By Sara Fulmer

(cover image by an_photos from Pixabay)

Dr. Sara M. Fulmer is the Teaching and Learning Assessment Specialist at Wellesley College. She supports faculty with implementing evidence-based teaching strategies, and assessing the impact of various teaching approaches on student learning and engagement. Her areas of research include student motivation in challenging contexts and teacher professional development. She received her B.A., B.Ed., and M.A. from Brock University in Ontario, Canada, and Ph.D. in Developmental Psychology from the University of Notre Dame. You can find her on Twitter @sara_fulmer or at http://www.wellesley.edu/pltc/for-faculty/mellon-grant/sarafulmer.

You’re a teacher of an elementary school mathematics class planning a lesson on addition. You’d like to incorporate concrete objects (“manipulatives”) into the lesson. You have a choice: 

There is no question that manipulatives engage students and capture their attention. If students are more engaged, this must mean that the manipulatives support learning, right?

Not always.

Sometimes, our intuitions about teaching and learning are inaccurate or insufficient (see also learning styles, right brain vs. left brain, multitasking). In the case of manipulatives, the research evidence does, in some cases, contradict our beliefs.

Our intuition: Manipulatives are beneficial for learning

Manipulatives are incredibly popular as an educational tool. Some of the reasons why we intuitively judge manipulatives as beneficial for learning are because manipulatives: (1), (2)

• Capture students’ attention and interest (attention is essential for learning);

• Ground learning in a “real-world”, practical context, especially when the manipulative resembles a familiar object (e.g., pizza slices to learn about fractions);

• Engage students in perceptual and motor/physical (“hands-on”) processing of information (dual coding promotes effective learning); and

• Offer opportunities for self-directed exploration or discovery of concepts.

The research evidence: Manipulatives can hinder learning

Manipulatives are just a tool. Like any educational tool, manipulatives can support or hinder learning. As educators, an understanding of the research can help us to make more informed decisions about the use of manipulatives in our teaching.

Although manipulatives can increase students’ attention, this attention may not benefit their learning. In fact, the very aspect of manipulatives that capture students’ attention—bright colors, visual appeal, realistic features—may be their downfall. Manipulatives that are more visually interesting or realistic can increase off-task behavior, such as building or sorting (1). This is especially true if students interact with that object in other contexts, such as during play time or outside of the classroom.

Manipulatives that contain additional and irrelevant features can also interfere with learning by distracting the learner from relevant features of the objects and the target concept (1), (2), (3). For example, 4th and 6th grade students who solved word problems about money using bills and coins that resembled real money (left image) solved fewer problems correctly, compared to those who used bland money (right image) or no manipulatives (4).

To use a manipulative effectively, children must be able to think about the manipulative in two ways: as an object (e.g., “this is a plastic teddy bear”) and as a symbol (e.g., “this teddy bear represents one unit”). This ability, called dual representation, develops during early childhood. If an object is visually interesting or realistic, or if learners are already familiar with the object, they have more difficulty viewing that object in terms of a new symbolic meaning (2), (5).

Research suggests that manipulatives can improve immediate learning outcomes (e.g., retention, recognition) but may impede transfer of learning (6), (7). Students who learn with manipulatives can become too reliant on the object and context, and as a result, have difficulty transferring their knowledge to new contexts, different testing formats, or to abstract representations (e.g., algebraic expressions) of the problem (1), (3), (6).

Based on what you have learned, which manipulative would you choose for the addition lesson? Hint: Think about how task-irrelevant features of the manipulatives, such as size, shape, color, and prior experience or familiarity, might impact children’s use of the manipulatives to understand addition and equivalent units, or lead to off-task behavior.

Resolving the debate: How can I use manipulatives effectively in my teaching?

As educators, we need to carefully consider the manipulative, our learners, and the pedagogy to ensure that students’ work with manipulatives supports their learning (3), (6), (7). Three recommendations are offered below:

1. Select the right manipulative for the task and your students

2. Structure the environment for effective learning

3. Support transfer from concrete to abstract

1. Select the right manipulative for the task and your students

With such a wide variety of manipulatives available—from plain, solid-colored discs to colorful and realistic-looking objects—educators are faced with a challenging decision (5). The manipulatives that we select should meet our learning goals for students and contain features that are relevant to the task (7), keeping in mind that more visually interesting manipulatives can be distracting (2), (3). Additionally, characteristics of the learner, such as age and prior knowledge, influence the effectiveness of manipulatives (7). Younger children have more difficulty understanding that a manipulative has a symbolic meaning, particularly if the same manipulative is used to represent different concepts.

Ask yourself the following questions:

• What do you want students to know or be able to do by the end of the lesson?

• What is the role or purpose of the manipulative within the lesson?

• What features must the manipulative have to support learning of the target concept?

• What features of the manipulative might distract learners or lead them astray?

• What prior knowledge or experience might students have with this manipulative, and how could that impact their learning?

2. Structure the environment for effective learning

In any learning environment, a balance is needed between autonomy and structure. Although we might be tempted to use discovery-based approaches with manipulatives—allowing students to explore their own learning with little instructional guidance—research suggests that these approaches lead to poor learning outcomes (7), (8). Without guidance, learners might not understand the symbolic meaning of the manipulative, or may engage with the manipulative in ways that do not support their learning (3, 7). Manipulatives are not a magic tool. They cannot substitute for effective teaching (2). Conversely, too much structure can cause learners to become dependent on the manipulative and context, leading to difficulty with transfer (3).

Thus, a moderate level of instructional guidance is needed for effective learning with manipulatives (7), (8). Learners need opportunities to explore and test their ideas and understanding with the objects, but do so in task-relevant ways that support their learning (3). 

Ask yourself the following questions:

• How will I communicate the purpose of the manipulative to students?

• How will I help students focus their attention on the relevant features of the manipulative?

• What prior knowledge do students need to use the manipulative effectively to understand the concept?

• How will I manage off-task behavior? (Tip: don’t allow students to use manipulatives in non-symbolic ways before or during the lesson (3))

• How will I model and scaffold use of the manipulative for students?

3. Support transfer from concrete to abstract

We want students to be able to apply their knowledge and skills to new problems and contexts. This is called transfer. The practice of concreteness fading is effective in helping learners move from an understanding based on concrete objects to a more abstract understanding where they can solve problems without using the concrete objects (1). This teaching approach creates a middle step between the concrete and abstract, helping learners with the transfer process by making the process gradual and explicit (1). Here is an example of the concreteness fading progression for learning about equivalence:                         

What features, ideas, or questions will you consider when planning your next lesson with manipulatives? Comment below! 

References               

(1) Fyfe, E. R., McNeil, N. M., Son, J. Y., & Goldstone, R. L. (2014). Concreteness fading in mathematics and science instruction: A systematic review. Educational Psychology Review, 26, 9-25.

(2) Uttal, D. H. (2003). On the relation between play and symbolic thought: The case of mathematics manipulatives. Contemporary Perspectives in Early Childhood Education, 97-114.

(3) Brown, M. C., McNeil, N. M., & Glenberg, A. M. (2009). Using concreteness in education: Real problems, potential solutions. Child Development Perspectives, 3, 160-164.

(4) McNeil, N. M., Uttal, D. H., Jarvin, L., & Sternberg, R. J. (2009). Should you show me the money? Concrete objects both hurt and help performance on mathematics problems. Learning and Instruction, 19, 171-184.

(5) Petersen, L. A., & McNeil, N. M. (2013). Using perceptually rich objects to help children represent number: Established knowledge counts. Child Development, 84, 1020-1033.

(6) Carbonneau, K., Marley, S. C., Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105, 380-400.

(7) Marley, S. C., & Carbonneau, K. (2014). Future directions for theory and research with instructional manipulatives: Commentary on the special issue papers. Educational Psychology Review, 26, 91-100.

(8) Alfieri, L., Brooks, P. J., Aldrich, N. J., & Tenenbaum, H. R. (2011). Does discovery-based instruction enhance learning? Journal of Educational Psychology, 103, 3–16.