By: Sara B. Vaughn

Whether it be in my personal life, in my career as a teacher, or in my former life as a retirement plan consultant , I’ve had my fair share of information gaps. We’ve all been there—one person has all the information, another has lots of questions, and they are left to negotiate the communications needed to share the required information in order to solve their real-life problems. 

This real-life skill is also translated to the math classroom as one of the eight MLRs in the Open Up Resources 6–8 Math curriculum. Like in real life, anytime you must rely on another human being to meet your needs, information or otherwise, it’s a scary event! Maybe that’s why I hear so many teachers fast forward or skip this important routine in the curriculum. Maybe I was even that teacher at one time, but now—three years into implementation—I see just how valuable this language routine is for all learners and not just English Language Learners (ELLs).

What are they?

Just in case you haven’t had an opportunity to see and work with Info Gaps, let’s start with a brief description of this Mathematical Language Routine (MLR4).

Students are in pairs. One person is issued a data card and the other a problem card that they do not show one another. Partners begin by silently reading information on their respective cards. The person with the problem card will likely make a list of what is known and what missing data is needed in order to solve the posed problem. As the person with the problem card asks for specific, missing information, the person holding the data card asks why that information is needed, always pushing for justification. This exchange of questions and answers between the respective cardholders continues until the person with the problem card has enough information to solve the problem. Without displaying the data card, partners each work independently to solve the problem. They then confer and refine their solutions.

Mathematical language is learned when you use it for real and engaging purpose. So if you’ve never experienced an Info Gap scenario, do yourself a favor and grab another math teacher and try one or two. The struggle is real and you, as an educator, need to experience this for yourself so you know the exact feelings your learners are having.

Info Gap Cards Taken from https://access.openupresources.org/curricula/our6-8math-v1/8/teachers/teacher_course_guide.html#supporting-english-language-learners  

In one version of this activity, Partner A has the general problem on a card, and Partner B has the information needed to solve it on the “data card.” Data cards can also contain diagrams, tables, graphs, etc. Partner A needs to realize what is needed and ask for information that is provided on Partner B’s data card. Partner B should not share information unless Partner A specifically asks for it. Neither partner should read their cards to one another nor show their cards to their partners. As they work the problem, they justify their responses using clear and connected language.

• READ, then THINK-ALOUD: The problem card partner (Partner A) reads his or her card silently and thinks aloud about what information is needed. Partner B reads the data card silently.
• QUESTION 1: Partner B asks, “What specific information do you need?” Partner A needs to ask for specific information from Partner B.
• QUESTION 2: When partner A asks, Partner B should ask for justification: “Why do you need that information?” before telling it to Partner A.
• EXPLANATIONS: Partner A then explains how he or she is using the information to solve the problem. Partner B helps and asks for explanations, even if he or she understands what Partner A is doing.
• FOLLOW-UP: As a follow-up step, have both students use blank cards to write their own similar problem card and data card for other pairs to use.

What is it about Info Gaps that makes them worthwhile?

In Mathematical Mindsets, Jo Boaler discusses a theory of Piaget’s regarding equilibrium (the balance and order we feel when we understand something) and disequilibrium (the imbalance we feel when we encounter new earnings that don’t fit into our current structure of understanding. Boaler says that reconciling and wrestling with disequilibrium leads to assimilation and understanding, boldly called wisdom. One purpose of a Mathematics Info Gap (Mathematics Language Routine 4) is to motivate learners to move from imbalance to balance by gathering/requesting information, aka data, to help answer a crafted problem. The problem laid out with Info Gap set-up creates a struggle for the participant with the Problem Card because they are not given hints about the solution that could be gleaned from looking at given data. The person with the Problem Card has little to no data available, but only the question to be answered. In order to solve the problem, questions must be posed to get needed data. The process of developing thoughtful questions and justifying why particular pieces of data are being requested pushes the person with the Problem Card to a level of struggle seldom experienced in routine problem solving.

Students struggle when directions are ambiguous. They want to be told step by step how to solve a particular problem and our well-intentioned reaction is to help them. But this reaction is not helping students become better problem solvers. Jo Boaler writes that students who are undeterred by ambiguity find the road from disequilibrium to equilibrium much easier to navigate than do learners who give up at the first sign of ambiguity. Info Gaps are ripe with ambiguity. The experience provided through the use of Info Gaps helps build persevering and driven problem solvers. Learners are working backwards and making leaps as they try to close the gap in information necessary to solve the given problem.

In addition to the challenge and ambiguity that are baked into the Info Gap experience are the concepts of equity and learning for all. Info Gaps level the playing field for learners. Regardless of a student’s status in the class, each person plays each of the two available roles by virtue of holding either the Data Card or the Problem Card. Information is power and each student experiences the position of power in the process of working through a pair of Info Gap problems.

What about when things don’t go right?

It may happen that the problem solver and the data holder get their heads together too soon, before serious struggle actually happens. While this is not ideal, the outcome is still desirable. Students thought independently, and then collaborated and the experience gave them a better understanding of the problem than they would have otherwise had. As you monitor, you may see that the person asking for data has an irrelevant piece of data. This is a sign that the person holding the Data Card was answering questions that were not actually being asked. This is a clue for the teacher to step in and question the process so students will gain a better understanding of the routine for the future. 

It may first appear that no learning is happening during the course of the Info Gap routine. The following lesson, however, sees students with deeper understandings ever ready to conquer more challenges in mathematics. The first couple of times you try an Info Gap with your classes will be a learning process for sure. As a teacher it will be helpful to model what good questions look like. It will also help to make your thinking visible by writing down information as the data person gives it. Having cue cards available so students have sentence starters will also be helpful. Here are examples of supports:

https://docs.google.com/document/d/17dKzdjJC5ZGbdq_sWl0HT5sP6Qn0liVBrrRxRKoa4q0/edit?usp=sharing

OR

Let’s Hear About Your Info Gaps

If you want to learn even more we are chatting about Info Gaps all month in our Virtual PLCs and it’s so easy to join!

Whether you are using Info Gaps to close a language gap, content gap, both or neither the other Community Coaches and myself would love to hear all about your experiences using the routine in your classroom. Consider sharing your thoughts, a classroom video, or a reflection on Info Gaps in your classroom in the Facebook Community, on Twitter using #OpenUpMath or even by email. We’d love to hear how you’re closing the Information Gap!