problem solving in reciprocal teaching

The Reciprocal Teaching Method (Examples, Pros, Cons)

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

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Reciprocal teaching is a teaching and learning strategy in which students take turns acting as the teacher in small groups.

Students are taught four teaching strategies that they apply when acting as the teacher in their group.

The 4 strategies used in the reciprocal teaching method are:

• Summarizing.
• Clarifying.
• Questioning.
• Predicting.

Students are taught to use these four strategies on their peers, thereby acting as teachers for one another.

This teaching method was developed by Palincsar and Brown in 1984.

The strategy is most commonly applied for reading and comprehension activities.

The Reciprocal Teaching Method: 4 Strategies

When students take on the role of the teacher, they are expected to scaffold their peers’ learning using the following four techniques. 

The teacher should model these strategies using guided practice before letting students have a go themselves.

1. Questioning

Questioning prompts students to reflect on their text and ensures they understand it effectively.

Without questioning, students may passively read the text. By asking questions, your student must actively engage with what they are reading.

Questions can begin with the phrases:

The teacher will need to model questioning strategies and potentially provide cue cards that students can read off. A cue card might contain an image with the phrase “Who?” or “What?” beneath it.

As students progress and become more comfortable with questioning one another, cue cards will not be required.

2. Summarizing

Summarizing requires students to explain the ‘big picture’ succinctly.

A summary should explain the key events or elements of a text and be paraphrased (in your own words). It needs to get across the important information without getting caught in too many details.

This capacity to identify what is important and what is not important is a skill that shows a student has successfully comprehended the text.

Summaries can include questions like:

• Write the main idea of the text in one paragraph.
• List the order of events in bullet points.
• Outlined the main characters or locations in the text.
• Explain the 5 key points.
• Explain the 8 elements of a story .

3. Clarifying

Clarifying involves 2 steps:

• Identifying when you don’t understand or have lost your place.
• Using strategies to clarify or ‘patch up’ your gaps in knowledge .

In the first step, students need to be open about what they don’t understand. If the group is reading together, the student might speak up and say “I need clarification” or “I am now confused”.

In the second step, students seek clarification by using the example strategies below.

• Re-reading a confusing passage.
• Identifying cues such as images or sub-headings that help guide their comprehension.
• Looking for important keywords that might help reorient the readers.
• Discussing the issue with peers to triangulate comprehension.

4. Predicting

Students make predictions about what they will expect to occur based on the evidence they have at hand right now.

A prediction does not have to come true. Simply, the student should make a prediction of something that may occur and be able to state why they feel that way.

Readers might use the title, images and contents pages to help students make informed predictions. If the front cover of a book has images of rabbits on it, there’s a good chance the book will be about rabbits, etc.

• Look: Students look together at the front page of a book.
• Predict: One student asks another to predict what will happen. They should start their sentence with “I predict…”
• Evidence: The student then asks their peer “Why do you predict this?” Their peer should respond “I predict this because…”

How to use Reciprocal Teaching in the Classroom

To teach these four methods, teachers need to slowly release responsibility to students using the guided practice method:

1. Explicit Modelling

The teacher has the group as a full class practice the four strategies explicitly. At this stage, the teacher retains control and asks students to practice the strategies in a very structured manner.

2. Guided Group Work

The teacher gets the students into small groups. The teacher retains control over the pace of the lessons by having students practice each of the four strategies one at a time. After practice, the teacher gets the students to turn to the front of the room and discuss how they went using the strategies with the whole class.

3. Independent Group Work

The students are each given a role (questioner, clarifier, summarizer, predictor). Each student must execute their role. At this stage, the students control the pace of their small group discussions. The teacher walks around the room supporting the students.

4. Individual Work

Once the group work has completed, the students should have internalized the strategies and will be able to use them when individually working away at their private reading and homework.

Theoretical Link

This teaching strategy is based on the sociocultural theory of learning . 

Sociocultural theory highlights the importance of:

• Discussion and social interaction for helping students progress their thinking.
• The use of a teacher as a ‘ more knowledgeable other ’ to guide or ‘scaffold’ learning.
• The use of group work to have students help educate one another ( peer learning) .
• The importance of language and ‘public speech’ in helping students to internalize knowledge.

Advantages and Disadvantages of Reciprocal Teaching

• Comprehension-fostering: The approach is comprehension-fostering, meaning it helps students to develop comprehension skills . By asking students to explicitly use comprehension strategies, students learn the processes required to comprehend written texts.
• Comprehension-monitoring: The approach is also comprehension-monitoring, meaning students internalize the four reciprocal teaching strategies and will begin to use them regularly. When successfully internalized, students will learn to use the skills whenever they read in order to test their own comprehension. In other words, the strategy develops from an explicit to  metacognitive approach.
• Distributed teaching: By teaching the students on how to scaffold one another’s learning, the teacher distributes their ‘teaching role’ around the class. Students support one another, freeing the teacher up to spend more one-on-one time with remedial students .
• Differentiation: The teacher can differentiate instruction , for example by providing different reading tasks to different small groups.
• Group work skills: Students need very strong group work skills for this to work. The teacher will need to spend a lot of time teaching students how to behave in groups.
• Peer learning: Some students may find it very difficult to learn from their peers. Arguments and bitterness can sometimes pop up, which the teacher needs to be aware of.
• Consistency: Many students start to forget or stop using the strategies. Prompts and cue cards are often required to help students to keep using these strategies. Similarly, the teacher may need to occasionally use refresher lessons.
• Level appropriateness: This comprehension strategy may not work if the students have not got sufficient reading skills already.

Final Thoughts

Reciprocal teaching can be an incredibly effective strategy when it goes well. Students feel empowered when they are given the freedom to ‘play teacher’. It can be a motivational strategy that simultaneously gives the teacher freedom to facilitate learning rather than be bogged down in explicit instruction .

Mayer, R. E. (1996). Learning strategies for making sense out of expository text: The SOI model for guiding three cognitive processes in knowledge construction. Educational Psychology Review, 8 (4): 357-371.

Palinscar, A.S. (2013). Reciprocal teaching. In Hattie, J. & Anderson, E.M. (Eds.), International guide to student achievement. (pp. 369-371). London: Taylor and Francis. 

Palinscar, A.S., & Brown, A.L. (1984). Reciprocal teaching of comprehension-fostering and comprehension-monitoring activities. Cognition and Instruction , 1 (2): 117-175.

Pilonieta, P., & Medina, A. L. (2009). Reciprocal teaching for the primary grades: We can do it too!. The Reading Teacher . 63 (2): 120–129. doi: 10.1598/rt.63.2.3.

Vygotsky, L.S. (1978). Mind in society: The development of higher psychological processes . Cambridge, MA: Harvard University Press.

Williams, Joan (2010). Taking on the role of Questioner: Revisiting reciprocal teaching. The Reading Teacher , 64 (4): 278–281. doi: 10.1598/RT.64.4.6.

Yu-Fen, Y. (2010). Developing a reciprocal teaching/learning system for college remedial reading instruction. Computers and Education , 55 (1): 1193–1201. doi: 10.1016/j.compedu.2010.05.016.

• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 25 Number Games for Kids (Free and Easy)
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 25 Word Games for Kids (Free and Easy)
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 25 Outdoor Games for Kids
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 50 Incentives to Give to Students

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Reciprocal Teaching in Mathematics

Return to: ETAP 623 Spring 2020 (Zhang) | Olivia's Portfolio Page ] | About Me

Welcome to my mini course on Reciprocal Teaching in Mathematics.

After reading over the summary of this course, if you are ready to begin learning click here

Purpose Of this Course

Purpose: The purpose of this course is to explore the idea of reciprocal teaching in mathematics, and the benefits it can have on your students to deepen their thinking process, begin to use protocols without assistance and facilitation, and to learn to speak to their work and the strategies they have chosen. Through this implementation, students will also begin to build their strategy 'tool box,' (as we will discuss in this mini-course) critically reflect on their work, ask themselves questions, and how to monitor their own progress.

This course will teach you to foster the use of 21st Century Skills in your classroom such as collaboration, critical thinking, and problem solving. Through the use of reciprocal teaching students will learn the benefit of meaningful discussion with their peers, strengthen their problem solving skills, and to critically analyze their own work. Furthermore, the implementation of reciprocal teaching will allow for a more student centered classroom.. isn't that every teachers goal?!

Summary of Needs Analysis

Summarization of Survey and concluded intent of this course: While Reciprocal Teaching has been widely explored in Reading and Writing Curriculums there is much less information and resources about Reciprocal Teaching within mathematics and the benefit it can have on students. While working in a focus school, I have helped to develop a strong math supplemental math curriculum to what we are already using (Eureka) to foster students learning through collaboration with their classmates, problem solving, and true analysis of math problems. To better build my course I surveyed 35 Pre-K through Grade 12 teachers. The 35 teachers were asked a total of eight questions, the first 3 being a bit on their background in teaching, and the remainder on reciprocal teaching or other aspects of it. Concluding the survey it became apparent to me that there is a strong understanding of reciprocal teaching but very limited understanding of how to utilize it in mathematics and to make a classroom climate more student centered. The intent of this course after my needs analysis is to help teachers create an understanding of what Reciprocal Teaching is, the benefits it can have in their classrooms, and to help create activities that can reach all students, as well as the ways in which it can be rolled out to help address misconceptions of how difficult it can be when transitioning to a student centered classroom.

Performance Objectives

This course is intended to educate on the importance of incorporating 21st Century skills into the classroom to create responsible and problem-solving learners, and Reciprocal Teaching in Mathematics is just the way to do so. After completing this course, learners will develop a complete full circle understanding they can take with them an incorporate in all subjects when adapted, but more specifically mathematics. Concluding this course, learners will:

• Define Reciprocal Teaching and why it can be used as a very student centered approach.
• Explain the importance of releasing the responsibility of learning onto the students.
• Create and develop lessons and activities to help roll out reciprocal teaching in their classroom.
• Define the major 21st Century skills being touched on with reciprocal teaching, and why each is important to instill in our students.
• Have a plethora of resources to begin carrying reciprocal teaching into their classroom.

Course Units

Prerequisites: An identified prerequisite skill needed for this mini-course is that the learning must have a good understanding of what a student centered classroom should look like. Click any of the following unit links to visit that Units Section.

Unit 1: What is Reciprocal Teaching.

1) Explore the importance of a student centered classroom

2) Benefits of meaningful discussion

Unit 2: Key 21st Century Skills and their importance in the classroom.

1) Critical Thinking

2) Collaboration

3) Communication

4) Creativity

Unit 3: Tying it All Together.

1) How Reciprocal Teaching is a great way to incorporate these 21st Century Skills

2) Gradually Releasing the Responsibility

Unit 4: Using Reciprocal Teaching in the Classroom.

2) Materials

3) Resources

4) Rolling it out

Curriculum Map

References and Resources

Applied Educational Systems, Inc. (n.d.). What Are the 4 C's of 21st Century Skills? Retrieved from https://www.aeseducation.com/career-readiness/what-are-the-4-cs-of-21st-century-skills

Hunt, B. (2017, March 4). Using Reciprocal Teaching in Mathematics. Retrieved April 2020, from https://prezi.com/uqu2gkqn0p7y/using-reciprocal-teaching-in-mathematics/

Lewis, B. (2019, October 16). Why Are Children Sorted Into Homogenous Groups in Education? Retrieved April 2020, from https://www.thoughtco.com/homogeneous-groups-in-educational-settings-2081647

Parent, L.. (2015, April 1). Reciprocal Teaching Math Lara Parent [Video]. Youtube. https://www.youtube.com/watch?v=4Vqe7laL5DE&t=6s

Ross, D. (2018, August 15). Empowering Our Students with 21st-Century Skills for Today. Retrieved from: https://www.gettingsmart.com/2017/04/empowering-students-21st-century-skills/

Stauffer, B. (n.d.). What Are 21st Century Skills? Retrieved from: https://www.aeseducation.com/blog/what-are-21st-century-skills

Sweat, S. (2017, April 3). 21st Century Skills: The 4Cs [Video file]. Retrieved from: https://www.youtube.com/watch?v=BXT2STtm_54

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• Cooperative Learning Techniques
• Think-pair-share : As probably the best known cooperative learning exercise, the think-pair-share structure provides students with the opportunity to reflect on the question posed and then practice sharing and receiving potential solutions. Its simplicity provides instructors with an easy entry into cooperative learning and it is readily adaptable to a wide range of course constructs. (Example: Where Do I Begin? Using Think-Pair-Share to Initiate the Problem Solving Process )
• Three-step interview : This structure can be used both as an ice-breaker which introduces students to one another and to provide students with a venue for soliciting opinions, positions, or ideas from their peers. Students are first paired and take turns interviewing each other using a series of questions provided by the instructor. Pairs then match up and students introduce their original partner. At the end of the exercise, all four students have had their position or viewpoints on an issue heard, digested, and described by their peers.
• Note-taking pairs : Poor note-taking leads to poor performance. Designing an exercise which requires students to summarize their understanding of a concept based on notes taken (with directed questions such as what is the definition of a concept, how is it used, what are the three most important characteristics of a topic) and receiving reflective feedback from their partner provides students the opportunity to find critical gaps in their written records.
• Jigsaw : For more complex problems, this structure provides students the opportunity to develop expertise in one of many components of a problem by first participating in a group solely focused on a single component. In the second stage of the exercise, groups are reformed with a representative from each expert group who together now have sufficient expertise to tackle the whole problem.
• Group grid : Students practice organizing and classifying information in a table. A more complex version of this structure requires students to first identify the classification scheme that will be used.
• Sequence chains : The goal of this exercise is to provide a visual representation of a series of events, actions, roles, or decisions. Students can be provided with the items to be organized or asked to first generate these based on a predetermined end goal. This structure can be made more complex by having students also identify and describe the links between each of the sequenced components.
• Dyadic essays : Students prepare for the in-class portion of this exercise by developing an essay question and model answer based on assigned reading. Students typically need to be guided to develop questions that integrate material across classes as opposed to ones that simply recite facts presented in the reading. In class, students exchange essay questions and write a spontaneous answer essay. Students then pair up, compare and contrast the model answer and the spontaneously generated answer. Subsequently, questions and answers can be shared with the larger class.
• Peer editing : As opposed to the editing process that often appears only at the final stage of a paper, peer editing pairs up students at the idea generation stage and peers provide feedback throughout the process. For example, the relationship begins as each student in the pair describes their topic ideas and outlines the structure of their work while their partner asks questions, and develops an outline based on what is described. See also, peer review .
• Send-a-problem : Students participate in a series of problem solving rounds, contributing their independently generated solution to those that have been developed by other groups. After a number of rounds, students are asked to review the solutions developed by their peers, evaluate the answers and develop a final solution. (Example: Understanding the Impact of (Fiscal and Monetary) Policy)
• Three-stay, one-stray : Even students working in groups can benefit from the feedback of additional peers. In this structure, students periodically take a break from their work (often at key decision making points) and send one group member to another group to describe their progress. The role of the group is to gain information and alternative perspectives by listening and sharing. The number of times the group sends a representative to another group depends on the level of complexity of the problem. This method can also be used to report out final solutions.

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Making meaning in mathematics problem-solving using the Reciprocal Teaching approach

Meyer, Kylie (2014) Correction to: Making meaning in mathematics problem-solving using the Reciprocal Teaching approach. Literacy Learning: The Middle Years , 22 (2), pp. 7-14.

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Description

This paper examines the application of the Reciprocal Teaching instructional approach to Mathematical word problems in the middle years. The Reciprocal Teaching process is extended from the four traditional strategies of predicting, clarifying, questioning and summarising, to include further cognitive reading comprehension strategies applied to the context of solving Mathematical word problems.

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Making meaning in mathematics problem-solving using the Reciprocal Teaching approach

• Kylie Meyer
• Published 1 June 2014
• Mathematics, Education

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• How to effectively implement Reciprocal Teaching in a learning environment

Students all learn in different ways which is why there are several different teaching techniques that teachers can use to convey course work effectively. Reciprocal Teaching is one of the methods being used by teachers to create more engagement and a better understanding of what students are learning. This teaching method has proven to be extremely successful in improving comprehension skills, reading ability, as well as encouraging critical thinking and creativity. An adaption of this learning method can also be used in an online learning environment and to facilitate service-learning activities.  

What is Reciprocal Teaching?

Ann Brown and Annemarie Palincsar developed Reciprocal Teaching as a method of reading comprehension instruction. This teaching technique is often said to be a scaffolded or supported discussion technique where students are taught to use strategies, questioning, clarifying, summarizing, and predicting, in a collaborative text-based dialogue[1]. This principle of teaching revolves around four global comprehension strategies: predicting, questioning, clarifying, and summarizing. In the classroom, the teacher explains these strategies to small groups using a shared text, first modeling their use, and then asking students to lead their groups[2].

The breakdown below provides insight into how to apply these four global comprehension strategies in the classroom[3]:

1.  Prediction

a.  Ask students to predict what they think the reading may be about. Get them to think about what is going to happen by asking questions as a detective might do.

2.  Question as you go

•       Right-there questions (answer in the text)
•       Between-the-lines questions (inference needed)

3.  Clarify

•       How do I pronounce that?
•       What does the word mean?
•        I think the author is saying…

4.  Summarize

a.  Students summarize verbally, within pairs, and then share with their assigned small group or record their summary and read it aloud to their small group.   

• After you have modeled the previous steps, students may continue working in their small groups by silently or orally reading the next sections of the reading while conducting the four-step process.

*Follow the link for useful Reciprocal Teaching templates and tools

This teaching method has been proven to be a successful comprehension strategy and can be implemented across several different teaching disciplines and grade-levels[4]. It also encourages students and teachers to actively get involved with what is being learnt and taught to create better understanding and a more collaborative learning environment.

Can this teaching technique be used in an online learning environment and still be as effective?

There is no doubt that Reciprocal Teaching has been highly effective in physical classrooms, but with an increase in digital transformation and more online education options being available, can these techniques be used in an online environment? To answer simply, no. These techniques need to be adapted for online learning in the form of Online Reciprocal Teaching.

Online Reciprocal Teaching builds on the same principles as Reciprocal Teaching, as they both promote the gradual release of responsibility to students. Where Online Reciprocal Teaching differs is the use of three specific phases:

• Phase 1: centers around computer basics, word processing skills, web searching, navigation basics, email and more. The length and breadth of this phase will vary by need, and the previous experience students have with computers[5].
• Phase 2: is a collaborative phase during which both teachers and students conduct think-aloud demonstrations and mini-lessons. Teacher modeling in the beginning of the phase gives way to student modeling in the latter half. Students take responsibility for teaching/leading/facilitating their peers with a variety of online reading comprehension strategies. Instruction also begins to move from search skills to critical evaluation and synthesis skills[6].
• Phase 3: students work, both individually and in small groups, at using strategies and skills from the previous phases to develop lines of inquiry around curricular topics. This type of project requires clear questions, multiple reliable sources, citations, and a final product that communicates that information to others[7].

This teaching method aims to build the online reading comprehension strategies of questioning, locating, evaluating, synthesizing and communicating[8]. Online Reciprocal Teaching also challenges students to think critically, communicate, and fosters creativity and collaboration.

How do these learning techniques tie into service-learning?

Both Reciprocal Teaching methods are focused on inquiry and problem-based tasks, which makes service-learning a perfect pedagogy for pairing with this technique. Through service-learning, students are challenged to investigate and research problems within their community and formulate an action plan for a solution in ways this could assist. Several service-learning projects can be implemented both inside the classroom and online, that fit into both the Reciprocal and Online Reciprocal Teaching techniques that will take students through the “5 C’s of Change”. These include[9]:

• Creativity: Students use divergent-thinking skills to generate their own questions and keywords for online searches. Their final projects require them to creatively express their own point of view.
• Communication : Students share what they learn as they work in small groups and with the whole class. They communicate this in the classroom or online with a broader audience by posting on a class blog.
• Collaboration: Students create collaborative knowledge through inquiry and social interactions. They comment and connect either in person or using technologies such as VoiceThread and support one another through instant messaging.
• Critical Thinking: Through these activities, students are challenged to think about different opinions, experiences and texts that they have read and then need to choose for themselves what to think. Through this, students learn to question perspective/s and biases.
• Comprehension: Students learn essential reading and comprehension skills,  by carefully reading; course work, research, articles, blog posts and editorials. They carefully read the texts they encounter to understand and evaluate different perspectives.

At the core of Reciprocal Teaching is a need to engage students and create interaction with their course work. These teaching techniques ultimately give students the responsibility for their learning while facilitating critical thinking. These teaching methods allow students to take control and take the lead while enhancing their learning experience through peer discussions, collaboration, and student-centered learning approaches. This aims to improve students’ understanding, application, and retention of what they are learning and promotes the development of communication skills, leadership and problem-solving capabilities.

For more on classroom management strategies that could help you click here  

[1] Lubliner, S. 2001. Reciprocal Teaching: An Alternative to Gatekeeping Practices.Classroom Leadership. Volume 5. Number 3. Viewed on16 July 2020. http://www.ascd.org/publications/classroom-leadership/nov2001/Reciprocal-Teaching.aspx

[2] J. G. McVerry, L, Zawilinski, W. I.O’Byrne. 2009. Navigating the Cs of Change.Teaching for the 21st Century. Educational Leadership. Viewed on 16 July 2020. http://www.ascd.org/publications/educational-leadership/sept09/vol67/num01/Navigating-the-Cs-of-Change.aspx

[3] Palincsar, A. S, Brown, A. (1984). Reciprocal Teaching of Comprehension-Fostering and Comprehension Monitoring Activities. Cognition and Instruction, 1(2), pp. 117-175.

[4] ReadingRockets.org. Reciprocal Teaching. Viewed on: 16 July 2020. Available at: https://www.readingrockets.org/strategies/reciprocal_teaching

[5]  J. G. McVerry, L, Zawilinski, W. I.O’Byrne. 2009. Navigating the Cs of Change.Teaching for the 21st Century. Educational Leadership. Viewed on16 July 2020. http://www.ascd.org/publications/educational-leadership/sept09/vol67/num01/Navigating-the-Cs-of-Change.aspx

[6]  J. G. McVerry, L, Zawilinski, W. I.O’Byrne. 2009. Navigating the Cs of Change.Teaching for the 21st Century. Educational Leadership. Viewed on16 July 2020. http://www.ascd.org/publications/educational-leadership/sept09/vol67/num01/Navigating-the-Cs-of-Change.aspx

[7]  J. G. McVerry, L, Zawilinski, W. I.O’Byrne. 2009. Navigating the Cs of Change.Teaching for the 21st Century. Educational Leadership. Viewed on16 July 2020. http://www.ascd.org/publications/educational-leadership/sept09/vol67/num01/Navigating-the-Cs-of-Change.aspx

[8]J. G. McVerry, L, Zawilinski, W. I.O’Byrne. 2009. Navigating the Cs of Change.Teaching for the 21st Century. Educational Leadership. Viewed on16 July 2020. http://www.ascd.org/publications/educational-leadership/sept09/vol67/num01/Navigating-the-Cs-of-Change.aspx

[9] J. G. McVerry, L, Zawilinski, W. I.O’Byrne. 2009. Navigating the Cs of Change.Teaching for the 21st Century. Educational Leadership. Viewed on16 July 2020. http://www.ascd.org/publications/educational-leadership/sept09/vol67/num01/Navigating-the-Cs-of-Change.aspx

Tara brings passion and a deep understanding of service learning, rooted in years of experience, to her training. Her training builds bridges from theory to implementation while generously sharing her resources and knowledge to ensure our success. Tara works with the whole school (administration, teachers, students, and SL leaders) to build a sustainable program that is embedded in the curriculum and tied to the mission. She energized a faculty on a Friday afternoon, no easy feat, leaving them with a desire to learn more about SL and to become more involved. I cannot recommend Tara highly enough.

Tara Barton

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What is reciprocal teaching?

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Reciprocal teaching in math

How effective is reciprocal teaching.

As a teacher, you know how difficult it can be to  personalize learning  to keep students interested in school subjects — especially when students don’t understand the subject matter.  Reciprocal teaching strategies  have been shown to increase student reading comprehension and improve overall literacy.

Reciprocal teaching not only helps with learning, but it also gets kids excited to participate in a lesson.

While this sounds amazing, what exactly  is  this strategy — and how do you introduce it to your classroom?

We’ll not only show you how reciprocal teaching works, but also how to incorporate it into your lessons. A 2009 study by Cooper and Greive suggests the skills used in reciprocal teaching go beyond helping students understand their readings.  Their findings stated :

“… the experimental group benefited from [reciprocal teaching] strategies in ways other than knowledge of the content of the readings. They gave evidence of finding the process interesting and were enthusiastic in their involvement.”

Reciprocal teaching gets students excited to learn by actively involving them in readings, making them more likely to understand given texts.

Reciprocal teaching  refers to a classroom activity where students are shown common comprehension strategies, in dialogue with the teacher and their peers, to better understand a text. These strategies get students more involved throughout the reading process, helping them stay engaged and improving their overall comprehension skills.

Reciprocal teaching follows the “I do, we do, you do” formula.

First, you demonstrate how the strategies work, then students work together in small groups to better understand the process, and finally, once students are comfortable, they use these strategies on their own.

What are the reciprocal teaching strategies?

There are four parts, or “building blocks” to improving reading comprehension and engagement, which are: predicting , questioning , clarifying and summarizing .

Each one of these building blocks plays an important role in helping students:

• Improve literacy   —  Rather than skipping over words they don’t understand, students are encouraged to figure out what they mean, helping them with current and future readings.
• Stay engaged   —  Students are actively looking for different clues and ideas throughout readings, helping them to stay interested in a text.
• Boost reading comprehension   —  The four building blocks give students the tools needed to decipher a text and understand the ideas being presented to them.
• Learn on their own or in groups —  Reciprocal teaching puts students in the position to improve their reading comprehension through teamwork so they are better suited to work by themselves on future projects.

Reciprocal teaching strategy: the four building blocks

To understand these strategies, it’s important to think about how we learn while reading a text. Good readers naturally piece together words and understand ideas in written form, but how do they get there?

Sullivan Palincsar and Ann L. Brown developed the original reciprocal teaching strategies in  their 1984 study . They demonstrated that using the “four building blocks”  actively supports student reading comprehension .

Let’s look at each building block in more detail:

1. Predicting

There are two parts to “predicting” a text. The first involves predicting what is going to happen overall in a reading; the other involves predicting what is going to happen  next  in a section or chapter. They sound similar but both have different processes.

• Part 1 —  Predict what will happen throughout a text by using the title, imagery (such as cover art), or even a brief summary. Then use those clues to make your prediction of what happens in the entire piece.
• Part 2   —  Skim the next bit of text you’ve been assigned to read, and pick out certain words, sentences, or images. From that quick overview make a prediction as to what is going to happen next in the text.

You want your students to avoid broad predictions that don’t give any real insight into what a reading is about. Predictions should state  what  the reader thinks the author’s purpose is in a text and give evidence as to  why  the reader has come to such conclusions.

Encourage your class to phrase their answers with evidence, for example:  “I think ‘X’ because of ‘Y’”.

Let’s say your class is covering World War ll in History class and your students are assigned Anne Frank’s  The Diary of a Young Girl . You wouldn’t want simple predictions like, “I think it’s about a young girl who writes a diary”.

Rather, encourage your students to work harder and predict something in greater detail: “Based on the summary on the back of the book, I predict this book contains real diary entries from a teenage girl trying to survive with her family during the Nazi occupation of the Netherlands.”

Making a prediction with evidence will help students connect more with a text and activate prior knowledge — making them more involved in the reading process. When learners are involved with the text, they are more focused, which will help them understand what is happening throughout it.

2. Questioning

Admitting you don’t understand something is a crucial part of the learning process. You want your students to take the time to pause and write down questions they have as they read through a portion of a text.

You also want students to question why certain things are important within the reading. However, asking questions can be hard and many students don’t know where to start. The easiest way is to ask:

Asking, discussing, and answering questions gets students involved with the reading, ensures they’re paying attention to important details and helps them use metacognitive strategies to make sense of a text.

Lori Oczkus, the author of  Reciprocal Teaching at Work , observes:

“Younger students naturally wonder and ask questions about the world around them. When students are encouraged and taught to ask questions as they read, their comprehension deepens.”

3. Clarifying

Clarifying is used to make sure students continue to understand what they’re reading throughout the entire process. This could be as simple as identifying unknown words to something more complicated such as explaining the key concepts of a particular passage.

Clarifying is a two-step process where students:

• Identify that they are confused by an idea or word
• Take steps to resolve the confusion and better understand the text

Give your students a good idea of what it feels like to misunderstand a passage so they can identify this problem themselves. In the book,  Reading Essentials: The Specifics You Need To Teach Reading Well  by Regie Routman, the author  states  that many young readers don’t know when they’ve lost meaning in a text.

Students can get tripped up by long, complicated words, hard-to-interpret images such as graphs or tables, convoluted sentences, or complex ideas. You need to show them some decoding strategies to resolve these problems:

• Reread the passage —  On average, we can only focus for  10-15 minutes  before needing a break. Sometimes, we don’t even realize our brains are distracted until several minutes later. An easy fix is to reread the passage to get a grip on the ideas that were just presented.
• Break down complicated parts —  Breaking down what’s confusing readers can help with overall comprehension. Have students read a complex sentence slowly and separate it into smaller parts, reading the bits on their own and clarifying the sections that don’t make sense by looking up words or asking for help.
• Find answers with problem-solving strategies — Show your students how to clarify different questions by saying things like, “This sentence didn’t make sense to me, so I reread the passage to understand it better”.

4. Summarizing

Summarizing involves condensing a reading to its most important points in both written and verbal forms. This can be a complicated task, but when done correctly, summarizing can greatly improve a student’s understanding of a reading.

Encourage students to stop often throughout a reading to make summative notes on the text. Summarizing each portion of a text creates a roadmap for students to see which parts they understand. During group work, students should be able to verbalize their summaries to their classmates.

At the end of the reading, students can combine their smaller summaries to make one full-length overview that gives you insights into your student's ability to understand the text.

What are the best ways for students to summarize a reading?

Ask critical thinking questions throughout the reading process that helps comprehension of the important points. Ask students questions like:

• What was this part about?
• What happened at the beginning, middle or end?
• What are the most important ideas from this paragraph, section, or reading?

Summarizing is a key contributor to improving reading comprehension. The ability to create a complete summary shows that students have been able to not only understand a reading but also describe it in their own words.

What is an example of a reciprocal teaching lesson plan?

Now that you know the different strategies of reciprocal teaching, it’s time to bring them to life in your lesson plan . Think of reciprocal teaching like any kind of physical exercise: If you want to see results, you will need to do it more than every once in a while. However, overdoing it can be exhausting. Aim to train students a couple of times a week and see how they’re doing over different periods.

Let’s get started!

Step 1: Teacher modeling

First, you need to teach your students the mechanics of the four building blocks: Predicting, questioning, clarifying, and summarizing.

Over the course of a week, spend a day on each building block. Take students through sample passages and show them how you would make predictions, ask questions, clarify foggy areas, and summarize the text.

Next, open the lesson up to the class and let various students try their hand at each of the four building blocks. If it feels like there are certain strategies the class doesn’t understand, you can spend extra time reinforcing those ideas.

During this step, you want to make sure you are giving relevant examples that are easy to understand, and also ensure your students are engaged with the discussion. Calling on students randomly to help with different examples is a great way to keep the whole class on their toes!

Step 2: Group work

Before you split up your class, do a quick review of the four building blocks to jog your students’ memories. Next, you should divide your students into small groups of four. In these groups your students will:

• Be given the role of either, predictor, questioner, clarifier, or summarizer
• Read a passage you have assigned
• Play the role of instructor for the strategy they were given at the end of the passage
• Rotate roles after everyone has presented and continue to the next passage

As your students are working through this cooperative learning assignment together, you will want to jump from group to group to answer questions, get involved in group discussions and see how group members are handling their roles. Try and lead your students to the correct path if they’re struggling, but don’t simply give them the answer.

You may want to put visuals up around the classroom to give students tips on how to fulfill their role.  The National Behaviour Support Service  gives some great visual guides you can use such as the one below.

Credit: National Behaviour Support Service

End your class with a discussion on how using the four building blocks helped the students understand their readings that day. Listen to feedback and see if there was any confusion that you can address in future lessons.

Step 3: Individual work

After modeling how to incorporate the four building blocks into readings and having your students work together for a few sessions, it’s time to see how they do on their own.

You’re gradually giving students more responsibility with each step, so make sure they’re prepared.

Give students a reciprocal teaching worksheet, like the one below, for them to work on as they complete their assigned readings.

The question-generating worksheet will help students stay on track as they work through readings on their own. It will also act as a way for you to track their progress as they build their reading skills!

Step 4: Track progress

Collect your students’ worksheets after they have completed them and the reading for the day. Read the worksheets thoroughly to see if there are any building blocks that need to be covered more in-depth.

Give students feedback  in their worksheets on how they’re doing, or give them tips to help with problem areas.

After reviewing the worksheets, you can work together as a class to clarify any problem areas. This is a great way to help students who are struggling with concepts more than others without singling them out or making them feel uncomfortable.

For the most part, the reciprocal teaching process we discussed helps students improve their reading comprehension strategies in language-based subjects. Is it possible to adapt these strategies to other subjects?

The answer is yes!

Mathematical literacy is the ability to analyze, problem-solve, and reason with the use of numbers and mathematical equations. It is the understanding of different mathematical terms such as sum or median, and the ability to decipher what math problems are actually asking.

A  2009 study  done by Yvonne Reilly, Jodie Parsons, and Elizabeth Bortolot showed that reciprocal teaching in math can significantly improve students’ understanding of  word-based problems  and “… students were able to explain … what they had done and how they had come up with the answer”.

Students who used reciprocal teaching methods to solve problems were able to better understand questions and solve more problems correctly than students who were not taught with the same method.

The strategies for reciprocal teaching in math are similar to those in language-based classes, however, there are a few differences.

• Predicting —  Once again, we have predicting as a fundamental building block. This time students will predict what type of mathematics they will need to use to solve certain questions, and also to predict what their answers will look like.
• Clarifying —  First, students identify all the words they don’t know within a problem. Next, readers state all the relevant facts they  do  know, such as values or statements from the problem. Finally, the students need to identify the information they do not yet have but will need to solve the problem. During the final step, students are encouraged to work together with classmates.
• Solving —  During this stage, readers solve the problem, explaining what they ’re doing in each step and how they reached the solution.
• Summarizing —  In this stage, students reflect on what they contributed to the overall group and how they would refine the solution they used to solve the problem. This helps students solve similar problems more efficiently in the future.

Applying the same integration as the language-based strategy (teacher modeling, group work, individual work, tracking progress) should yield similar results in the comprehension of word-based math problems.

Tracking progress in math classes is even easier with game-based learning platforms like Prodigy Math , which you can use to assign problems, see results, and make decisions based on how your students are learning.

The 2009 study  revealed incorporating reciprocal teaching into the classroom to be an overall success saying that “as a student’s comprehension increases they are more able to identify the mathematics which is required for the solution”.

If there is required language comprehension of any kind in the subject you’re teaching, then reciprocal teaching is an effective way to help your students understand the content more deeply. The strategy has been shown to help in subjects like English, math, science, and history.  

Reciprocal teaching strategies are based on incorporating four fundamental building blocks into the classroom so students have a better idea of how to digest assigned readings. These building blocks are:

• Questioning
• Summarizing

Children often have trouble identifying  why  they don’t understand certain readings. Properly incorporating the strategies we listed above can help your students with  the learning process  and improve their overall reading abilities!

Create or log in to your teacher account on Prodigy English  — a free, game-based learning platform that assesses student progress and performance as they play. Aligned to Common Core State Standards for grades 1 to 5, it's an engaging adventure that helps kids get excited about building literacy skills.

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Reciprocal Teaching in Mathematics RECIPROCAL TEACHING IN MATHEMATICS

Related Papers

AJHSSR Journal

The study was conducted to determine level of performance using reciprocal teaching in Mathematics among Grade 9 students in Lauis National High School of Zone 1, DepEd Division of Zambales. Reciprocal teaching was used in this research because it was believed to be useful technique for enhancing students' performance. This research study employed quasi (descriptive-experimental) research design. Descriptive and inferential statistics were used for data analysis, interpretations and discussions. Findings show that the pre-test performance of the Grade 9 students in parallelogram in terms of 'proving that both pairs of opposite sides are parallel' was Approaching Proficiency. However, the pre-test performance on 'proving that both pairs of opposite sides are congruent'; 'proving that both pairs of opposite sides are both congruent and parallel'; 'proving that the diagonals of the quadrilateral bisect each other'; and 'proving the pairs of opposite angles are congruent' was Beginning. The post-test performance of the students in terms of proving that both pairs of opposite sides are parallel and proving the pairs of opposite angles are congruent was Approaching Proficiency. While the posttest performance on 'proving that both pairs of opposite sides are congruent'; 'proving that both pairs of opposite sides are both congruent and parallel'; and 'proving that the diagonals of the quadrilateral bisect each other' was Developing or Fairly Satisfactory. Moreover, a significant difference on the students' performances on pretest and posttest in proving that both pairs of opposite sides are congruent; in proving that both pairs of opposite sides are parallel; in proving that both pairs of opposite sides are both congruent and parallel; in proving that the diagonals of the quadrilateral bisect each other; and in proving the pairs of opposite angles are congruent was established. The researcher recommends that Mathematics teachers may take opportunities to further improve the skills in the utilization of reciprocal teaching in secondary Mathematics. Mathematics teachers in secondary schools in the Division of Zambales may utilize further the reciprocal teaching and other teaching pedagogies and learning activities aimed for the students to further learn parallelogram primarily proving that both pairs of opposite sides are congruent; proving that both pairs of opposite sides are both congruent and parallel; and proving that the diagonals of the quadrilateral bisect each other. The public secondary school in the Division of Zambales may introduce the use of reciprocal teaching to learners in the Junior and Senior High school levels. They may formulate policies that would encourage teachers to utilize reciprocal teaching approach for their classes to maximize teachers' potential in making more effective strategies. Lastly, the Mathematics teachers are encouraged to conduct an indepth study on the effects of reciprocal teaching and other teaching pedagogies in Mathematics in other year levels (Junior and Senior High school) in secondary schools in the Division of Zambales.

International Journal of Research Publications

Rosemarie Bachar

Jurnal Elemen

Dina Apryani

This study is intended to result in instruction that will help pupils improve their mathematics understanding skills. The similarity of strategies in both the scientific and reciprocal teaching approaches makes it difficult to choose which approach is better. This investigation aims to investigate and explain (1) Improving pupils' mathematical understanding through comparison of scientific approaches and Reciprocal Teaching based on PAM; (2) The impact of the interaction between learning approaches with pupils' PAM on enriching pupils' mathematics understanding ability. It is a quasi-experimental research project that uses two experimental classes. The results of this study are (1) Pupils who learn through the scientific approach and pupils who learn through reciprocal teaching strategies based on PAM pupils have different mathematical thinking abilities, with the average value of improvement in the scientific approach class being more significant than the reciprocal tea...

Reciprocal Learning for Cross-Cultural Mathematics Education

Cynthia Zhu

International Journal of Multicultural and Multireligious Understanding

Nunung Azizah

The most significant concern in teaching mathematical concepts is developing and improving mathematical communication skills. However, the reality reveals that communication skills possessed by students are still relatively low. This causes students’ difficulty in understanding the material, solving problems, and conveying mathematical ideas both in oral or written form. Furthermore, students’ teaching material is not adequate to support the expected learning goals. It creates students’ difficulty in understanding the materials and it doesn’t integrate mathematical communication skills. This study aims to develop teaching materials in the form of mathematics module based on reciprocal teaching to improve students' mathematical communication skills. This is a research development that employs Four-D model. Subjects of the study are the teachers and the seventh grade Junior High School. In collecting the data, the researchers employ observation, interviews, questionnaires, and mat...

Journal Of Educational Experts (JEE)

Aang Rohimat

This research is motivated by the lack of connection capabilities junior high school students in Bandung West. This study will examine the achievement of matemati connection capabilities of students usinglearning reciprocalteaching with the usual approach. The method used is an experimental method to design pretest-posttest control group, ie design involving at least two groups and randomly sampling classes. At the beginning and end of the study both classes were given the test. The population in this sample is the entire junior high school students in Bandung West whose characteristics have a low ability mathematical connections. Of the entire junior high school in West Bandung randomly selected and elected SMP Negeri Bandung Barat representing the characteristics of the population. The sample was selected randomly, where class G into the experimental class VIII, and VIII F be the class of the control. Collecting data in this study using a test description that has been tested firs...

Kylie Meyer

This paper examines the application of the Reciprocal Teaching instructional approach to mathematical word problems in the middle years. The Reciprocal Teaching process is extended from the four traditional strategies of predicting, clarifying, questioning and summarising, to include further cognitive reading comprehension strategies applied to the context of solving mathematical word problems.

Online Submission

Diane Tracey , Rebecca Todd

(JIML) JOURNAL OF INNOVATIVE MATHEMATICS LEARNING

Agung Prasetio s

This study is a pretest-postest experiment control group design having a goal to analyze the role of Previous Mathematical Ability and Reciprocal Teaching in mathematics (RTM) on students’ mathematical reasoning ability (MRA) and self concept in mathematics (SCM). The study involves 66 seventh grade students, a PMA test, a MRA test, and a SCM scale, and student’s perception on RTM. The study revealed that RTM took better role than PMA on obtaining MRA and SCM. For entirely students and of students with high PMA in both teaching approaches and the grades of MRA and SCM were at high level. Besides that, study found there were no association between MRA and SCM and there were no interaction between PMA and teaching approaches toward RMA and SCM. Like that, students expressed positive opinion on RTM, even if, student still realized few difficulties in solving MRA,

Jurnal Pedagogy

Umi Yawisah

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The 2024-25 Outstanding Teaching Awards: Bradley Elliott

Each Wednesday, UKNow is highlighting one of the winners of the University of Kentucky’s 2024-25 Outstanding Teaching Awards, given by the Office for Faculty Advancement with the Office of the Provost.

LEXINGTON, Ky. (July 17, 2024)  — Bradley Elliott, Ph.D., lecturer in the  Department of Mathematics  in the  College of Arts and Sciences , is one of nine winners to receive the University of Kentucky’s 2024-25 Outstanding Teaching Awards.

These awards identify and recognize individuals who demonstrate special dedication to student achievement and who are successful in their teaching. Recipients were selected via nomination and reviewed by a selection committee based in the UK Provost’s  Office for Faculty Advancement  and the  Center for the Enhancement of Learning and Teaching . Elliott is one of three Category 2 winners, which honors lecturers and clinical title series faculty.

“Winning this award is meaningful to me partly because I know how much great teaching goes on throughout the university,” Elliott said. “The pool of nominees must have been very strong. I think UK’s CELT is partially to thank for raising the ​quality of teaching across UK.”

In the mathematics classes Elliott teaches, he focuses on active learning and student collaboration. He designs lessons and assignments that develop students’ problem-solving skills, so students are better prepared to solve novel problems in the future.

“I try to personalize my lessons by using what I know about my students (their names, major, goals),” he said. “I want them to feel a connection to what we learn. I also use technology where appropriate to enhance the lesson — with so much helpful technology at hand, it doesn't make sense to teach the same way we did 30 years ago.

“Our students deserve excellent teaching. Considering the barriers some of our students overcome just to make it to class each day, we as teachers should match their level of effort and dedication to help them succeed.”

Uwe Nagel, Ph.D., professor and chair of the math department, nominated Elliott for the award.

“[Elliott] appears to do wonders in and outside the classroom no matter how difficult the task is,” Nagel said. “He has taught College Algebra (MA 109), Contemporary Mathematics (MA 111) — [these two courses] serve mainly nonscience majors who often have had unsatisfactory prior mathematics experiences and are not very motivated to study the subject. Moreover, these classes are taught in lectures of about 70 students. Elliott is very aware of the challenges and addresses them very thoughtfully using a variety of methods.”

Elliott is a member of Project NExT (“New Experiences in Teaching”), a national program for new faculty in mathematics. Since 2022, he has been participating in the Teaching Innovation Institute, a CELT program at UK, which focuses on strategies to improve education.

During the summer, he is a faculty member at the Kentucky Governor's Scholars Program, working with high-achieving high school seniors.

Most recently he was named a 2024 Great Teacher by the UK Alumni Association and received 2023 Outstanding Teaching Award from the College of Arts and Sciences.

A two-time graduate of UK, Elliott earned his bachelor’s in computer science and his master’s in business administration before heading to Emory University to earn his Ph.D. in 2020.

This year’s Outstanding Teaching Awards were given to six faculty and three graduate teaching assistants. Each winner received an award certificate, a commemorative engraved gift and a cash award in recognition of their teaching excellence at a campus ceremony on April 25.  Read more here .

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How to Teach Problem-solving to Preschoolers: 10 Effective Ways

• July 18, 2024
• Kangaroo Kids

Raising a kid is no small feat and requires a lot of patience and understanding. It requires you to train them for their future life as adults. An important part of raising kids is making them adept at quickly making correct decisions. Consider yourself; you must make a lot of decisions in your day-to-day life. This could be anything ranging from taking the shortest route to your office by avoiding traffic, deciding what to cook, especially when you are in a time crunch, or having a difficult conversation with your partner. You can skillfully navigate all of these because you already learned the art of problem-solving. Well, now it’s time for your kids to learn it, too.

What is Problem Solving for Children?

Problem-solving is the ability to handle a difficult situation with calmness and patience and reach a solution that benefits all parties. It is a great virtue that must be cultivated in all young minds.

Consider the situation where your child and his/her friend are playing with a toy car, and all of a sudden, one of them pushes the other and snatches the toy. This is a conflict situation that arose clearly because the toy was unequally shared between both. However, it could have been avoided if the kids had problem-solving abilities. Instead of pushing, the kid could have requested to play with the toy next, patiently wait for his turn, or ask for help from an elder.

Between 3 and 5, a child experiences tremendous cognitive, social, emotional, language, sensory, and motor development. Such abrupt changes often leave them confused, overwhelmed, and intimidated. The world around them can often seem unfair, and when a child does not get what he/she wants, he/she throws some serious tantrums. In these cases, teaching children problem-solving skills can help them act rationally and with patience. If your child acquires this ability, he/she will clearly communicate the problem and think out a creative solution apart from reacting logically.

How to Teach Problem-solving Skills to Children

There is no hard and fast formula for teaching problem-solving ability to kids. It can be tricky, and the strategy changes for every kid. This is because different kids interact in different ways with his/her surroundings. However, when you go to teach them this important skill, make sure that you identify the problem, think out the prior solution before asking them to innovate a probable solution, then guide them while they apply the solution and finally evaluate how good the outcome is.

10 activities that can develop problem-solving skills among preschoolers:

• Give them simple real-life problems : Problem-solving skills are an ability that has to be used continuously. The best way to learn it is by giving your kid simple real-life problems. This could be anything from arranging a few light items in the pantry to arranging their toys at the right designated spot in the house.
• At times ask them to find some possible solutions to a problem you faced: Suppose your kiddo is solving his/her mommy or daddy’s problem. This is no small feat. But think for a moment; your kid will eventually grow up to be an adult who has to solve his/her own This training will not only help him/her think critically but also give them enough confidence to trust their ideas.
• Give them math problems : In mathematics, you have to follow a set of rules and reach one specific solution. This is good training for finding a logical solution while following rules and not getting carried away by emotions.
• Help your kid look for alternative solutions: Open-ended questions work well in this. Whenever your child loses something, instead of searching the entire house, ask questions related to when they last saw the item or what they will do if they don’t find it.
• Puzzles and board games: Puzzles and board games are fun ways to stimulate critical thinking in a young mind. They are continuously presented with a challenge that they need to overcome if they are to win the game.
• Books and stories: Read your kid some books that tell the tales of how the heroes overcame a difficult situation. This will help them associate with situations outside their own and help them think critically about the problems.
• Teach them to handle strong emotional responses: Acting out with emotion to a particular problem is quite natural but it never takes you towards the solution. Teach your child to acknowledge his/her feelings without guilt or shame and react appropriately with the right phrases.
• Behave well around your kids: Make sure that you never lose your cool when you are around your kids. When it comes to children they model the behaviour of their adults and try to imitate them. Even though it might be difficult to always keep your calm , take a moment and think about your toddler. What would he/she learn from it?
• Break down problems: Instead of approaching a problem as a whole, teach your child to separate problems into chunks and deal with each of them individually.
• Teach them to ask questions: Encourage inquisitiveness in your If they learn to ask questions, it will be easy to teach them how to find solutions.

Problem-solving for kids is a great life hack and must be taught to all budding minds to prepare them for the upcoming life. Parents must ensure that their children develop critical thinking skills and act logically when faced with problems. Teachers at the pre-schools also play a critical role in this. So, if you are looking for a school that promotes holistic development in students, you need to consider Kangaroo Kids International Preschool . We employ the best teaching force to help your child think logically when presented with tricky situations. To learn more about our curriculum, contact us today.

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Elsevier Science Ltd.

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