Iddo Gal is an Associate Professor and past-Chair, Dept. of Human Services, University of Haifa, Israel, with an MA in Personnel Psychology from Tel-Aviv University and a PhD in Cognitive Psychology, University of Pennsylvania. Gal enjoys multidisciplinary interests that span two fields of research and applied practice: the first being teaching/learning and assessment of adult numeracy and statistical literacy, and systemic aspects of developing related functional competencies; and the second being managerial issues in service organizations, in particular empowerment of frontline workers and empowerment of clients of service organizations, and related issues such as service satisfaction, customer complaints, and accessibility of services to diverse populations.
Episode Description
Being able to read and write is necessary to be successful in work, at home, and in civic life. Do parallel skills associated with critical reasoning from numbers and data carry similar weight? What do you need to know to be an informed consumer of numeric information, and to use such information? That's the focus of this episode of Stats+Stories with guest Iddo Gal.
+Full Transcript
Pennington
Being able to read and write is necessary to be successful in work at home and in civic life. Do parallel skills associated with critical reasoning from numbers and data carry similar weight? What do you need to know to be an informed consumer of numeric information and to use such information? That's the focus of this episode of stats and stories, where we explore the statistics behind his stories and the stories behind the statistics. I'm Rosemary Pennington. stats and stories is a production of Miami University's Department of Statistics and media, journalism and film, as well as the American Statistical Association. Joining me as panelists John Bailer, Chair of Miami statistics department, Richard Campbell is away. Our guest is Iddo Gall, a retired associate professor and past chair of the Department of Human Services University of Haifa. Gal enjoys multi disciplinary interests that span two fields of research and applied practice. The first being teaching, learning and assessment of adult numeracy and statistical literacy, the second being managerial issues and service organizations in particular related to issues of empowerment. Gall is a past president of the International Association for statistical education, and past editor of the statistics education research journal. He currently serves as a consulting editor of the Journal of disability policy studies and associate editor of the journal numeracy. Iddo. Thank you so much for joining us today.
Gal Sure. My pleasure.
Pennington Just to get our conversation started, could you explain what numeracy is and why it became a research interest for you?
Gal
Let me start from how it became a research interest. For me, my original training was in occupational psychology. And I worked in the area of personnel selection for several years in large organizations in Israel, before I got my PhD. And so I became very interested in the issue of skills and how people acquire skills and use them and how they behave with the assistance of different kinds of skill sets that they acquired. And mathematical skills or numerical skills, or anything that has to do with understanding of information is one of those cognitive skills. And eventually, I got my PhD in the area of Decision Sciences, or decision making, and became interested in how people acquire mathematical and statistical skills, how they learn to reason about probability, and so on. And this is how I got into mathematics education and statistics, education, and so on. So this is the answer to the first part of your question.
Bailer
Very good. Well, well, you know, it is, again, it's a delight to have you with us. I mean, I think that this idea of studying and measuring and evaluating quantitative literacy skills or numeracy skills, there's so many ways that we talk about this, I mean, when I was first introduced to thinking about these ideas, I started thinking, you know, there was it wasn't just statistical literacy, you know, reasoning from data. It's also some sense of magnitude comparisons. Also some sense of kind of relationships. I mean, you know, so I'm just curious when I don't want to dive into the splitting hairs that define these different groups. But, when you think about numeracy, what does that entail?
Gal
Yeah, so the notion of numeracy is something that has been with us for more than 100 years. And it relates to people's ability to cope with the mathematical and statistical demands of the world, to interact with information to critically interpret it, and if needed to, to talk about it, to communicate about mathematical information and to take action in this regard. So numeracy is a complex competency that involves both cognitive knowledge, skills and know-how as well as attitudes, beliefs, and so on, because if you don't think that you have a good skill, you may not actually cope with different situations, you will avoid them. And as we know, this is something that we have in mathematics and statistics very often. So numeracy is a complex capacity in schools and education systems take some steps towards imparting it or developing it and people but people very often develop the numeracy also through their practices through their interactions with different environments, and they may grow or not grow well beyond what they have learned in school. And unfortunately, what we know is that many people are not well equipped to deal with all the mathematical and statistical challenges that reality throws at them.
Bailer
Let me just do a quick follow up to that. You know, one thing when when we think about literacy, the ability to read and write if you did not have that, that would be viewed very negative But but yet some, you know, you'll occasionally hear, you know, some people will speak almost with pride that they can't do math, or that they, you know, in some sense they're affirming their numeracy. I mean, why do you think that that distinction is acceptable?
Gal
I think it's acceptable because it's widespread, widespread to widespread. And it's almost the only area where we have a phobia, except for maybe computer phobia that is generated or created by the educational system is the area of mathematical phobia, or mathematical anxiety, and statistics, anxiety, and so on. And I think this relates to the way we teach mathematics and statistics with students. And learners depend a lot on our teachers. And so many people experience a negative sense in this regard.
Pennington
I think I might have talked about this on the podcast before but I had a deep, deep fear of math and stats for you know, much of my childhood, I think part of it was around just having some teachers who did not communicate very well. And then by the time I got to college, it just felt very overwhelming. And then it was when I was in grad school, and was forced to take the stats class, as part of my PhD. And the professor actually made us like run correlations and linear regression by hand, and sort of walked us through, like the logic behind it, and sort of, you know, what it helps you understand, as terrible as it was to sort of run those, those formulas by hand, it gave me this understanding of, of what it allows me to know about the world. And I feel, you know, obviously, I'm hosting this podcast now, with john and i would i would not do if I did not feel comfortable with numbers, but um, but it just definitely gave me this this sense of like, Oh, if only someone earlier in my life had been able to sort of harness this kind of concrete kind of explanation of what this allows me to know about the world, you know, I might not have avoided certain classes in college, maybe I would have changed my major or had a different kind of double major, who knows what opportunities would have opened up if someone had been able to communicate like that the way math works to me in a way that just sort of, you know, resonated.
Gal
Right, I have had the same experiences when I was growing up. And by the way, I wasn't very good at mathematics. But I discovered statistics as a kind of a much more logical, organized area. And it was easier for me to relate to it. And until I started using it as an applied psychologist in personnel selection, validation studies and other things. And I discovered both of UT as well as the complexities of communicating information. But let me relate to something that you said rosemary. I think most educators, whether they teach mathematics or statistics, and many of those who teach statistics are not statisticians. They come from the disciplines, and they teach it in their own context. Most of these people are interested in teaching statistics. Whereas what I think we should be focusing is on what you need to do out there in the world, when you encounter statistical and mathematical information is a way to engage people. So to focus on the expected behaviors, and skills that you need, and then build from it back, or backtrack into the knowledge that is needed. So for instance, in the world, citizens, and even many workers seldom encounter mathematical or statistical issues. In the abstract they encounter, they usually embed a lot of text in a lot of textual information, in articles in, in leaflets, and so on and so forth. But nobody propels them to read and to think about communication, because the classes focus on the beauty of the abstract aspects of mathematics and statistics, too often.
Bailer
So I'm curious, you know, in some of your writing you make this distinction between sort of critical and functional skills. Can you expand a little bit on what you mean by those two kinds of labels, and then we can dive into some of these other areas of application as you described earlier?
Gal
Sure. So many scholars have worked . I'm just one of many people who have been interested in the critical aspects of mathematics and statistics. So when you think of functional aspects, usually you think of some tasks that you need to deal with in the everyday world, commercial transactions, paying, buying, calculating things. And so there is a product that you need to produce some numbers. And it may have to be very precise, or it may, it can be an approximation, and the only thing that you need is to think about whether you've done the calculation correctly. Did you make any mistakes? That's the critical part of things. But when you are a consumer of mathematical statistical information, then you are exposed very often to information or to points of view to arguments that others are producing. And they may use the numbers in a one sided way or in a biased way or to their advantage. And there are many, many examples, such as you know, whether you use percents or absolute numbers in order to bolster or hide a certain phenomenon. So you need to be able to interpret things from a critical perspective, you need to know what questions to ask about the source of the information, the interpretation that is provided, and in many, many other issues. Nowadays, there are new domains that are emerging, such as sub area about the political science and quantum quantification of the world and how powers societal powers use numbers in order to hide or to bolster, things that they want attention to and hide, things that they don't want the public to be aware of. There is an area of the sociology of numbers, and so on. So overall, people need to be able to be critical about many things. And usually we do not teach to be critical in statistics. I can elaborate on this if you want, but there are many, many examples for this.
Pennington
I have a question related to, actually, journalism. And I'm thinking that given that people encounter statistical information and mathematical information, often in news stories, sometimes local TV news, sometimes newspapers, I wonder what advice you would give to journalists to be able to communicate mathematical or statistical knowledge in a way that is critical and is informative for their audience, right? Because we think of journalism as a public good part of the work of journalists is sort of make sure citizens are informed.
Gal
Yeah, well, I'll be very humble on this, because there are quite a few experts in task forces in journalism that have produced excellent guides for journalists. But the nature of journalism is such that many people drift into journalism without necessarily getting all the information or the support that they could. And maybe they took maybe one course in, in basic statistics, but they have not learned about the statistics of journalism. And so my advice is that they should seek out the guides and the training manuals that are written for journalists about how to use statistics properly, and how to report it properly, properly, because most of them probably just don't know that these guides exist, and that they should follow them. I think this can improve much more than me giving a two minute advice on what journalists can do.
Bailer
You know, I also would suggest that the collaboration with statisticians is another thing that we both benefit from. You know, a lot of times we think about collaboration and research projects, you know, it's in scientific inquiry. But I think there's a great opportunity for statisticians to work with journalists who clearly have a vested interest in this statement. But I let her buy into this because I think that there is a framing of argument that journalism brings. That's, that's very instructive for, you know, kind of a statistical community. But then there's also a formalization of signal and uncertainty, that's important for journalists to appreciate.
Gal
Right? So I would assume that naturally, many statisticians and mathematicians that have to speak to journalists to speak on on in on television interviews, and so on, many of them will gravitate to professional jargon, or they will make assumptions about what to understand and don't understand that we've seen a lot of this. Over the last year and a half during the pandemic in many countries, some countries have established panels or task forces that are responsible, and they have different names for this in different countries. But the Task Force is responsible for Responsible reporting of science to the public, and they involve journalists as well as statisticians, and so on and, and so many journalists, they go to these panels or task forces in order to get advice and to see how to interpret things properly. But the nature of journalism very often is that it happens very fast, especially during the pandemic. For instance, things move very rapidly from reporting to the public, there is no time to digest and to filter and to modify the way some things are communicated. And because of this, the public will be exposed to information that might be vague or imprecise, and on occasion will contain errors. And so the public needs to be aware of how the journalism machinery works. Understand how new stories are created and edited, and so on who decides on the header, as opposed to the content and so on. And so very often you'll see headers that are designed to capture attention and so they put things in a more bombastic way. And because of this, there may be stalled certain certain things more than the professionals would like them to be.
Pennington
You’re listening to Stats and Stories, and today we're talking with the University of Haifa, Iddo Gall. Iddo, I wonder what advice you have for educators, given the work you've been doing around numeracy and statistical literacy, about how to teach people to think about how to critically engage in numbers. So you talked about sort of, you know, we can get caught up in the abstract beauty of math and stats, but sort of what of what needs to be happening in the classroom to help people have a much more kind of, I guess, applied understanding, in the context to be able to, you know, sift through the numbers when they encounter them in the real world, right?
Gal
So of course, it's difficult. The question is very important, I think that we don't have time to go into details of this because there are different contexts within which people teach mathematics and statistics, and it doesn't fit everybody the same way. But I have to be very bold and maybe provocative. I would say the teachers need to, I think, devote 25 to 30% of total class time to engaging with the way statistics and mathematics are reported in different contexts. It may be in the media, it may be in professional publications, and to make sure that learners are exposed to the way information is communicated. Because eventually, they will need to either produce such communications on the job, whatever job they go to, or they will need to be consumers of this kind of information. And not just not just devote all the time to teaching procedures, and statistical tests, and so on. And to give you an example, okay, in statistics, for instance, we don't really teach students to be critical about statistical information, they may not even learn about how statistics is used wrongly in the world or in a way that may distort certain phenomena. Statistics students very often learn about error, for instance, just in the context of learning about specific statistical procedures, such as when you run the regression. So the reason is the aerotherm, all the reasons, variance explained and so on. But this is technical, how does it relate to a prediction that you predict when your company asks you to foresee you know, to predict the sales figures for the next five or 10 years, and so on. So these students need to engage with the actual task with which they will have to deal with as graduates later on. And so the application needs to be taught in the context of tasks that reflect reality, and not just provide abstract skills assuming that later on, smart people will be able to apply it somehow. Because transferable skill transfer, which is a cognitive term, skill transfer doesn't happen unless you train people on skill transfer.
Bailer
You know, that's so you've hit a really I mean, this, this distinction, even between variability and uncertainty, sort of, they're sort of fundamental concepts that are critical for carrying forward for people. You know, I wonder how often you get into the minutiae of calculating something versus appreciating what you're trying to characterize. But I want to get to you know, you touched on this a little bit and then just your recent remarks also follow up with that there's the need to train the trainers because I think it is, I love this suggestion about 25 to 30% of the time to be spent on kind of this connection. In some ways that's setting the stage that's motivating I've, I've often thought you have to open the hearts before you open the heads. And you know, this type of activity really engages people into why they motivate and inspire. But how do we help the people that are training to be these teachers at the secondary level, and actually even at the university level, to have this type of engagement?
Gal
Right? Well, this is an excellent point, John, and actually a challenge for all of us. In the area of statistics, education, only over the last 10 or 15 years, we've seen some programs emerging that focus on the pedagogy of teaching statistics and trying to educate people on how to teach statistics. I think the pioneering program in the United States was at the University of Minnesota through John Garfield and Bobtail Mass and their colleagues, University of Florida now and, and Santa Fe University of Georgia and several other institutions are now pushing forward with very impressive initiatives on pedagogy. Teaching statistics. But most of the people who teach statistics still come out of graduate school, they may learn statistics, they may understand it well, they usually don't have any exposure on this. So I know that the American Statistical Association and a couple of other organizations such as the Royal statistical society and the German stochastics group, are taking some steps in this regard. But this needs to be elaborated in many countries. And nowadays, we have the way to encapsulate this knowledge through videos through MOOCs and other courses and through digital resources that can be accessed more widely, because the principles are general, and can be now shared with the rest of the world in a better way than they used to be before.
Pennington
While we're on this topic of education. I wonder, you know, if you could talk a bit about this article, you co authored about metaclasses? And how just maybe, maybe you can talk through sort of what that article was about and sort of what you think the implications are coming out of it for education and in this area,
Gal
Right? Well, I think so. You know, a few years ago, I started a collaboration with a colleague Irie now grant check from the University of Ljubljana in Slovenia, who, like me is working in in two fields in the area of service and Tourism Management and the economics of tourism on the one hand, and in the area of statistics, education. And so we've written several papers, but one of them was our efforts to combine insights from the domain of service science and service management, and how to improve service systems and apply to the area of statistics education, and we focused on mega classes, hybrid classes in 2017. We published a paper on this where we kind of foreshadowed something that we didn't know would happen later on. Because, you know, in the early 2000s, we began to see mega classes, statistics, dedication, huge service courses, in some universities being offered to hundreds or sometimes 1000s of students. And then it was followed around 10 or 15 years ago, with some books beginning to appear in several countries teaching introductory statistics to the masses. So these are loud service systems that serve very diverse populations, but they also face major failures, because the percentage of people who actually graduate from them with good scores, the percentage is very low. And so we began to ask ourselves, how can you improve these kinds of things? And how can you improve the value of the learners of the customers derived from the systems. And the problem is that during the pandemic, we realized that all of the world was shifting into a mega class or a hybrid between situations. And so what we realized is that there are many processes that many educators are now engaged with, that are flying under the radar of education systems, traditionally, research and statistics, education, or attempts to understand what is happening in a statistics class, whether for statistics majors for regular students, research focused on understanding on cognitive skills on whether they got or didn't get certain points, or on attitudes. But there are many other things that happen that affect the quality and the resulting value that learners derive from it. For instance, self management, you know, learning through the internet, or learning in remote distance syndication requires a lot of self management and metacognitive skills that are very different than what students need when they sit in class, and somebody looks them in the eye, when there is a teaching assistant that comes to them, and they can look over the shoulder and so on. There is a lot of social interaction that is happening and bulletin boards on WhatsApp lists on a lot of other social media where students consult with each other outside of this. So there's a lot of dependency on technology, and all of these things are not researched properly. So if you ask yourself, what do we know about the factors that affect the success of the products, the value that is derived by learners? We see that actually traditional research and statistics education covers only some of it, but a lot of the things are still not fully understood. To give you one example, a lot of the interaction that happens in a in a mega mega class or habit class is through texts, students send different questions by email, or by Facebook or by whatever and the teacher or the teaching assistant is answering them and nobody's analyzing this thinks, in the same way that we analyze customer interactions with a contact center in order to see what questions come up, how do we learn from it? How do we design good responses to it, you know, frequently asked questions and answers, and so on. So there's a lot that can be done on analytics of these kinds of causes, text analytics, voice analytics, and so on in order to understand what are the things that affect the dropout, not just performance, but dropout, and how to detect students who are about to drop out and identify them in exactly the same way that service organizations are trying to identify customers that are disengaging from the service provider and are going to switch to another service provider. So methodologies, we don't have to invent them, we need to apply them and adopt them. But there is a lot that can be done.
Bailer
That's a really interesting idea of technology transfer from one meal to a very unusually unexpected case. I really liked the point that you made about self management. It's sort of MOOCs are classic examples of lots of people starting very few finish. Yeah, and it's a and, you know, I've, I've done that, too, I finished them, but I think I've probably failed to finish more than I finished. Although I think I've gained value, I've gained some of the value that I want. But I'm also a different kind of learner. And, you know, I think about this in light of some of your interests in adult learning. And I'm hearing a couple of things that are coming up. One is this idea of skills and self management. There, I'm thinking about the idea of making sure that you engage in these domains. I mean, you talked about domains of financial health, digital, civic workplace, lots of areas where this occurs, I just as I think about a kind of last question, I wanted to loop back to where you're talking about functional versus critical application of skills. And, you know, when when you were saying this, I was thinking about in terms of functional, one idea that comes to mind for me and see if this is correct me if I'm wrong, that that, you know, if you were going to refinance your house, you're going to get a new, you know, or if you're going to start saving for retirement, why do you start doing this early? Those are kind of decisions that you want to make, but also, there's, there's kind of these are not independent, because I think about critical and functional in terms of should you get a vaccine? You know, yeah, you know, that's, that is both a functional component, your critically consuming information and then acting on it. So can you just just, you know, kind of help? Maybe, you know, deconstruct that a little bit for us?
Gal
Well, I can, I can try. So So first of all,
Bailer
We ask all the easy things here, you know, this, you know, yeah, she asks you all about how to fix that education. I'm asking you about decision making in life.
Gal
So, you know, John and Rosemary, this is why we write papers that are a minimum of 5000 words. A space in here, we need to encapsulate it briefly. But the critical and the functional, they go hand in hand. You know, I still remember a story from a colleague of mine that spent some time in Morocco in the Peace Corps, and how his his landlord was an illiterate woman who was the shrewdest bargainer in the market, as you know everything about numbers and she could, nobody could cheat her because she knew how to do a lot of things and to think critically about quantities and numbers and so on, even though she was completely retail, because for her livelihood required that she is able to look back at yourself or look from the side of the self and monitor her own understanding, and monitor things and ask about accuracy and, and, and well, she can be better and, and so we all are illiterate in some way. In some areas of life, we may not feel very comfortable with our own skills. Very often people may not know enough about commercial transactions, or how to take a loan and how to refinance or calculate and so on. And people may not understand fully, all the statistics that float around on the pandemic, and they may not understand what positivity radiator, or why do they calculate the seven day moving averages, and so on. But they should feel comfortable to ask questions about it and to seek more information and, and seek explanations and guides on this. And they should be able to ask questions even if they don't know the domain. The whole point about being critical is that you don't feel that you know something 100% but you're able to ask questions. Can you explain more? Where does this number come from? How did you calculate it? And it happens in every domain of life. It happens in the medical field, you know, so one of my relatives recently went for a genetic counseling and the doctor said to her, so for women in your age group, the risk of having the The following side effect is between 30 and 40%. And she asks her How do you know? Do you have statistics about women in my condition? She didn't know how to calculate it, she hardly knows what is a 3040 to 40% risk, because this is not something that anybody ever teaches us anywhere. But he was able to ask the question and then the doctor began to mumble a little bit. And then there was a conversation that tell care, to put things in perspective and get an appreciation for the fact that the will some of the risks and they will non trivial, but the CI could rely on on medical practice, and make decision and she took the procedure in exactly the same way that we deal with the vaccine nowadays, you know, there are there are people who are anti Vax, or anti anti Vax, or hesitating, and so on. And many of them just don't understand the numbers very well. Or they rely on shady or questionable sources. And they need to be able to ask themselves critical questions about these sources as well. And very often they don't, because they maybe they don't trust the government, you know, but they do trust somebody else. And they don't question these other numbers. So the bottom line for this, John, is that we need to combine being critical and being functional in any and every context of life. And we need to make sure that this is also part of education, in mathematics and in statistics. And teachers need to realize some of what they do in this regard. And this will help, I think, make students and learners feel more comfortable with this because we will see that the teacher is trying to relate to the feelings and to equip them with tools that are helpful, not just technical knowledge, per se.
Pennington
Well, that's all the time we have for this episode of Stats and Stories. Iddo, thank you so much for being here today. Thank you. Thank you very much. Stats and Stories is a partnership between Miami University’s Departments of Statistics, and Media, Journalism and Film, and the American Statistical Association. You can follow us on Twitter, Apple podcasts, or other places you can find podcasts. If you’d like to share your thoughts on the program send your email to statsandstories@miamioh.edu or check us out at statsandstories.net, and be sure to listen for future editions of Stats and Stories, where we discuss the statistics behind the stories and the stories behind the statistics.