Mapping Power


(I chose to look at the binary men/women but the structure could be mapped with various criteria. I acknowledge that I am using a binary and inferences made based on names/photos found on PSU’s website which is wholly insufficient!!!!! I highlight the lack of women in power/leadership positions.Below I chart out the power structure from my perspective (a tenured member of the mathematics and statistics department at Portland State University).

More sides to a figure means more power, thus triangle has less power than rectangle, and rectangle has less power than pentagon, etc.

At Portland State University where I work 60 percent of the faculty identifies as women according to

In the mathematics department where I work there are 22 tenure track (TT) faculty, with 20 of the 22 being men (18 tenured, 2 untenured), and 2 women (1 tenured, 1 untenured)

Mathematics and Statistics Department Portland State University 2020 tenure track faculty only

in addition we have 11 non tenure track faculty (NTTF), 9 of these are women and 2 are men.

Mathematics and Statistics Department Portland State University 2020 tenure track and non tenure track faculty.

The yellow dot represents me … and following up the power structure at my university it looks about the same. At the chairs level in my college (College of Liberal Arts and Sciences, CLAS) we have 24 departments and programs, of those 24, 18 are chaired by men and 6 by women.

College of Liberal Arts and Sciences Department Chairs 2020.

Following up the chain of power next come the deans, and here we have 10 deans, with 9 men and 1 woman

Portland State University Deans 2020

Following up the chain of power next comes the provost, this is the only level in the power structure that is dominated by women and also the only level that only has one person in it.

Portland State University Provost 2020

And finally at the highest level of power we have the board of trustees, 14 members, 4 of them women and 10 men. And the president is also a man.

Portland State University Board of Trustees and President 2020

Thus the power structure above me does not represent the 60% of the faculty who identify as women.

Mapping Collaborations

In an effort to understand connectivity to ones home university I have started to map out my collaborators in the United States (this is still in progress). I went through my CV and included everyone I collaborated with on any form of publication or presentation. Here is a visual for the US if you follow the link you can click the dots to see the location. Data points were collaborators, so the darker the spot the more collaborators I worked with in that place. CLICK ON THE MAP TO GET TO AN INTERACTIVE LINK.

And a visual for worldwide

A different way to visualize the same data is to take each publication, presentation as a data point and then map out each of the collaborators for each of them. So while one person would only count once in the charts above, below each person was counted as often as I collaborated with them. This leads to the following maps

In a third version I created the number of collaborations and the names into the chart, as well as whether at the time of publication the collaborator was a graduate student or a faculty member

This map can be used to calculate that about 29% of my collaboration is at Portland State University. This is a mix of 8% with faculty, and 21% with graduate students. The rest of my collaborations are spread across the United States and internationally. In total my collaboration is about 95% in the United States and about 5% international.

Mathematics To Understand and Critique the World

In this PSU funded project (Faculty Enhancement Grant, 2018, $15,000) I developed and explored tasks designed to teach mathematics through understanding and critiquing the world. For example teaching fractions, decimals, and percent through making sense of the world such as what percentage of the world comes from the United States. Students in the United States often do not know what percentage means (comparing the whole to 100 and then cutting the whole into 100 pieces and each of those pieces representing 1 of the 100 pieces or 1 per one hundred, or percent. By shrinking the work down to 100 people and using books or videos to examine those 100 people we can simultaneously learn about the world and about mathematics topics. For more information see LINK

New Podcast Episodes

Mathematics Teacher Educator Podcast – NEW episode

What do the editors of the Mathematics Teacher Educator journal have to say? Listen to them discuss their recent editorials and where the journal is right now.

Teaching Math Teaching Podcast – NEW episode

Brand new Teaching Math Teaching podcast … we are talking with Don Berg who is the Executive Director of Deeper Learning Advocates, which is on a mission to embed the psychology of learning in K-12 policy so that policy stops undermining learning.

Paper published June 1st 2020: Mathematics to Understand and Critique the World: Reconceiving Mathematics in a Mathematics Content Course for Elementary School Teachers.

Published June 1st – for full paper click here


There are long-standing and ongoing calls for making mathematics meaningful, relevant, and applicable outside the classroom. In other words, to help students see mathematics as a tool for understanding, analyzing, and changing the world. However, there are also tensions between a focus on classical mathematics goals and a focus on analyzing and understanding social and political issues, which does not always lend itself to focusing on a specific mathematical concept. In this study, we redesigned a mathematics content course for prospective elementary teachers (PTs) to examine whether we could engage PTs in learning both about the classical mathematics content and about understanding and critiquing the world. We examined their learning in both areas and their evolving views of mathematics teaching throughout the course. We found that PTs learned both the mathematics and about the world and in addition they reconceived of mathematics as a tool to make sense of the world. Thus, mathematics content courses can be designed to allow PTs to develop their knowledge in both areas and experience a classroom where teaching math for social justice is a focus.

view video version of abstract here

Numeracy in the Time of Covid-19 – #3

Should Georgia reopen? or How to decide whether news are true?

Shall we reopen? Is a question many places in the US are asking these days. As in my prior posts numeracy helps us try to answer this question. In this post we focus on statistical literacy.

Numeracy includes basic statistical literacy which is the ability to understand and reason with statistics and data. The abilities to understand and reason with data, or arguments that use data, are necessary for citizens to understand material presented in publications such as newspapers, television, and the Internet.

One of the essential aspects of statistical literacy is to decide whether you agree with findings presented in a chart.

Basics of charts are

  • That we typically lay out charts in ascending/descending order on the axes, so as we go up and as we go right the value increases/decreases.
  • Distances on the axes are in regular intervals (linear meaning that we have the same increments going from one data point to the next, exponential meaning that we go by the same multiple as we go from one data point to the next).

Using this basic assumption we can make sense of data presented.

If we do not follow these conventions we can make the data say anything we would like – and might get away with it. Exactly this happened in Georgia where the Department of Public Health published a graph that was entirely misleading. Let’s consider this graph:

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Chart retrieved from:

It shows a downward trend over time of confirmed Covid-19 cases. We make this implication because the title of the graph is Top 5 Counties with the Greatest Number of Confirmed Covid-19 Cases.

BUT if we take a closer look we see that the dates on the x-axis (the horizontal line) are not listed in ascending or descending order. While the y-axis is linear going from 0 to 50 to 100 to 150, the x-axis seems to be randomly chosen dates. (Well maybe not randomly, maybe the data was purposely organized to show a decreasing trend).

In addition the counties are not in the same order as we move from date to date.

If we rearrange the data to follow our conventions it looks like the data in the next image.

This image has an empty alt attribute; its file name is image-21.png

Chart retrieved from:

What does statistical literacy have to do with this? Always check the data that is presented to ensure that it follows conventions and that the claims made based on the chart match the chart.

Numeracy in the time of Covid-19 – #2

or Why we need to teach math to make sense of the world.

Trump says the US leads the world in testing


Today we will tackle the understanding of numbers needed to make sense of the quote from CNN Trump says the US leads the world in testing. But it’s far behind in testing per capita, studies show. The article featured the statement “America leads the world in testing” so let’s make sense of what that means?


Let’s begin with a smaller example. Let’s consider 2 villages, Village 1 has 100 people in it Village 2 20. Now let’s assume that Village 1 tested 10 people and Village 2 tested 5 people (see image).

While Village 1 tested 10 people and thus more than Village 2 which tested 5 people, Village 2 tested 5/20 which is 1/4 of their population (or 25%) while Village 1 tested 10/100 which is 1/10 of their population (or 10%). We can see this also if we replicate Village 2 five times to make it the same size as Village 1.

Thus if we consider the percentage of the village tested Village 2 is ahead, if we consider the absolute number of people tested Village 1 is ahead. We see that Village 2 would test 25 people out of 100 people while Village 1 would test 10 in 100.

Now let’s return to our quote, one way to look at this is to look at the number of tests done in the US. The article states that “By May 12, the US had conducted about 9.6 million tests, according to the COVID Tracking Project.” at the time of writing this blog that number is at 10,269,996 ( So if no other country tested more than that number the statement above is true if we compare absolute numbers.

According to there are 235 countries with but only 91 of them even have a population larger than 10,000,000. So if the Unites States were the same size as the remaining 144 countries this would mean that we would have tested all the people in our population at least once so we would have everyone tested.

However, the United States has 331,002,651 people according to If we compare the number of people tested 10,269,996 to the number of people in the country 331,002,651, we see that for every tested person in the United States there are 32 untested people, since the number of people in the United States is 33 times the number of tested people. So of every 331 people there are 10 people who are tested.

A different way to look at this number would be to compare how many people out of 1000 people got a test, and in our case that is about 30 since 3 x 330 = 990 which is close to 1000, so we would have 10 tested for every 330, which results in 30 tested for every 990.

So if we look at the raw number of how many people got tested, the United States is first, but that is because it has a large population (the 3rd largest in the world If we look at how many people get tested for each one million of total population the United States ranks 38th with 31,027 tests per one million people.

We cannot simply compare the total numbers across countries in this case because the countries do not have the same number of people. While the United States has conducted the most tests, it has not tested as many people comparatively to the population as many other countries.

The question to ask is: What numbers are being compared? And does it make sense to use those numbers?

Numeracy in the time of Covid-19

or Why we need to teach math to make sense of the world.

Numeracy “the ability to understand and work with numbers”

(google the term)

Numeracy is essential to understand the world around us. However, unfortunately numeracy is not always a goal in mathematics education. Often the focus is on what algorithms to apply and when rather than to make sense of a situation. That leads to many adults who are not thinking quantitatively when participating in their world.

However numeracy is essential to understand our current situation and statements such as the

The United States crossed another threshold Tuesday — 1 million known coronavirus cases.That is nearly one-third of all the world’s known coronavirus cases. To put the enormity of that into context, the U.S.’s 328 million people is just over 4% of the world’s population.”

source – NPR

To really understand the statement above we need to understand (among other things)

  • what 4% means
  • how 4% relates to one-third.

Let’s begin with understanding percents. Much of the adult population (at least in the United States) does not regularly calculate percentages in their head or connect to the meaning of percent. When recently teaching a college course hardly any of my students realized that per cent stands for per 100. To them it was just a word that when with a calculation.

To mediate this fact in a society that relies heavily on using percentages to calculate tip and sales prices stores put up charts that help customers understand how much their current prices are. Restaurant receipts typically come with recalculated tip prices. And a variety of apps exist to calculate tip or sales prices.

Thus 4% might not mean a lot to people reading the statement above. One way to make sense of 4% is to look at 100 people. For every 100 people in the world 4 people come from the United States.

This number is often overestimated by adults in the United States. When asked to predict how many of 100 people representing the world would be from the United States the estimates range between 7 and 50. So hearing/reading the 4% in the quote above might be counterintuitive to readers if their belief is that the population of the United States is larger.

Now let’s examine the second part of the statement, the United States has one-third of the world’s known coronavirus cases. If we were to represent this we would that for every 100 people in the world who are infected with Covid-19, 33 of them come from the United States.

So now if we put these pictures side to side we can see that even though only 4 of every 100 people in the world comes from the United States, 33 of every 100 people who are infected comes from the United states. If infection rates were equally distributed this number would also be 4. This means that our number is about 8 TIMES higher than it should be (if numbers were equally distributed) since 4 x 8 = 32. Thus we are about 8 times worse off than equal distribution.

Thus, to really understand and engage with the numbers people need to have numeracy. This is only one of many reasons why we should teach mathematics in a way that allows students to engage with the world around them so they are able to consume the news and make sense it.