Henry Kranendonk is a mathematics educator, curriculum developer, and former mathematics curriculum specialist for Milwaukee Public Schools. In a career spanning more than four decades, he’s been a classroom teacher, teacher educator, curriculum writer, and mathematics specialist with the Marquette University Educational Opportunity Program. Kranendonk has authored numerous mathematics textbooks and instructional resources, including the Data-Driven Mathematics series, and has contributed to mathematics education initiatives at the local, national, and international levels.
We asked him the following questions to find out more about him, his broad career path, and his work in both K–12 education and teacher preparation.
Journey and Inspiration
What initially drew you to teaching? Did anyone inspire you? If so, who?
I have two older sisters. As I was growing up, my oldest sister was a teacher in a one-room rural school in my hometown of Oostburg, Wisconsin. I was six at the time. I recall she would bring home stacks of papers to correct with a red pen. I thought that was so neat! I watched her as she marked papers and organized her daily presentations.To keep me busy, she gave me a red pen and some discarded papers to pretend I was correcting. I was in my glory! My sister and her dedication to teaching were an inspiration.
My younger sister, who is 10 years older than I am, entered college when I was seven with the goal of teaching high school math. Unfortunately, she lacked the courage to speak in front of people, so she practiced with me. She pretended she was a teacher and I was a high school math student. So, for several years, I learned high school math through her “lectures”—and loved it. By the time I reached high school, most of the math classes addressed what she taught me. Years later, she completed her college studies in computer science. She became a programmer, and I became the math teacher.
In (maybe) 1963, I was selected to be in a special math class of eighth-graders. The math curriculum was radically changing due to the connection of number systems to computers. I recall working with base 16 and base 2 as major topics and skills. My teacher was very frustrated as he tried to explain it! My memory is that he got lost in the details of why this was important. I thought the connections to emerging work with computers were exciting. As a result, for several months, I was the teacher of the class. My friends said I explained the material well, and yes, that also inspired me to be a teacher.
The work with my sisters and my eighth-grade school teaching combined to help me develop my early interest in teaching math. I entered college and knew from day one that teaching high school math was my goal. I never really considered any other option.
Your early career focused on mathematics and computer science. How did statistics become a significant part of your professional work?
In 1980, I accepted a teaching position at Rufus King High School in Milwaukee. The school had just received acceptance in the International Baccalaureate program. Similar to AP, but with a European focus, the school also wanted to offer a new course called IB Computing Studies. I had experience teaching intro computer courses during my time at Carroll College. The IB coordinator asked if I would teach this course—and of course, I was very excited to give it a try!
It was an interesting time to teach computer-related courses. To be honest, the guidelines for the course were very vague, thus I could pretty much do what I wanted. I decided to teach a programing language and to help students develop the key components of coding. The course I initially taught was essentially learning the BASIC programming language. (We later switched to Pascal.) I soon realized that simply teaching the structure of a computer language was not engaging to most students. As a result, I refocused the course on developing projects. Almost all the projects were connected to collecting data and writing programs to summarize the data. This led to an interest in statistics and probability, which I soon connected with my math classes. Most of the projects involved surveys. Students submitted topics of interest, and I had them write the survey, collect completed surveys, and begin analysis of collected data. The students then wrote the code to graph and summarize the data. Topics explored were often related to the school environment, issues about preparation for college, the physical plant of the school, asthma, generations, and teenage challenges in life. Students were excited to present their results. I organized a “press conference” to conclude the project, in which students summarized their results for news media, the school board, parents, community members, and political leaders.
The course evolved into IB Computer Science, and for 20 years, I served as the senior teacher for the course. The IB organizing committee in New York City selected me for this position. During several summers, the New York office sent me to schools across the country and world (Egypt, Germany, and Canada) to assist them as they developed the course. The goal was to structure a genuine data analysis computer science course. I assisted in writing the curriculum for the course and expanding its outreach. For most of my time as senior teacher, I also served as the assistant examiner for this course and worked with other teachers across the country to develop statistical projects and computer science objectives.
What is the Marquette University Educational Opportunity Program, and how did you get involved? What lessons from that experience still influence your thinking about education today?
My first teaching job was in 1971 at West Division High School, near Marquette University. This was a difficult high school. It was going through an urban transition marked by racial and economic tension. It was experiencing the impact of students from some of the poorest areas of the city mixing with middle-class students, whose families were desperate to move out. The school was known as the melting pot of the city with African Americans, Puerto Ricans, Mexicans, Native Americans, and whites all part of the student body. Unfortunately, the student interactions were a mess, with little preparation for teachers and little counseling for the student population.
In 1973, Marquette received a grant from the Office of Education (the Department of Education was not cabinet-level at that time) to start a program called Upward Bound. This program identified local high school students from low-income families who had an interest in attending college. Furthermore, the families were considered “first generation,” as students’ parents were not college graduates. Students accepted into the program generally lacked the skills to be accepted by Marquette. Their grades and test scores were not acceptable without academic support.
During the summer of 1973, Marquette recruited me to teach a math class for their initial Upward Bound students. Interestingly, most were my former high school students from down the road. They were 11th-grade students who lived on the MU campus for six weeks during the summer, and they were treated like college students. This connection for me was special. I then had several of the students from this summer program work with me during the school year.
The director of the program asked me to assist Marquette in exploring ways to incorporate their work with students after regular school hours during the academic year. I accepted a part-time position that targeted the development of a mathematics lab at the university for students in the program. This eventually led to a full-time job in 1974 that marked a turning point in my career. The position I accepted was to counsel and instruct college students accepted into the program and high school students. To this day, I remain in contact with several of the students from the program. Many of them are now active citizens in the Milwaukee community.
Legacy and Philosophy
You’ve authored and co-authored several textbooks, including People Count and Making Sense of Statistical Studies. What gap in statistics education were you hoping to address through these materials?
My projects and books were all connected to what I define as “modeling” with data. Teachers are driven to teach skills and ensure students can apply them at the next level of learning. I agree with that, but there must also be an equal focus on the purpose and relevance of what students are learning. Modeling has many definitions, but for teachers of statistics, I favor one that develops students’ ability to ask and answer “what if” questions. What if the parameters of the investigated problem change? What if the story of the investigation alters? Behind most statistical questions are structures that provide students a chance to alter the question and discover how those changes influence the outcomes. Understanding these structures is the first step in my definition of modeling.
In Making Sense of Statistical Studies, for example, Roxy Peck and I developed a lesson around the question, “Are teenagers responsible?” Students designed a survey, collected data from their school community, and analyzed the results. The project naturally led to additional questions: Would students in another country respond differently? What might explain any differences? For me, that process of extending a statistical investigation through new questions is the essence of modeling with data.
In my book People Count, students applied a comparison of the count of people in one age group (for example, the count of people in 2015 who were 15–19 years old) to the count of people 20–24 years old in 2020. For the United States, the comparison showed a greater count in 2020. What does that mean? The added count was explained by immigration, but what if the percentage increase in that age group continued into the future? What would the age distribution of the United States look like in 2050? Here again, I contend that answering these questions requires modeling with data. I received considerable help from several ASA and NCTM colleagues, including Jerry Moreno, who edited the book, presented the material at local workshops, and helped me with presenting it at two ICOTS conferences in Brazil and Slovenia.
Looking back on your many textbooks and educational resources, is there one project you were especially proud of?
This is a difficult question to answer. I’ve contributed to several books and resources in probability and statistics education, including Navigating Probability, Focus in High School Mathematics: Reasoning and Sense Making in Statistics and Probability, and work within the Data-Driven Mathematics series. Across these projects, my focus has been on helping students engage with data through meaningful “what if” questions and real-world contexts.
Yet, the book I am proudest of is clearly People Count (and Their Data Stories). This book was in the making for more than 30 years. I conducted several workshops as I was developing this book. I also used it with my Marquette University Upward Bound students and my students in several introductory classes to statistics at Marquette University. A version of the book was reviewed by a committee of the ASA/NCTM Joint Committee on Curriculum in Statistics and Probability for Grades K–12 in 2020. A statistician who reviewed the book completed a 25-page report that highlighted suggested revisions and strengths of the book. I remain the proudest of his concluding comment:
My hope is that this review will be useful for both the ASA/NCTM Joint Committee as well as the author. I would like to conclude by thanking the ASA/NCTM Joint Committee for the opportunity to review the text as well as the author for creating an invaluable resource, which I firmly believe will greatly improve statistical education in high schools, community colleges, and undergraduate statistics.
The book is included on the ASA website as a K–12 resource. I’m not sure if it has been used. Unfortunately, the ASA was unable to complete a formal publication.
How would you describe your teaching philosophy? Can you give us one or two principles?
Consider the following scenario: A person learns to swim by first learning the skills of swimming—how to float, how to move your arms, or how to kick to move through the water are starters (skills). Then, this person uses these skills to swim to the other side of the pool (application). But then, the person also needs to think about “Why do I want to swim to the other side?” (Addressing relevancy.)
Consider the following diagram of what I would describe as a learning continuum:
Continuum of Learning in Mathematics, Statistics, and Data Science
To make sense of the above model, I need to define my levels. For starters, here are my definitions of some of these terms used in the above diagram:
- Skills are procedures or steps in solving problems that demonstrate little evidence of reasoning.
- Working with Applications involves students solving problems they may encounter or will encounter in life.
- Addressing relevancy and reasoning involves students solving problems that answer or at least address the question, “Why is this problem (task) important?” Students apply reasoning in the development of their solutions or answers.
I think my concern for high school and college students is that they are often stuck in the skill development level (Level 1) or early-level application (Level 2). Students often miss the level of “Why am I doing this?” or “Why is this important?” In defense of their teachers and schools, this lack of finding relevancy is often due to the first-generation, low-income background of the students I taught. Students may learn the skills of measurement and fractions, and they may even work with problems that apply those skills, but they may not learn or experience why this is important due to their life experiences. (Their life experiences may be different from the life experiences of other students in the community.) If their life experiences don’t connect with the problems presented in the lessons or curriculum, they’re often wondering, “When will I use this?” As students understand these applications are relevant, they become more successful in these disciplines and are less likely to “hate” the discipline. And please do not equate my definition of relevancy as totally linked to a student’s passion or interest in problems. Problems could be of low interest but still be understood as relevant. Relevancy is simply being aware that the task or problem plays an important role in someone’s life.
Was there a particular student, classroom experience, or project that reinforced why you chose a career in education?
West Division High School (my first teaching job) was going through some rough times in 1971—many hallway interruptions, many spontaneous fights during school assemblies, many angry words in my classes. I was overwhelmed. My “dream” when I took this job was to follow in the footsteps of Sidney Poitier and his inspiring movie To Sir with Love. (Just for the record, I have little resemblance to Sidney Poitier.) But, like the character in the movie, I threw the assigned books in the corner of the classroom and began in earnest to teach math differently. I really wanted my students to see a meaningful reason to learn this stuff.
All of this chaos connected me to my students in a powerful way. Two students (Rick and Leonard) were pulling for me to make it. Our friendship was not just a student/teacher friendship—it was deeper. We later described it as an equal partnership in survival and an opportunity. Rick helped me survive. He protected me. He helped me understand the challenges of an urban culture (which we called the “inner city” at the time). He helped me understand the ins and outs of the neighborhood, the harsh vocabulary in the hallways and streets, the humor, and essentially a culture that is both beautiful and ugly. And I helped Rick (I think) understand that he was a strong and capable student—that when he graduated from West, he would be ready to pursue a college degree, something he wanted to do but was concerned might not be possible. Both Rick and Leonard introduced me to their families. I also saw the strong role families played in their lives, especially the support Rick and Leonard received from their mothers.
I am most proud that Rick earned his BS in engineering at the same time I completed my master’s degree in mathematics—we both participated in the 1980 graduation. Leonard earned his BS in computer science a year earlier.
Reflections and Advice
If you could improve one aspect of how statistics is taught today, what would it be?
I have a personal bias that statistics should focus on the connection between a sample and a population. It’s no longer simply about zs and ts and confidence intervals or significance tests. Statistics is about making sense of data and understanding why it matters (or doesn’t matter).
So, how does that translate to classroom teaching? In my introduction to statistics classes at Marquette, I began with the study of demographic age and sex distributions of the United States and other countries around the world. My goal was for students to understand the whole population before we started studying the data based on a sample. The key to this study of the whole population were questions such as: “What if this country increased (or decreased) its immigration rate?” “What if the birth rate increased?” “How would the country change?” My goal was to involve students in understanding the dynamics of a country’s population and have them interact with a basic model that would study changes in the future of that country.
The key aspect of my opening is to highlight modeling (granted, I have a specific definition)! Math, statistics, data science … the point is to explore the “what if” questions and connect those to the countries studied and the impact on the people in those countries. Yes, this is what I hoped would happen with my People Count text. The recursive procedure developed (which is rather simple) is key to understanding a dynamic study of the future and the purpose of linking the data to the “what if” questions.
After this foundation, the traditional study of samples, distributions of a population, and links to the traditional topics of statistics make more sense. Behind every sample is a population, and this population is what we want to understand. My goal has been to make sense of what a z, or t, or mean, or median, or mode tell us about a population. Skills, applications, and relevancy are connected. In my view, balancing these learning outcomes is important.
What advice would you give educators who want to make statistics more engaging and relevant to students?
If students don’t experience the relevancy of problems presented in the curriculum, they often wonder, “When will I use this?” If students experience the relevancy of the problems, they become more successful and less likely to “hate” the discipline. Statistical problems could be of low interest but still be understood as relevant. Relevancy is being aware that the task or problem has a purpose or meaning. Students experience relevancy when problems are questioned, connected to a context, viewed as part of a story that may or may not be totally understood, or linked to other problems or questions that are part of a larger story. And, when possible, I try to bring out a “what if” scenario to the story. Statistics is a discipline that connects to a context. So, unlike what students may experience in trying to understand some problems in mathematics, connecting problems to a context is essential in statistics.
A student completing a survey project in my class looked puzzled when I tried to understand his analysis of survey questions related to our study of asthma. When I asked him to tell me “why students who live with a family member who smokes” is an important connection to whether the student has asthma, I saw his interest light up as the study became relevant to him. The student found a link that made his work important.
What skills do you think are most essential for future statistics educators? Do you have any advice to offer future teachers?
The array of skills for statistics will be linked, in my definition, to a focus on modeling. I have addressed what I define as modeling and its structure to statistics. I hope it made sense. The future for statistics (and math and data science) will be to address the study and treatment of data as a human and value-focused study. We cannot get caught up in the often trivial explanations in our classrooms or textbooks. We must challenge ourselves and our students in the study of what is important and why. Don’t let a summary of AI drive the study of what we teach and what students learn. Understanding the values related to a summary of data is not something an AI study can accomplish. This reworking of our disciplines will be both exciting and challenging.
What changes have you seen in how statistics is taught in schools since you first began teaching?
My first experiences of teaching statistics involved a lot of paper and pencil computations (1970s). Clearly, the development of technology in hardware and software was a major factor. But, the primary function of what is behind statistics did not change during that time. The study of samples, sampling distributions, connections to significance, hypothesis testing, etc., did not radically change. I think we are living in a complex time in which our definitions of statistics, mathematics, and data science are changing—and we don’t know where it’s going! To some extent, these disciplines are trying to prove why they are important. AI is conveying that it can handle a lot of what is in this discipline, so skip teaching it. I have strong opinions on this matter, and I hope we can bring out the “human element” in our study. It will be a challenge!
What is the human element? Obviously, my summary would take a lot of space, and I’m still thinking about much of it. I hope we continue to challenge ourselves and teach our disciplines with a connection to modeling and questioning. The questions we raise may be answered by AI interventions, but I don’t think they’ll encompass the entire range of “significant” questions we need to address.
If you could leave one message for today’s statistics educators, what would it be?
Explore and teach the “human element” of data analysis, mathematics, and statistics. See my responses above.
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