productive 
Struggle research as well. Granberg (2016) states that mathematics without struggle involves fast 
ways that will always lead to the correct answers. While this is an ideal output and useful in 
saving time, it does not prepare students for the future. Teachers wish for their students to 



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succeed. Some teachers find that when leading their students, they break down the problems until 
they no longer require critical thinking (Brousseau & Gibel, 2005). Effective teachers do not 
simply provide their students with procedures but allow the students to solve problems on their 
own and develop the skills necessary for all subjects. 
 
The earlier students are supported in working through difficult problems, the better prepared 
these students will be throughout their education. Problem-solving skills are not limited to 
mathematics. Students who are supported in developing their own methods will likely be more 
successful in many other school subjects. Teachers may not initially acknowledge the time spent 
teaching Productive Struggle as worthwhile, but their students’ test scores will reflect the 
benefits. More importantly, the students will become confident problem-solvers, an important 
life skill. 
 
Benefits for Students 
 
Researchers consider Productive Struggle as a crucial and natural part of the learning process in 
mathematics (Murdoch et al., 2020; Russo et al., 2021). Math problems are not meant to be 
similar. They are intended to be implemented in a variety of situations and designed to prepare 
students for life after the classroom. Through intellectual struggle, students learn from their own 
mistakes. Instruction in Productive Struggle encourages students to implement this knowledge in 
other tasks and improves their ability to be self-directed (Lemley et al., 2019). 
 
Productive Struggle provides students with opportunities to thoroughly study difficult problems 
in order to determine similarities between them. This helps students to develop a deeper 
understanding of mathematics (Ewing et al., 2019; Lemley et al., 2019; Russo et al., 2021). 
Allowing students to correct their mistakes is another means to build mathematical 
understanding. This knowledge cannot be achieved unless students can determine how their 
mistakes were made, or if their teachers specifically guide them to where they erred in their 
understanding. 
 
The idea of struggle can be defined as students attempting to understand something in 
mathematics that is not clearly discernible at first glance (O’Dell, 2018; Warshauer, 2015; 
Warshauer et al., 2021). The problems meant for Productive Struggle are difficult, but not 
impossible. Problems requiring students to think about the process of finding solutions provide 
challenge as they use their thinking and reasoning skills. Importantly, if they can immediately 
use memorized information, the problem does not promote Productive Struggle. Struggle is only 
productive when teachers implement it correctly, and students are able to gain understanding and 
problem-solving skills from the effort. Herein, lies the benefit for students engaging in 
Productive Struggle. 
 
Productive struggle builds students’ understanding of mathematical concepts (Warshauer et al., 
2021). The more students do on their own will promote future mathematics learning. By 
productively struggling, a more thorough knowledge of the topic is developed. Students 
remember concepts longer and better than if they had only been taught the steps to solve by their 
teachers (Vazquez et al., 2020; Warshauer et al., 2021).  
 



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Productive Struggle indicates where students are lacking in their knowledge (Amidon et al., 
2020; Granberg, 2016; Murdoch et al., 2020; Vazquez et al., 2020). If a teacher walks the student 
through a problem, there is no critical thinking involved. The students cannot determine if they 
know how to do all the steps on their own. By allowing the students to figure out the problems 
for themselves, they can discern the differences between their current knowledge and what they 
are trying to understand (Granberg, 2016). These students will be able to make their own 
connections to other topics, which will help them with encountering future concepts and 
reviewing learned material. 
 
Students feel positive emotions when they productively struggle. When students are successful in 
their struggles, they feel pride (O’Dell, 2018). There is something special about being able to 
solve something without any aid from others. The more often students are afforded opportunities 
to feel prideful in their work, the more likely they are to see mathematics in a positive light. 
Students were also noted to feel joy when they finished a problem (O’Dell, 2018). When a 
teacher can link happiness together with mathematics, students will benefit. When students can 
fail and still want to continue dealing with difficult problems, Productive Struggle instruction is 
successful (Livy et al., 2018). 
 
How to Teach Productive Struggle 
 
Effective teachers instruct students in how to think like problem solvers. Through guiding and 
questioning, students become encouraged to determine exactly what is necessary for solving 
math problems. In general, a student’s response to Productive Struggle is to practice, ask for 
assistance, or persist in struggle (Warshauer et al., 2021). When a student seeks assistance, it will 
usually come from a lack of understanding. The goal for teachers in this situation is not to tell the 
students specifically how to solve the problem, giving them steps and protocols, but instead, to 
scaffold and support them with guidance by providing students with strategies to help them to 
create their own methods and be able to solve the problems themselves in the future (Ewing et 
al., 2019; Warshauer, 2015).  
 
There are several different strategies that can be used to teach Productive Struggle. For example, 
during instruction, the teacher talks the students through what they already know and provides 
them with questions requiring deep thinking. Providing questions for students encourages them 
to take the time to make sense of the problem they are trying to solve (Ewing et al., 2019). 
Unfortunately, there is not a set list of questions to ask. Productive Struggle requires teachers to 
adapt to each individual student and instruction varies with each type of problem (Lemley et al., 
2019; Murdoch et al., 2020). 
 
Another strategy used to teach Productive Struggle involves teachers inspiring their students to 
reflect upon their own work and become capable of explaining how they arrived at a particular 
answer. The ability to explain their own thinking enables students to develop their problem-
solving skills. When students explain or show their reasoning behind how they arrived at their 
answer, the teacher helps guide the students with the knowledge of where they erred. In this way, 
students improve understanding and develop those skills for the next problem (Baker et.al., 2020; 
Betts & Rosenberg, 2016; Murdoch et al., 2020).  
 



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Another strategy to implement Productive Struggle instruction entails teachers initially providing 
students with problems in a new concept, and then providing instruction after the students have 
had time to explore (Vazquez et al., 2020). This strategy builds on student understanding of the 
material because the students can develop their own reasoning on how to solve the problem. 
They determine the elements of the problem and create connections with problems they solved in 
the past with similar elements.  
 
A common problem when teaching Productive Struggle is to reduce the cognitive load. Teachers 
are accustomed to achievement that seems to be effortless (Livy et al., 2018). Most teachers wish 
to help a student who seems to be struggling. Not doing so appears neglectful, but this is not 
always the case. Students require adequate time to develop persistence to be able to complete the 
tasks themselves. When teachers help students solve problems, they diminish students’ chances 
to build critical thinking skills, support their dependence on others when confronted with 
challenges, and extend students’ struggles in the future. 
 
The key to teaching Productive Struggle is to provide students with the tools to independently 
solve the problems (Warshauer et al., 2021). Similar to reading instruction where students learn 
to decode words themselves, teachers can help their students develop the ability to create a list of 
approaches to solving a problem. The more the students can do by themselves, the more effective 
their learning.  
 
Effective teachers purposefully plan the time to create an environment where students are able to 
develop a deeper understanding of the topics. They encourage learning through process and 
building knowledge rather than attaining correct answers. While these teachers maintain high 
expectations of their students and their abilities, they prepare for and support Productive 
Struggle; when they do not, they deny students opportunities for growth and understanding 
(Ewing et al., 2019).  
 
Productive Struggle in the Classroom 
 
In Productive Struggle instruction, the goal is not for students to consistently and correctly solve 
the problems. Effective teachers shift their understanding of success to create opportunities for 
their students to build knowledge, not just show correct answers (Vazquez et al., 2020). Students 
who always get the correct answers do not necessarily understand how or why their answers are 
accurate. Students who fail can develop useful strategies for solving problems and determining 
where they went wrong (Amidon et al., 2020; Livy et al., 2018; Russo et al., 2021).  
 
Hearing or seeing students’ failures will help teachers. When Productive Struggle is happening, 
it is important the process is documented. The teacher’s responses, the ways in which a student 
attempts to solve a problem, and records of how and why a student becomes “stuck” become 
important components that will be necessary to consider the next time the lesson is taught 
(Zeybek, 2016). The goal is to provide students with the necessary tools to independently solve 
the problems. 
 
It is common for teachers to want to reward their students with free time to do as they wish, but 
in mathematics, that time can be used to benefit the more efficient students. Ewing et al. (2019) 



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discuss their study about a teacher who allowed the students to read when they were finished 
with their math instead of offering more challenging problems. Those students lost an 
opportunity to build upon their knowledge and gain a deeper mathematical understanding. In 
contrast, Betts and Rosenberg (2016), describe how students who finished quickly were 
challenged to find multiple solutions to the same problem. A problem with multiple routes to the 
solution not only engages higher-achieving students, but also encourages students to use other 
avenues that support their mathematical strengths. 
 
Time is the key to Productive Struggle. In several studies, it was determined that given adequate 
time, ability to work in small groups, and an environment where students feel safe, students were 
able to solve the difficult problems (Ewing et al., 2019; Warshauer, 2015; Zeybek, 2016). Time 
is imperative for students to develop their own strategies and figure out whether the strategies 
will work or not. It also provides teachers with an opportunity to identify struggling students and 
guide them towards the correct path without hindering students’ critical thinking. 
 
Potential Productive Struggle Problems 
 
Productive Struggle instruction is not without challenges. If the wrong tasks are chosen, students 
are likely to grow frustrated and will be unwilling to try again. A teacher that provides too many 
steps, reduces the cognitive load, or does not provide enough time will undermine Productive 
Struggle. A teacher who does not allow students to learn from their mistakes is preventing them 
from building a deeper understanding of mathematics (Ewing et.al., 2019). 
 
Productive Struggle can lead to uncomfortable feelings in students. When a student is tasked 
with facing the unknown, it will often lead to anxiety (Murdoch et al., 2020). The first few times 
a student struggles productively, it will be difficult. Prior to this new problem-solving 
instruction, students were previously taught the specific steps to follow. In the former model, 
they did not understand what they did, only that they had to follow the identified steps. In 
Productive Struggle, many students push back, asking for help or saying they do not know what 
to do. They are unwilling to try because of the anxiety of getting the problem wrong. 
 
Before students learn to productively struggle, many of them perceive their struggle as a 
weakness. When students observe themselves falling behind their classmates, it is seen as 
shameful. Shame will cause students to withdraw, lash out at others or themselves, or cause them 
to avoid the issue (Amidon et al., 2020). If this shame remains unchecked, the students could 
forever see themselves as “bad” at math. One effective strategy teachers use to deal with 
shameful feelings is to place less emphasis on correct answers and more focus on the learning 
process (Amidon et.al., 2020). 
 
The benefits of Productive Struggle outweigh the challenges that may occur. Students develop a 
deeper understanding of mathematics, including the disparities between what they do and do not 
know. Even though Productive Struggle may lead to feelings of shame and anxiety in students 
practicing this method, the benefits include pride and joy in their accomplishments after 
succeeding in solving the problem. Regarding the time and effort, Productive Struggle evidences 
value for both teachers and students. 
 



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Parents and Productive Struggle 
 
The effectiveness of Productive Struggle instruction is influenced by parents as well. Many 
parents were taught mathematics differently than current instruction. This causes parents to grow 
frustrated with new instruction methods and, sometimes, insist on the ways they are familiar with 
using. This will only cause problems for the student in the classroom. Once parents understand 
the benefits of Productive Struggle instruction and why teachers are choosing to implement this 
method, they will appreciate the advantages for their children.  
 
Unlike teachers, parents are less likely to understand the necessity for struggle. They may not see 
the struggle as beneficial, only as a waste of time. Parents want their children to succeed, so the 
parents are likely to talk their child through the process, or just provide the correct answer and 
move on (Russo et al., 2021). Mothers who helped their children with their homework reported a 
negative attitude toward the experience. This was caused not by having to help, but because they 
thought of their child as helpless (Vazquez et al., 2020). This idea is not beneficial to the student 
or the parent. 
 
Parents react differently to Productive Struggle in their children’s homework. Parents who view 
their children as “good” at mathematics are more likely to allow their students to struggle 
because they believe their child has the background knowledge to solve difficult problems 
(Vazquez et al., 2020). Some parents were not content leaving their students alone. Parents with 
strong stereotypes linked to math are more likely to interfere with their child’s homework 
(Vazquez et. al., 2020). In order for Productive Struggle instruction to be effective, a united front 
in implementation between the parents and the teachers becomes necessary. 
 
It is helpful to inform parents about Productive Struggle instruction and how it includes teachers 
making time for students to solve the problems themselves. It is important for parents to 
understand that if a teacher tells the students how to solve the problem, the students lose the 
opportunity to develop a deeper understanding of the process. Additionally, parents may require 
assurance that teachers understand how a student’s struggle will more effectively prepare them 
for the next lesson. However, the more a teacher knows about the topic and the moments in the 
problem-solving process with the highest potential to derail the student, the more effective the 
instruction will be along with increased opportunity for greater positive outcomes. Instruction in 
Productive Struggle cannot succeed in the classroom without parental support on the home front. 
Productive Struggle in the classroom requires many elements working together, including 
teacher and parent cooperation and understanding, to enable the students to be successful. 
 
Conclusion 
 
Productive Struggle is an essential method of instruction for mathematics (Amidon et al., 2020; 
Baker et al., 2020; Ewing et al., 2019; Granberg, 2016; Lemley et al., 2019; Zeybek, 2016). The 
key to this method of instruction is to allow students to struggle and come to appreciate the 
benefits of the process. If they do not understand the reasoning behind their struggle, they are 
more likely to give up on the difficult problems. Students engaged in Productive Struggle realize 
an additional advantage. Productively, struggling students outperform students with similar 



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capabilities who did not participate in this problem-solving instruction of Productive Struggle 
(O’Dell, 2018; Vazquez et al., 2020; Warshauer et al., 2021). 
 
Productive Struggle encourages students to take risks (Livy et al., 2018; Murdoch et al., 2020; 
Russo et al., 2021). In order to build their own knowledge and understanding, students try out 
ways to find solutions. These methods may be successful or not, but by engaging in this process, 
students become more effective at problem solving in the future.  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 



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