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Using an Interactive Simulation to Support Development of Expert Practices for Balancing Chemical Equations



05/15/15 to 05/21/15

The ability to balance a chemical equation is a foundational skill in chemistry, yet it is still most frequently taught traditionally, through explicit instruction followed by drill-and-practice. Using a guided-inquiry activity coupled with feedback from a PhET interactive simulation offers an opportunity to foster student development of this skill via an inquiry-driven approach. Here, we describe how student groups in a preparatory (pre-General) chemistry course make use of the Balancing Chemical Equations simulation to build increasingly expert-like practices with non-redox equation balancing. Student discussions during this process offer insights into the ways that multiple representations in the simulation – including symbols, molecular pictures, and balance scales – each facilitate different stages of student development. Finally, noting that student approaches to balancing vary depending on the features of the equation, we will discuss how instructors might select post-activity practice equations to scaffold student skill development.



Balancing chemical equations is a foundational skill for the learning and practice of chemistry. Yet, equation balancing is typically taught via traditional methods; namely, direct instruction, followed by drill-and-practice. As teachers, we provide our students with a definition of a balanced equation, but often struggle when it comes to supporting our students in non-algorithmic approaches to balancing. Often, our advice to students relies on heuristics -- helpful hints such as balancing the largest molecule first or hydrogen atoms last. While such tips can be helpful, heuristics also lend themselves well to memorization, leading students to later reference these half-remembered guidelines as if they were absolute rules for the process of balancing [1].

In addition, little is known about what makes an equation challenging for novice balancers, nor even what distinguishes expert and novice approaches toward an unbalanced chemical equation. Literature on equation balancing has historically focused either on providing new algorithmic approaches to balancing to reduce cognitive load [2] or on studying student balancing as a binary of success or failure [3, 4].

Here, we will focus on understanding and supporting student process development in equation balancing, using an inquiry-oriented approach facilitated by an interactive simulation. We will show not only that students are able to learn to balance chemical equations without explicit instruction, but also that the representations used in the simulation impact the development of student balancing practices.

In the Classroom

The focus of this paper is an in-class activity which uses guided-inquiry prompts coupled with feedback from a PhET interactive simulation to introduce students to equation balancing. The activity took place in a Preparatory Chemistry class at a primarily undergraduate public university in the western United States. The course targets students identifying as underprepared for traditional first-semester General Chemistry. Course content was primarily delivered via in-class group work on guided inquiry activities, occasionally supported by PhET simulations. In earlier classes, students had covered content on empirical and molecular formulas. This activity marked the students first in-course exposure to the topic of balancing chemical equations.

On the day of the activity, students were seated in 12 groups of 2-3 students and provided with activity worksheets and laptops pre-loaded with the PhET interactive simulation, Balancing Chemical Equations [5]. The instructor told students that the day's activity would focus on chemical equations and then directed them to begin the activity, alternating control of the laptop and simulation amongst group members. No directions were given on how to use the simulation.


Part I of the activity focused on the Introduction screen of the simulation (Figure 1) and prompted students to compare the total number of molecules and atoms on the left and right sides of the equation once balanced. Each of the three available equations provided visual and audio confirmation when successfully balanced.



Figure 1 - The Introduction screen of the PhET Balancing Chemical Equations simulation when first opened by the student (left) and when an equation is balanced (right).


Part II of the activity focused on the Balancing Game screen of the simulation (Figure 2), and asked students to specifically focus on the strategies they were using to balance the equations presented at each progressively more challenging level of the Game. Each level presented students with five equations randomly drawn from a pool of questions of similar challenge. Level 1 offered equations with only 3 coefficients, i.e. either decomposition or combination reactions. Level 2 and 3 both presented equations with 4 required coefficients, with larger coefficients being generally required at Level 3. At all levels, students had two chances to enter the least coefficients for a balanced equation, receiving feedback each time they submitted an answer to be checked by the simulation (Figure 3).


Figure 2 - An example challenge equation in progress at Level 3 of the Balancing Game screen.


Figure 3 - Examples of feedback which could be received by students from the Balancing Game portion of the simulation.

During the class, the instructor facilitated several whole class discussions to solicit student views on the requirements of a balanced chemical equation and their balancing strategies. Including class discussion time, student groups spent a total of 30-50 minutes on the activity. Groups who finished early moved onto another related activity about chemical equations and stoichiometry. We collected simultaneous audio and screen capture recordings from each student group during the class period. In total, we successfully recorded and analyzed data from 10 student groups.

Results and Discussion

When student groups in Preparatory Chemistry were provided with a guided-inquiry activity which leveraged interaction and feedback from the PhET Balancing Chemical Equations simulation, all groups were able to craft operational definitions of equation balancing and successfully balance chemical equations of varying difficulty.

It is encouraging to note that these students were able to balance equations without explicit instruction, but we were specifically interested in looking at changes in students’ process of balancing. We will report a more detailed analysis of students’ evolving practices elsewhere, our early analyses of student actions and discussion around balancing tasks offers several insights particularly useful for teachers.

Here, we focus on student groups' use of different representations in the simulation and reflect on how these usage patterns may inform our approach to teaching balancing, with or without an interactive simulation.

Student use of symbolic and pictorial representations

Throughout the activity, the simulation supports student balancing by displaying concurrent symbolic and molecular-scale pictorial representations of the atoms and molecules in the chemical equation (e.g. Figure 2). The simulation was designed to cue students to the connection between these two disciplinary representations, with additional molecules appearing as coefficients are increased.

Because these representations offer a shared visual for all group members, they can be leveraged to facilitate communication between students and clarify meaning. For example, in one group, a student initially declared that a balanced equation was one with equal numbers of molecules on both sides. The student then demonstrated his meaning for the group by counting the number of atoms of one element and indicating these atoms on-screen with the mouse. This behavior suggests that the student was, in fact, correctly counting the atoms on each side of the equation, but simply used the incorrect term in his statement to the group. This type of terminology mismatch is not uncommon among early chemistry students, so it can be valuable that the representations in the simulation may help the group members more accurately convey their intended meaning.

More than this, we suggest that the concurrent availability of both symbolic and pictorial representations supports chemistry learners in bridging these two key disciplinary modes of thinking. We analyzed student actions and dialogue while groups balanced equations presented in the Balancing Game, looking specifically for cues that students were leveraging either the symbolic or molecular representations.

Cues indicating student use of the symbolic representations included “mousing” over equation terms with the cursor while counting aloud, reading formulas aloud as written, or verbalizing the multiplication of coefficient and subscript to calculate the total number of atoms of an element. Notably, student focus on the symbolic representations was highlighted in groups who balanced the equation for the combustion of ethanol (presented in the simulation with the formula C2H5OH). All groups who encountered this equation initially treated the ethanol molecule as if it contained only five hydrogens. For example, one group (i) set the coefficient of ethanol to two, (ii) indicated the subscript “5” with the mouse cursor, and then (iii) verbalized their total as ten, demonstrating that they were not attending to the sixth hydrogen in the formula. In none of these cases was there any indication that groups were miscounting the number of hydrogen atoms with reference to the pictorial representation. Instead, this common error likely resulted from students unfamiliarity chemical formulas that include functional group information.

Cues indicating student use of the molecular-scale representations included mousing over each atom or molecule while counting aloud, or making verbal reference to the colour or size of the atoms depicted. For example, students referred to hydrogen atoms while balancing by saying that, “There are too many white ones on this side” or that “We need more of the small ones.” Groups who referred extensively to the pictorial representations also tended to immediately increase all coefficients from zero to one when presented with a new equation, allowing them to view and leverage these images for balancing.

Student groups who seemed new to balancing tended to consistently leverage the pictorial representations in their practice, but all groups engaged with the symbolic representations. This suggests that novice balancers may be served by concurrent support from both representations, but that their heavier use of molecular-scale representations in balancing does not preclude them from attending to and using symbolic representations. In fact, it seems likely that their use of both representations will support them in coordinating these key disciplinary modes in future practice.

Student use of a “balance scale” representation

In addition to canonical symbolic and pictorial representations, the simulation also offers the option of additional representations to focus students’ attention on the core idea of equation balancing.

When students first load the simulation, the Introduction screen presents three typical unbalanced equations (Figure 1). Unlike the Game screen previously highlighted, the Introduction focuses on student exploration of balancing and allows students to add bar chart (Figure 4) or balance scale representations to their view (Figure 5). Both of these representations were designed to focus attention on whether there are an equal number of atoms of each element at any given time. Combined with the “happy-face” feedback students receive when an equation is balanced, this design was intended to support students in developing their own operational definition of a balanced chemical equation.


Figure 4 - Bar chart representation in the PhET simulation, showing the number of atoms of each element.


Figure 5 - Balance scales representation in the PhET simulation, showing the number of atoms of each element.


In our study, no student groups made active use of the bar charts, although some did open this view in passing after balancing the equations. However, 4 of the 10 groups made use of the balance scales while still engaged in balancing. In addition to keeping the balance scales visible during their balancing process, the students also indicated their use of this representation with mouse gestures or verbal references.

For student groups with members that seemed to have little or no prior exposure to equation balancing, the balance scales seemed extremely valuable to their ability to figure out the task at hand. For example, one pair of students exploring the simulation makes multiple attempts to adjust the coefficients in the equation for the synthesis of ammonia, all without balancing the equation. One asks, “What are we looking for?” and the other replies, “I don’t know.” When the pair adds the balance scales to their view, both students immediately indicate that the “H” scale is unbalanced and, in only 2 actions, adjust the coefficient on H2 to balance the reaction.

Balance scales also assisted groups in self-correcting misunderstandings about balancing. One group assumed at the start of the activity that the equation must be balanced when no more molecules could be added, but revised this idea as soon as the balance scales were viewed.

These examples highlight the potential for this non-traditional representation to facilitate student conceptualization of their task. The dynamic feedback from the balance scales supported new learners to clarify that the number of atoms of each element must be equal on either side of a balanced equation and helped to disconfirm incorrect prior ideas about the role of the total number of molecules or total atoms in balancing chemical equations [6].

However, a limitation of the balance scales is that an emphasis on balancing individual atoms can encourage balancing practices that focus on each element in isolation. When relying primarily on the balance scales, students may not be looking at the bigger picture - which elements are connected together in molecules, or relationships between molecules in the equation as a whole. The balance scales seemed to provide a useful stepping stone to the basics of balancing, but further development was needed as more challenging equations were faced. In this study, once students moved onto the larger pool of equations Balancing Game, where the balance scales were unavailable, students developed more expert practices and transitioned beyond their earlier elements-in-isolation focus.


Our analysis of students engaged in a guided-inquiry activity around the PhET Balancing Chemical Equations simulation suggests that students leveraged multiple representations in developing their balancing practices. Students who seemed to have little or no prior background in balancing chemical equations seemed to particularly benefit from the use of concurrent symbolic and molecular-scale pictorial representations, as well as the less traditional balance scale representation. The balance scale representation seemed to support student understanding of the basic goals of balancing chemical equations, i.e., that an equation is balanced when the atoms of each element are equal. For these students, further development of practice was needed to move beyond a focus on individual atom types towards a more holistic perspective of the chemical equation.


1.    Nyachwaya, J.M.; Warfa, A.-R.M.; Roehrig, G.H.; Schneider, J.L. “College chemistry students’ use of memorized algorithms in chemical reactions.” Chem. Educ. Res. Pract. 2014, 15, 81-93.

2.    See, for example, (a) Porter, S. “How should equation balancing be taught?” J. Chem. Educ. 1985, 62, 507-508. (b) Tóth, Z. “Balancing Chemical Equations by Inspection.” J. Chem. Educ. 1997, 74(11), 1363-1364. (c) Hutchings, L.; Peterson, L; Almasude, A. “Pre-matrix balancing of challenging chemical equations with a simple formula register and middle school arithmetic.” J. Math. Sci. Collab. Explor. 2007, 9, 119–133.

3.    Niaz, M.; Lawson, A.E. “Balancing chemical equations: The role of developmental level and mental capacity.” J. Res. Sci. Teach. 1985, 22, 41–51.

4.    Staver, J.R.; Jacks. T. “The influence of cognitive reasoning level, cognitive restructuring ability, disembedding ability, working memory capacity, and prior knowledge on students' performance on balancing equations by inspection.” J. Res. Sci. Teach. 1988, 25, 763–775.

5.    A revised version of the activity is available for download at The simulation is available online at

6.    AAAS Project 2061 Science Assessment Items.


Bob Belford's picture

Dear Yuen-ying, Emily and Katherine,

Thank you for sharing this thought-provoking paper on the use of a simulation to enable students to develop their own techniques for balancing chemical equations.  There are several questions I’d like to pose for potential discussion.

First, it seems this module approaches the needs of high school/remedial college courses, and well, my question is, do high school students find equation balancing a difficult subject?  (This may be more directed towards some of the high school teachers on the list).

Second, you mention that the students do not use the bar-chart representation.  Could you speculate a bit on that?  Do you think a different cohort of students might use it? 

Third, it seems one of your goals was to try to identify student problem solving strategies. Now, I am going to step back a bit, but the way I cover this is probably what you would call one of the algorithmic cognitive load reducing approaches.  I cover types of reactions first, like single displacement, double displacement and combustion before balancing equations, and then use different techniques for different types of reactions. This leads to my real question here.  Did you see any evidence of your students generating different problem solving strategies for different types of reactions?  Was there evidence that their techiques for balancing a combustion reaction was different than a double displacement?  Was there evidence that they balanced complex ions (when they were conserved) instead of the atoms in the complex ion?  Or did they try to generate one technique to apply to all types of reactions?

Thank you again for sharing this nice work.

Bob Belford

rpendarvis's picture

It has been my experience that students often have trouble balancing equations simply because they do not understand what the formulas represent. Simple things like understanding that copper (II) nitrate contains 2 nitrogens and 6 oxygens give them a lot of trouble. Is this something which should be better managed earlier?

I have seen a lot of software devoted to various aspects of balancing equations and yet this basic skill is often missing. In the end, much of the problem is rooted in the fact that the many resources available are not used. What can be done about this problem? Does anyone have grades tied into these resources? It seems to be the only way to ensure their use.

Best Wishes

malkayayon's picture

Yuen-ying, Emily, and Katherine,
Thank you for the ideas shared in your paper and for the activity in PhET. We find many of the simulations suitable for our students.
I think that the strategy described is very good, students could find different ways to balance the chemical equations. It is a good way to promote different ways of thinking instead of only one. I will try this teaching strategy next year in my HS.
Do you think that the groups should be homogeneous - students of similar level? or heterogenous?

BTW, I think that many students don't realy understand that the reactants dissapear as products are formed from the SAME atoms. Many are only counting atoms before and after. Maybe there should be a final simulation after students answer correctly in which it shows that the SAME atoms apear in the reactants and cond differently to form the products?
It could be a good idea to work with plastic models as well, simultaneously.
What do you think?

Yuen-ying Carpenter's picture

Dear Malka,

Thank you for your thoughtful reply. I really resonated with your statement that this might be a route to promoting more than one way of thinking about problems (certainly a valuable skill for our students in all types of problem-solving!). I am excited to hear that you will try this with your HS students next year!

(1) As to your question about the mixture of student levels in the groups -- this is a very interesting question, and there has been a lot of work in looking at group dynamics along these lines. In this specific activity, however, I do not think that the composition of the groups makes a substantial difference. Although I cannot answer conclusively, since our study was quite small, allow me to reflect on some of the differences I did see. In our study, we had groups of both types, since students self-selected their groups. While the conversations in the heterogenous groups did tend to involve dialogue where one student was offering answers to the other students (sometimes suggesting half-remembered strategies from HS, for example, or defining terms for their peers), this did not seem to substantially impact the practices the group engaged in during balancing. Although the group “expert” might confidently suggest that they always start with the products, their process still went through similar iterations as groups with no “expert” member.

However, I would say that with heterogenous groups, it was especially important that the students took turns in “driving” the sim or directing the group’s actions for balancing, since this sometimes revealed that one member of the group was struggling more than the others. When the students took turns, this allowed the group members (whether at the same or different levels) to really assist each other in building more functional practices for balancing.

This turn-taking was faciliated by the instructor’s directions at the start of class, as well as, I believe, by the use of laptops that we brought into class. In previous studies, we’ve seen that the barrier to turn-taking in group use of the sim is higher when students are using one group member’s personal laptop.

(2) I agree that having students also work with physical models could be a great opportunity to engage them even further with aligning the various representations in chemistry and the meaning we associate with each. Extending the idea of equation balancing to discuss with students where the atoms originate could also serve as an interesting springboard to begin discussing reactions in a dynamic way, and using other simulations and animations to talk about the interactions that are happening when reactions actually occur.


Yuen-ying Carpenter's picture

Thank you for sharing your experience, Dr. Pendarvis. I certainly agree that one of the common struggles students face is in mapping chemical formulae to their molecular/atomic-scale representation - for example, understanding the differences between subscripts and coefficients in order to determine the total number of atoms in a complex molecule. We certainly can support students in building this representational competence early; for example, the PhET simulation Build a Molecule targets specifically this concept, and could be used at an earlier stage in an introductory course:

That being said, this is potentially still a relatively new skill for students at this level, and can be supported as shown here by the use of multiple representations as they build more complex skills like equation balancing.

To your second question, with regards to the use of resources, I think that the best route to ensuring that resources are used by students will depend heavily on the course structure. In the class setting presented here, students were actively using simulations as part of in-class activities throughout the course. Although these were not graded, class participation and use of these resources was the norm. I have also seen these resources integrated successfully into TA-led recitation or tutorial activities, again a ungraded but core component of student time. In both of these cases, students are making use of the resources because those resources have been framed by the instructor’s course design as an expected and key part of their learning experience, rather than as “extra practice.” That being said, I have also seen instructors have success incorporating sims and other resources into graded homework activities.

As designers of educational resources, we also try to help support teachers in using these simulations and getting their students to make productive use of them as well, by providing tips for usage both in class and outside of class on our website(, and a database of teacher-submitted activities ( That being said, we would love to hear from teachers about the successes and challenges they have had in adopting and using our sims so that we can support and facilitate increased use of this resource.


Yuen-ying Carpenter's picture

Dear Bob,

Thank you for your interesting questions - you've certainly picked up on some of the more interesting details of this area.

(1) While I do not, myself, have experience with high school chemistry students, and would welcome any input from HS teachers on the ConfChem list, I can offer a few thoughts from the literature and my experience with these students (some of whom had no HS chemistry background). The literature suggests that this skill is not one of the most challenging ones that students encounter during their chemistry curricula, but it is one that often gets retained as a memorized algorithm, at best. Indeed, students tend not to map this skill onto the molecular-level representations that expert chemists associate with the chemical equation, so I would argue that the sim-support is one way to support that mapping while they are learning balancing, rather than divorcing balancing from the atomic scale.

(2) Anecdotally, one of the high school teachers I have worked with in the past has described her students over the years as verbalizing a preference for the bar chart representation. This is, however, in a context where students were explicitly asked to explore each representation and state if they might find one helpful. Bar charts are certainly a more familiar representation, so may be a comfortable representation for many students, if asked.

In our context, however, the groups who leveraged the balance scales were really doing so in order to understand what task it was that they needed to accomplish. The idea of equal numbers of atoms of each element seems to be more directly represented by the scales, so this may be why they were favoured by these groups.

Alternately, groups tended to open these additional representations ONLY if they needed “help” in figuring out their task. The available representations are arranged as “None” then “Balance Scales” then “Bar Charts”, from left to right. When groups were looking for additional information, they moved from “None” to the next available option, “Balance Scales” first. For all of these groups, this representation immediately offered some clarity on their task, and became an active part of their sim use. They may not have used the bar charts simply because they no longer had need of another “helper” representation.
It would be interesting to see if the representations were arranged in the opposite sequence whether the bar charts would have a similarly illuminating effect for new students.

(3) This is a fantastic question. First, to give some context, at this point in the course, students had not yet discussed the classifications of reactions you’ve mentioned, so they would not necessarily have reason to be sorting or grouping reactions by type (e.g. as combustion reactions) when they were tackling the task of balancing. Second, the simulation has no examples of equations with complex ions, since it is intended to introduce the skill and practice of balancing regardless of whether students have learned about complex ions yet. Indeed, when discussing practice questions assigned to students with the instructor, we agreed that having students recognize and treat complex ions as whole units (as experts would) was not a primary goal at this stage.

As to the students’ strategies, in general, their approaches were similar across all equations. However, I would note that the strategies they tended to verbalize when prompted in the class discussion (e.g. “we started with the biggest molecule” or “we always started on the left”) didn’t seem to adequately capture the increasingly sophisticated approaches they were actually executing in practice. Instead, I would characterize their successful balancing in terms of how broad their focus was when looking at the reaction. As I mentioned briefly in the paper, students sometimes struggled early on when they really focused on each element in isolation, rather than considering elements as parts of molecules, or taking into account the needs of the equation as a whole. We are currently wrapping up a more detailed analysis of student balancing practices along these lines and hope to share this manuscript soon.


The paper and Dr. Pendarvis raise interesting questions about why students have trouble with balancing equations.  Let me suggest an analysis from the perspective of recent research in cognitive science (the study of how the brain works).  Those studies suggest that the visualization tools recommended in this paper and others are vitally important no matter how other chem topics are initially taught.

The cognitive science is described in some detail here:  www.ChemReview.Net/CogSciForChemists.pdf   

But before you click, let me suggest some ways in which that research specifically applies to balancing.

1.  A primary cognitive principle is:  Break the more complex task into components -- and have students automate the component skills first. For balancing, this would include having them practice counting atoms represented by terms in a balanced equation.   Such a question might be

“Name and count the atoms represented by “5 Al2(PO4)3 “ (please pardon my ignorance if I failed to convey the subscripts in this editor)

Before they can balance, they need to be able to interpret the terms and count atoms.

2.  To balance, etc., they need to look hard and to write to distinguish Co from CO  and Cl from CI and NO from No and Po from PO, etc. Prep chemmers won’t know this is important unless you point it out.  The fact we sometimes forget is called “expert blind spot:”  instructors are often unconscious of what we do fluently.

Another practice question might be: “Name and count the atoms represented by “5 Co(CH3COO)2 “

When you see  CI4 , you think “carbon tetraiodide!” automatically, but in some fonts, to prep chemmers it looks a lot like Cl4 (4 bonded chlorines), and they don’t yet know why it can’t be.

3.  “Automate” means they need to be able to do the steps from memory, without hesitation.  This means that before they go to balancing, you need to give an announced, brief, closed notes quiz (or online homework problems with a time limit) that require them  to be able to do the steps from memory.  Cognitive studies recommend clicker questions and other short frequent quizzes to promote “spaced practice.”  They tend to pay attention just before the quiz, yes? 

4.  A central reason today’s students have trouble with something as simple as balancing a chemistry equation is that, under the state K-12 math standards in most states, between 1995 and 2010, teachers were required to have students use calculators for arithmetic starting in 3rd grade.  As a result, many don’t know their times tables.  To check whether this is true for your cohort, try this quiz with a sample of students:

“On this paper, showing your work, without a calculator, multiply   A)  47 x 56       B)  78 x 92  ”   And prepare to be appalled.

Can they balance if they don’t know their times tables?  Maybe.  But if they need the calculator to balance, in going back and forth between the paper and buttons and screen and paper, they tend to lose their place.  Or they simply become frustrated by the tedium, and dismiss going on to gen chem.

The only answer I know for this is, for students in prep chem, who are likely those with poor automated math skills, which is why they did poorly on the math placement test, require at the start of the course that they memorize their math facts.  Suggest flashcards if necessary. Give the quiz above variations until they get them right, fast, every time. 

In general chem, where lots of examples are based on simple whole number ratios, the examples won’t be simple unless their math facts are fluent.  By mandating use of calculators on 3rd grade state math tests, we now know from cognitive studies that states made a mistake (see the reference above) which is one thing the common core math standards do fix by limiting calculator use.  But meanwhile, math facts aren’t remediation:  In most states students were never required to learn them.  

5.  Require they learn a standard algorithm  for balancing using the component skills above.  Since 2010, cognitive  experts has been in emphatic consensus that novice learners (including all undergrads) cannot solve a problem of any complexity by reasoning:  They must recall a memorized procedure (algorithm).  The reference above will explain this.  New measurements of brain function are forcing change in prior theories.  But first --

6.  Here’s the key:  After they have mastered first the components and then balancing by arithmetic, they will get balancing right every time, and remember HOW to do so for stoich problems including titration, etc.  BUT indeed, they won’t understand the chemistry.

That’s where the visualization approaches are INVALUABLE.  Once they have mastered the component skills, they will be able to look at the molecular visualizations and see the molecular shapes and angles, the bonds that break and form, the fact that the coefficients mean we are representing ratios between particles, etc.  That is the most important part in chem.  But if they have not mastered the components first, the visualizations will tend to overwhelm their limited novel working memory with too much new information, which makes them confused.   

When the component facts and procedures have previously been  automated, there is room in novel working memory to notice and store context elements in long-term memory, which is how conceptual understanding is gradually constructed.

7.  Is novel working memory not a familiar term?  Take a look at the reference above.  I think in chem ed, a conceptual understanding of what novel working memory can and cannot do will help our anecdotal observations on student learning make sense. 

So – components, then algorithms, then multi-modal practice, especially with visualizations.  That’s what science says is the fast and efficient way for students to gain conceptual understanding. 

If the above raises any questions, this might be a good time to discuss them.  The cognitive science on "automaticity" has been tested, proven science for at least a decade, but in chem ed, discussion of the science according to cognitive scientists often times seems suppressed.

-- rick nelson

Yuen-ying Carpenter's picture

Hello Rick,

Thank you for your thorough and thoughtful reply. I would like to address three particular ideas that you highlighted.

(1) In your first and second points, you describe introductory students' relative unfamiliarity with chemical formulae. This is certainly a challenge we face in chemistry instruction, and as I mentioned above, the PhET simulation Build A Molecule is our effort to support early student development around this concept. However, I would argue that leveraging both symbolic and pictorial representations throughout skill development, as is the case in Balancing Chemical Equations, is helping to bridge that gap for learners, as shown here.

(2) I would disagree with your contention that a major stumbling block to the practice of balancing is basic arithmetic. At least in the context of the preparatory chemistry students in this class, none of the student conversations suggested that the arithmetic was, for them, a challenge, and none were making use of calculators for the arithmetic, when delving into questions inside or outside of the simulation. Student attention was focused on the challenge of making sure there were enough atoms of each type, not on struggling to confirm how many atoms were actually needed.

(3) Finally, I would argue that algorithmic practices for balancing are the *opposite* of what introductory students need.

Indeed, Staver and Jacks’ paper [reference 4, above] directly looking at working memory and balancing by inspection concludes that it is not an overload of working memory (but rather an inability to restructure the problem) that presents the primary stumbling block for balancing.

More to the point, the practices that we observed the students developing during the course of this single class session more closely resemble the practices we see in expert balancing than the algorithmic or arithmetic methods that have been suggested in the literature. While I can believe that increasing automaticity might be valuable for some tasks, what we observed in this activity is that an open inquiry approach can yield productive balancing practices by allowing novice students to build their own strategies with support from multiple representations.

I say this, of course, with the caveat that these students are not balancing redox reactions in this activity, for which even experts tend to rely on algorithmic or semi-algorithmic approaches.


If these were students in “liberal arts” or “non-science major” chemistry, I would not have a problem with encouraging “novice students to build their own strategies.” 

However, to the extent that many of these students aim to go on to work in medical settings, do we want to encourage them to learn and apply time-tested algorithms and procedures -- or to “build their own strategies” that may or may not work as well?

I would emphasize that in my reading, I have found that cognitive experts agree that there is real value in visualization activities as support in learning structured procedures and when to apply them.

-- rick

Yuen-ying Carpenter's picture

I certainly agree that visualizations can provide good support for learning both structured procedures, as well as conceptual or adaptive approaches. I also agree that structured, well-defined procedures can be extremely helpful for some tasks. However, based on my observations of this class, and preliminary interviews and observations of experts (grad students, and faculty) balancing equations, I would contend that balancing is not best suited to an algorithmic approach, regardless of the student population in question.

Indeed, the practices experts engaged in were similar to students’ approaches in that they were likewise non-linear in nature, and, when facing a challenging equation to balance, were marked by cycles of selecting a strategy, assessing their progress, and then revising their strategy as needed. This is exactly the type of behavior that we see in novice student groups, albeit with more rapid assessment and changes of strategy in the expert group.

It is worth noting as well that while students were building their own strategies for balancing, all of the students were, in fact, succeeding at balancing. It’s also worth remembering that these students are building these approaches with facilitation and support not only from the simulation, but also from their instructor, who takes time to lead class discussions where he revoices and summarizes features student approaches that led to success. The students are not by any stretch left floundering with unsuccessful strategies.

Moreover, in thinking about teaching our students how to become expert at problem-solving more generally — to be able to not only choose appropriate strategies, but assess and evaluate and change strategies as needed — it seems useful to begin this training with a comparatively simple case like balancing, where students can actively check the correctness of their answer to know if they are successful or not, before we challenge them to apply expert-like problem solving behaviors in more complex cases.

I am curious which time-tested algorithms you would suggest for balancing - there are well-accepted algorithmic approaches to redox equations (e.g. half-reaction approaches), but many of the algorithms proposed in the literature for non-redox equations rely heavily on algebraic manipulation (e.g. solving linear systems of equations), which, as you've highlighted, presents an increased challenge for students in prep chem classes. Alternately, many textbooks offer step-wise approaches that highlight such tips as leaving O or H to last, but these tips and heuristics do not generalize well, and we see students attempt to apply the 'leave O to last' in reactions that aren't combustion and therefore are not made simpler by this approach.



You asked “I am curious which time-tested algorithms you would suggest for balancing.”

In our prep chem text (published by WW Norton), the lessons Don Dahm and I use for teaching balancing lessons I have posted here:


The method shown there uses “completion problems” recommended by cognitive studies:  Cover the answer below the stop sign, work the step, uncover, then do structured practice with answers (given at the end of the chapter).  These pages work great as homework -- to give more time in class for active learning.  In our experience, IF students know their times tables, subsequent balancing success rates are 100%.  BUT they need to know their times tables first.

In my 10,000 career hours in front of first-year gen or prep chem-level classes over 40 years, what I found was, from 1971 to 1985 (yeah, I’m a dinosaur), success of this approach was always 100% because students had learned math without calculators. 

With increased calculator use since then, success rates in gen chem have fallen dramatically nationwide.  Even flagship state universities have added "prep chem" that never needed it 25 years ago.  Multiple studies have found gen chem success best predicted by tests of student skills in mental arithmetic (including Wagner et al. 2002 and Leopold and Edgar 2008 in JCE).  The recent cognitive research, reviewed at


has made clear why mental math mastery is an absolute pre-requisite for quantitative science courses success.

Our recommendation is to require mental math mastery, using quizzes, at the start of prep chem.  For those interested in experiments with math fluency to improve success rates, we have materials to help with that which I would be happy to share.   Please contact me offline (EANelson@ChemReview.Net)  to review them.

Once math balancing is mastered, students do balancing right in future calculations without difficulty (we teach the redox balancing algorithms similarly later in the course) , but students do need to do visualizations like yours, after learning the component skill, to see the concepts.

The sequence that learning science says works most efficiently and effectively is first algorithms -- then practice aimed at concepts – to work around the well-documented limits in human working memory.  Cognitive experts say that starting with concepts simply doesn’t work for undergraduates.  Our brains are products of natural selection -- and not what we might wish them to be.

-- rick nelson

osrothen's picture


You may be a dinosaur, but you bring considerable wisdom to this discussion.

It's no accident that "smart people know stuff" - a lot of stuff. I wish I could remember where I first heard this quote. I now have a new quote, however: "Our brains are products of natural selection -- and not what we might wish them to be." I love it! Thanks for sharing your thoughts and knowledge in this discussion.

Otis Rothenberger

Yuen-ying wrote, "I am curious which time-tested algorithms you would suggest for balancing…"

You can see the my approach on page 303 of

One part of it suggests, "If [an] element is mentioned in two or more formulas on the same side of the
arrow, skip it until after the other elements are balanced. (See Example 7.2.)" This is a more general guideline than the "skip O and H" guideline. It gets to the heart of the reason why skipping O and H is sometimes a good strategy. An even more general approach is, "If you find an element difficult to balance, leave it for later."


Eric Nelson wrote, "If these were students in “liberal arts” or “non-science major” chemistry, I would not have a problem with encouraging “novice students to build their own strategies. However, to the extent that many of these students aim to go on to work in medical settings, do we want to encourage them to learn and apply time-tested

My first reaction was, do conscience majors need to balance equations at all? They should be able to interpret the information in a chemical equation, including the information given by the coefficients, but I don't see balancing equations as an important life skill for non-science majors. For non-science majors, it seems a shame to spend time on teaching them a skill that they will most likely never use when the time could be spent on other, more important and interesting things.

For science majors, it's important that they be able to balance equations, but in my experience, science majors have very little trouble doing so. Redox equations can be tricky, but even for those, a simple algorithm works great. (page 303)

Now for the part that sort of relates to our discussion. I think that providing students an opportunity to construct their own understanding of things is great, and animations can be very useful for this, but I also think that for some tools, old-style is OK. Instructors and students have a finite time to teach and learn chemistry, so we need to be careful not to spend too much time on something that can be done quickly. If we can teach a topic quickly, it leaves more time for things that really require more time. For example, there's so much to do in general chemistry that I think for skills that are ultimately algorithmic in nature, we should present the algorithm, show them how to apply it, give them a opportunity to practice it, and move on to topics that are more challenging and important, such as energy and climate change. (Eric - Is this what you were suggesting?)

As many of you know, I'm a big fan of the use of animations to help the students visualize the particle nature of matter, and I have created a lot of them myself. But just because we "can" create an animation for something, doesn't mean we "should", especially if using the animation takes a significant amount of time.


SDWoodgate's picture

I must say that I agree in some measure with Mark. However, I would not exclude the teaching of balancing equations for non-majors. Mass conservation is such an important principle. But there is no need to make a meal of it, and the exercise should focus on reactions that they will either meet in other contexts, like the preparation of ammonia, reaction of sulphuric acid with sodium hydroxide or are industrially important. Textbooks are littered with exercises balancing equations for obscure reactions.

I have evidence that high school students (15 and 16 year olds) are not particularly challenged by the task of balancing equations. I have two BestChoice activities on balancing equations by inspection. Both of these have three groups of equations. In the first group, you can more or less just write in the coefficients without back-tracking. In the second group, back-tracking is required (adjusting of coefficients when balancing the next element messes up the atom balance for others). The third group are equations where polyatomic ions are involved.

1000 16 year-olds did one of the activities in 2014, and it runs at an average of 83% first right over 12 equations. Interestingly the best performance was on the two at the end that involved polyatomic ions. 300 15 year olds did the second who which is very similar with one or two different reaction systems. Their performance was similar until they got to combustion of butane where it dropped to 55%. They did not recover in the last two concerned with polyatomic ions which each had a 73% first right.

These activities were some of the first that I wrote. The performance didn't suggest that I needed anything simpler. That is certainly the exception to the rule. Usually when I write a BestChoice activity, I discover that the students didn't know as much as I thought they did, and I find that I have to go back a notch and do something more basic. The same thing is true of the redox reaction ones where they balance both of the half equations and then combine them.

My definite impression from studying lots of responses to BestChoice questions is that writing the formulae from scratch is by leaps and bounds more challenging for them than balancing the equation.

By the way, I had a look at your reactants and left-overs activity because I also know that limiting reagent is a very hard concept for them. It was interesting, and I found my strategy changing from just counting atoms in the molecules at the beginning to a greater reliance on the balanced equation. BUT then I wondered about how the connection could be made to the next step which is the actual calculation.

Have you thought about how the jump could be made from the visual stuff to the calculation?

Yuen-ying Carpenter's picture

Thanks for your thoughtful response, and for sharing your experiences and data from these BestChoice activities and student responses. I am not surprised that the students found the combustion of butane a comparatively challenging question, and appreciated that you highlighted this example.

Although not something we tackled in this study, I certainly agree anecdotally (and based on the chem ed literature) that writing equations for chemical reactions from scratch (or from words) is a more challenging task than balancing a provided equation. I only narrowed my focus to the balancing portion since not much had been explored in terms of characterizing exactly how balancing happens (while numerous studies exist on student approaches to stoichiometry from a word problem).

I also appreciated your reflection on the reactants, products and leftovers simulation - your change in strategy is, at least anecdotally, what we see in student interviews with the simulation as well! Sarah Hansen's paper (#3 in this ConfChem) delves much more deeply into the changing patterns of student use and attention in the reactants, products and leftover sim, and I think she would have much to share on how one might approach extending students' conceptual development to more quantitative problems. I will say, however, that I think the two skills are synergistic, and that students who have this visual support as they tackle balancing and stoichiometry may be able to better connect the stoichiometric calculations to an expert-like molecular view of the reaction.


At the end of his post on this visualization discussion, Mark Bishop asked:   “Eric - Is this what you were suggesting?”  What I (Eric) was trying to gently suggest was this. 

Until 2001, it was assumed among many learning researchers that the brain could hold and process newly acquired information from calculators, computers, or recent reasoning as easily as it processed information that could be recalled from well-organized long term memory.  Only gradually between 2000 and 2010 did measurements of brain function make clear that for well-structured problem solving, that assumption was incorrect.   For undergraduates, when solving the type of “precise, agreed upon right answer” problems that are the focus of initial science-major chemistry courses, the working memory where you reason has room to hold the unique problem goal and data, plus every relevant fact and algorithm you can recall from your long-term memory, and essentially nothing else. 

This means you can only “reason” with information that has previously been well memorized. 

The ideal that undergraduates can “solve like experts” has been firmly proven by cognitive experts to be incorrect.  To solve like an expert, you need the long-term memory of an expert, and that takes 10 years of focused study in a discipline to neurally and biochemically construct.

Among experts in the study of the brain, the implications of the recent measurements of cognitive limits were argued between 2001 and 2010, but since that time, the necessity for thorough memorization is no longer contested.  And when formerly controversial scientific contentions are asserted but are not contested, Thomas Kuhn famously called that the definition of a new scientific consensus.

We can argue over whether 5 years without debate by scientific experts in a field is long enough to be sure we have consensus.  But frankly, the measurable data on this issue has been widely discussed among experts in how the brain works for the past 15 years. In chemistry education, the work we do is primarily about how the student brain works and how we can help those brains learn to solve problems.  To the extent that researchers in chemistry education are not aware that the issue of memorization and reasoning was scientifically debated for 10 years, and for the past 5 years has been settled among the experts, then, in chemistry education, we have a serious problem.

I hope we will try to fix the problem, not individual blame.  For our institutions, however, I would hope that the managers of chemistry education journals would put in place mechanisms that recognize a responsibility to note new discoveries and controversies on the subject of how students learn.  Readers deserve to be informed of controversies in learning, to hear both sides, and to hear of the outcomes when those issues become settled among cognitive experts.

As we noted in our recent article in the journal Foundations of Chemistry ( at www.ChemReview.Net/CogSciForChemists.pdf   ), for over 10 years, leading cognitive researchers have been making an effort to inform educators of the importance for students of “automaticity” in the recall of fundamental facts and algorithms in science -- and the math pre-requisite for chemistry study.  Math journals paid attention, published the research, and discussed automaticity extensively.  As a result, “automaticity” and “fluency” (automatic recall across a topic) are a prominent part of the 2010 widely-adopted in the US common core math standards.

Now try this experiment.  Search for “automaticity” in your favorite chem ed journal.  Try to find a positive mention of the word.  Just one.  Have readers been kept in the dark?

When math education moves so much faster than chemistry education, and K-12 reform moves faster than chem ed reform, it is dismaying, and it should be a matter that is addressed.

I personally want to thank Foundations of Chemistry editor Eric Scerri (of the UCLA Chem Dept.) for having the courage to publish science that was accurate, and needed to be discussed, but was not what some in his audience wanted to hear. 

As instructors, we need to tell our students an inconvenient truth.  Before they can gain conceptual understanding of a scientific topic, they need to move a good many fundamental facts and algorithms about the topic into their long term memory.  Recent cognitive science gives instructors advice on how we can help students do that. 

These are recent discoveries, but we now know that telling students “think like a scientist” and “don’t memorize” will retard their progress in learning science.  If the conclusion that this is what cognitive experts are saying is at all in doubt, it needs to be discussed within our community.  To our students, this topic matters.  Bigtime.  For instructors, finding time to learn about cognitive science is difficult I know, but in learning, the progress of science has made cognitive science central to what we do.

And again, in my reading, cognitive science says these visualization tools are invaluable in developing needed conceptual understanding -- if the components of the visualizations are present to at least an initial extent in the existing frameworks of a student's long term memory.

Mark --  did I answer your question?  -- Eric A. (rick) Nelson

Yuen-ying Carpenter's picture

Dear Mark,

Thank you for your reply - as I mention in my response to Eric, above, I certainly will not dispute that when it comes to tasks that are ultimately algorithmic in nature, it is wise to teach these procedures to our students (e.g. redox reactions, as you mention). My argument is, however, that watching experts balance non-redox equations shows that balancing is not ultimately algorithmic in approach.

I also appreciated your comment about the limited amount of time we have with our students, and how we must prioritize how we spend this time. I would highlight, however, that this activity took a total of 50 minutes of class time (or roughly one class period), including instruction, practice, and discussion. In a high school or preparatory chemistry environment, it would not be unusual to spend one class on equation balancing even if we were to approach "old-style", as you say, it by direct instruction, and drill-and-practice.

I agree that visualizations like this simulation should only be used if there is value-added; however, I would argue that the ways that students are leveraging the multiple representations demonstrates that this is a value-added case, particularly for students encountering chemistry for the first time who are only just beginning to establish representational competence.


Emily Moore's picture

It seems that there are some themes emerging from discussion. Here are a few that stand out to me, and some thoughts on these. I welcome others to share any themes they notice from this conversation, and their thoughts.

1) Is balancing chemical equations difficult for students – or not?
It seems that the answer may be “sometimes yes and sometimes no”. In Yuen-ying’s study, I don’t think our findings directly address this question. From the discussions students were having, many students seemed very unfamiliar with the topic – perhaps they had been exposed to the idea before, but they did not seem to be drawing upon prior knowledge. Indeed, they seemed to be stumbling through figuring it out fresh (as we all stumble around a bit when exposed to something new!). So I don’t think this particular work gives us a measure of how “hard” it is for students in general…it must be at least slightly challenging at the beginning, until a student “figures it out”.

Comparing the data that SDWoodgate shared (thanks for sharing this!), I believe we saw a similar trend in the study of the Balancing Chemical Equations simulation, where students were able to balance most of the equations, but seemed to struggle more with some than others. This seems to indicate that easier balancing problems are “not hard”, and harder balancing problems are “hard” (surprise!). So again, I think that the takeaway is that sometimes balancing is difficult for some students. Perhaps this is an indication that there is something about balancing chemical equations that we (as teachers and researchers) do not understand, since we can’t seem to adequately characterize the difficulty of balancing (e.g., what reactions will be harder to balance than others, and why).

2) Should balancing be taught as an opportunity to teach students how to enact *one* strategy for solving a problem, or as an opportunity to teach students how develop *multiple* strategies for solving a problem?
I don’t think there is one “right” answer to this question. I think we will all bring our own perspectives of teaching and learning, and personal experiences with students into answering this question. I see many benefits to using balancing as an opportunity for students to develop *multiple* strategies for problem solving and to deepen their understanding of representations in chemistry – though there are certainly many opportunities throughout a chemistry course to do this.

3) How do we support students to relate the ideas of balancing (e.g., conservation of mass) with the dynamics of reactions?
Or, in other words, how do we build on students developing skills of balancing reactions to include the dynamics of chemical reactions – moving students toward a more holistic understanding of chemical reactions? I think this is an area that interactive visualizations are uniquely suited for, taking “static” and “flat” representations of reactions and moving them into a more dynamic space. In our work presented here, we intentionally focused on developing the skills associated with effective balancing. This involved keeping the reactions static, but allowing for interactions with the representations – namely the coefficients. Before this particular class and after it students would spend time focused on other aspects of reactions and chemical equations. The representations we show include particle-level views of the atoms in “reaction chamber” like areas, in an attempt to blend some of the representations used for chemical reactions, while also supporting students to count atoms (e.g., the atoms/molecules are bouncing around the containers). Are there better ways to blend these ideas for students, while still supporting balancing skills?

4) What can cognitive science help us understand about teaching and learning chemistry with interactive visualizations?
Please note, I am not an expert in cognitive science, or learning science. In my research, I have spent many, many hours with students working in groups in classrooms using interactive simulations to help them learn. From my research in these environments, I have found it necessary to focus on the actions/interactions/verbalizations of the *group* (rather than individuals) to answer my research questions. In fact, it can often be impossible to follow and make sense of individual student actions/interactions/verbalizations without analyzing at the group level. Another significant component to take into account is that students working in groups in these environments have a lot of support available to them – through their group colleagues, the teacher facilitating the class, and the affordances and constraints of the simulation. I have found ideas from distributed cognition – which is based on the idea that knowledge does not reside solely in a person’s head, but can be distributed across multiple people and their environment – to be enormously influential in my work.

I want to suggest that your research should be approached from the perspective of conceptual understanding and not the algorithmic 'problem solving' perspective. In my opinion, balancing chemical equations is not a de-contextualized activity like solving algebraic equations, and therefore should be always seen through the conceptual lens of chemical reactions. The study of conceptual meaning making of equations in physics may be a good source for a similar theoretical framework. For example, Sherin's (2001) "How Students Understand Physics Equations" is a good starting point, and Tuminaro, J., & Redish, E. F. (2007). "Elements of a cognitive model of physics problem solving: Epistemic games" might be also helpful.
This leads to my second point regarding the activity itself, the game-like "training" environment is very similar to the abundance of math games that are out there. It indeed seems like a "mental-training" device, with very little meaning making alongside the practice. I understand that there was a worksheet that accompanied the activity and provided some more "chemical" context to the activity, but couldn't this be integrated into the activity itself?
An example of an activity that used visualizations for learning about chemical reactions but did not treat balancing equation in isolation was reported in Chiu and. Linn (2014) "Supporting Knowledge Integration in Chemistry with a Visualization-Enhanced Inquiry Unit".

Yuen-ying Carpenter's picture

Hi Elon,

Thank you for your very thoughtful response and references.

I agree that equation balancing (or any other individual aspect of a stoichiometric problem) is a contextually-situated practice, and that integrating any one aspect of practice into a larger chemical picture and conceptual framework is a crucial goal for instruction.

The activity here was designed to utilize and integrate the simulation support, but also be an authentic piece of the curriculum sequence and teaching style already planned and facilitated by this instructor throughout the semester. There is certainly room to more deeply integrate the context through a multi-week sequence of activities (similar to the multi-activity sequence reported in Chiu & Linn) that would delve into both the static and dynamic representations Emily mentioned, above. I think, though, that integrating these ideas into the activity really would require changes to the scaffolding and learning activities which precede and follow it, and this was not our goal at this time.

One additional reason we chose to delve more deeply into only the students’ balancing practices was that the literature in chemical education has historically skipped over this aspect of student practice. We wanted an opportunity to look at this practice without confounding factors of having students also translate word equations or predict products in a larger integrated problem, since we wanted to just understand how students were accomplishing this one task.There are many very interesting discussions in the literature about student conceptualizations of reactions and stoichiometry, or of coefficients and subscripts, but little that talked about how students actually got from an unbalanced to a balanced equation - most papers merely report whether students succeeded or not. One thing we observed when looking at novice chemistry students was that even when students could clearly articulate what needed to be balanced and what they could manipulate, this did not initially imply that they could actually implement an effective practice. As well, there was a change in their actual practices as they became more experienced, which seemed to reflect a more holistic view of atoms as parts of molecules, and of the equation as a whole, much like experts might view the equation when presented to them.

That being said, I agree that there is still a gap between viewing a static equation “holistically” in order to balance it and conceptualizing that equation along with all of the dynamics of reactions, the nature of the compounds and their reactivity, and understanding what information the equation does not relay (e.g. kinetics, mechanism, etc.).

I appreciate your challenging me to think more broadly about the scope of this practice in context, and to extend the integration of these and other activities in future.