Math-infused Science

Students aren’t the only ones who struggle to determine the best way to display data in graphic form. Because there are usually many representations that can be used, and each may encourage the reader to make slightly different conclusions, deciding on the most appropriate graph can be tricky. In this 1.5 hr. workshop, participants will learn a repeatable technique for helping students consider the strengths and weaknesses of potential visual representations. Participants will experience three methods for deciding on the best graph, so they have a selection of approaches to use with different types of learners.

Although the examples in this workshop will be based in math and science, this 1.5-hour workshop is open to teachers of all grade levels and subject areas.

In this 1.5 hr. workshop participants will use an example data set to explore different methods of depicting the same set of numbers in several different ways. We will define the relationship between the research question and the visual representation of data and address the impact visual presentations make on conclusions. As a participant you will be guided through activities you can use with your students in either a synchronous or asynchronous teaching platform. All activities in this workshop will be focused on helping students determine the most appropriate type of graph for their data.

Although the examples in this workshop will be based in math and science, this 1.5-hour workshop is open to teachers of all grade levels and subject areas.

How do we talk about data? How do we write about data? In this 1.5 hr. workshop you will discover ways to help your student be specific, using the correct terms, in context, as they identify and describe trends in a set of numbers. We will play two games useful for building a working vocabulary and increasing student reliance on mathematically accurate communication. We will touch on formal statements of ‘statistical significance’ as well as informal statements of primary trends, disruptions, and outliers. We will exemplify the connection between evidence and reasoning (in the CER argument). The activities used in this workshop are applicable to students at any grade level and can be an introduction to descriptive mathematics for younger students or a repeatable method for answering free response, data-based questions for students taking an AP or IB exam.

Although the examples in this workshop will be based in math and science, this 1.5-hour workshop is open to teachers of all grade levels and subject areas.

Using manipulatives found in our homes, we will simulate two common field science experiments:  Lincoln’s Index for measuring abundance and Simpson’s Index for measuring biodiversity. Participants in this 1.5 hr. workshop will gather evidence and make calculations that can be used to describe the health of and changes in an ecosystem. Each activity will be followed with the creation of a student-designed experiment that can be performed at home to reinforce the technique and assess the students’ understanding of how biodiversity and abundance estimates can be applied.

Although the examples in this workshop will be based in math and science, this 1.5-hour workshop is open to teachers of all grade levels and subject areas.

In this workshop we will practice a repeatable structure for introducing a topic that will be studied through scientific exploration using a remote teaching and learning platform. We will help our students conduct a preliminary investigation at home developing interest in a particular phenomenon by generating data and making observations and hypotheses. We will then assist our students in recognizing and naming potential variables that may be responsible for impacting this phenomenon. Participants will learn to guide their students through this process and identify variables that could be adequately explored within the constraints of at-home learning.

This 1.5-hour workshop is open to science and math teachers of all grade levels. We will focus on employing the Next Generating Science Standards (NGSS) instructional practices for teaching math-infused science.

In this workshop we will pick up where Part 1 of this series left off. We begin with a list of variables our students have identified as potentially impacting a particular phenomenon they have explored. Using a think-pair-share process, we will give students the structure needed to write steps for a scientific investigation using the independent variable of their choice. Students will work in lab groups to share their ideas and coalesce on an experimental design that addresses their research question. With the teachers in this workshop acting as the students we will practice conducting a peer review in an asynchronous (posted class assignment) or synchronous platform (video meeting). This workshop is most suited for teachers who have already taken Part 1 of the Student-designed Experiments series.

This 1.5-hour workshop is open to science and math teachers of all grade levels. We will focus on employing the Next Generating Science Standards (NGSS) instructional practices for teaching math-infused science.

Teachers will play the role of the students, collecting data in their own homes and pooling their observations and measurements in a spreadsheet shared by their lab partners. We will conduct data analysis within lab groups during the workshop to experience how this process can be performed using remote teaching and learning platforms. Peer critiques will help improve the preliminary data charts, graphs, and analysis to produce a curated product from each lab group before going on to the final steps of drawing conclusions. This workshop builds on the process taught in Parts 1 and 2 of the Student-designed Experiments series, but it can be used as a stand-alone workshop if desired.

This 1.5-hour workshop is open to science and math teachers of all grade levels. We will focus on employing the Next Generating Science Standards (NGSS) instructional practices for teaching math-infused science.

This workshop will focus on the content and demands of the conclusion section of a lab report, with applications to data-based questions and internal assessments for IB students, and free response questions for AP students. The conclusions drawn from experimental data must be limited to the scope of the experiment, but it is also important for students to be able to understand how their individual work is related to the broader world. This workshop will employ an activity teachers can use to help their students identify the implications of their conclusions and connect the work they have done to topics that may be relevant. This workshop builds on the process taught in Parts 1, 2, and 3 of the Student-designed Experiments series, but it is not necessary to have taken the previous sessions to join and benefit from this workshop.

This 1.5-hour workshop is open to science and math teachers of all grade levels. We will focus on employing the Next Generating Science Standards (NGSS) instructional practices for teaching math-infused science.

Whether in the classroom or at home, how do we initiate the process of student-designed lab or field experiments? The first step is to help the students see potential research questions and the data in the world around them. In this 1.5-hour workshop we engage in several demonstration activities to help teachers see sources for inquiry that are easily accessible. We will use spreadsheets to gather large amounts of data very quickly, and then look for trends in the data to expand our initial question into additional research questions. This repeatable technique is one that can be used in a synchronous or asynchronous class, in-person or in a distance-learning environment. Each data-generating activity explored can be used with students to practice analysis and graphing, or to develop a sophisticated investigation for use as an independent research project or Internal Assessment.

Although the examples in this workshop will be based in math and science, this 1.5-hour workshop is open to teachers of all grade levels and subject areas.

All measurements include some degree of uncertainty or error, but how it is reported is decided by the person collecting the data. Because analysis is dependent on the data collected, the method used to report error can substantially impact the strength of the claims made and conclusions drawn. In this workshop, we will explore five ways uncertainty is described using different instruments commonly found at home. We will practice making decisions about the method that is most appropriate in different situations and defend our choice to our peers with evidence and reasoning.

This 1.5-hour workshop is open to science and math teachers of all grade levels.

Often by middle school and certainly by high school, students default to the mean as the best way to describe data without much consideration for how they might defend that choice. So, you might think, what’s the harm in that? Everyone knows what is meant by this descriptor, it is familiar and understandable, easy to calculate, and informative, right? In this workshop, we will use an activity to collect data and consider the options we have for describing data so we can tell the story of what we observed. This workshop will help you clarify the strengths and weaknesses of common descriptors of central tendency so you can, in turn, guide your students on their choice.

This 1.5-hour workshop is open to science and math teachers of all grade levels.

The variance, standard deviation, and standard error of the mean are excellent methods for describing data because they convey the variability of the observed data around mean. Anyone teaching Pre-AP, Pre-IB, or college-bound students will likely want to know how to calculate these values, what they indicate, and how to contextualize them so they can better prepare their students for use in scientific research. In this workshop, we will calculate each descriptor by hand using a small data set and practice using the formulas to automatically calculate these values in a spreadsheet. We will breakdown the impact each variable has on the outcome and relate these descriptors to the bell-shaped curve to better understand what each says about the data collected. You do not need any previous knowledge of statistics to take this workshop.

This 1.5-hour workshop is open to science and math teachers of all grade levels.

Error bars are placed on a graph to give a more detailed account of what was observed.  Although there are many descriptors that can be used to draw error bars, in each case the value is used to express the uncertainty or variability of the data. Error bars created from certain calculations are especially informative for giving the reader a hint at the significance of the difference seen between two variables, and can at times be a substitute for a statistical hypothesis test. In this workshop, we will practice using error bars on different types of graphs, analyze different data sets, and defend the choices we would make in each case.

This 1.5-hour workshop is open to science and math teachers of all grade levels.

Parts 5-8 continue the Statistics for Science series to include the skills required in high school Advanced Placement (AP) and International Baccalaureate (IB) science courses. In these workshops, we will learn how and when to use each of the most common statistical tests that are used to test hypotheses. A hand-calculation will be done using a very small data set so participants can see how the outcome is impacted by common issues such as a small sample size, variation, and outliers. Participants will learn how to write the spreadsheet formulas for each equation, how to interpret the calculated values using tables, and the significance of the p-values obtained in their results. I invite you to join us even if you are math-phobic or do not have a background in statistics, this series of workshops is tailored to science teachers who need some help providing context and explaining these concepts to their students.

This 1.5-hour workshop is open to science and math teachers of all grade levels and is particularly relevant for teachers of AP or IB science courses and any class that includes independent research.

Parts 5-8 continue the Statistics for Science series to include the skills required in high school Advanced Placement (AP) and International Baccalaureate (IB) science courses. In these workshops, we will learn how and when to use each of the most common statistical tests that are used to test hypotheses. A hand-calculation will be done using a very small data set so participants can see how the outcome is impacted by common issues such as a small sample size, variation, and outliers. Participants will learn how to write the spreadsheet formulas for each equation, how to interpret the calculated values using tables, and the significance of the p-values obtained in their results. I invite you to join us even if you are math-phobic or do not have a background in statistics, this series of workshops is tailored to science teachers who need some help providing context and explaining these concepts to their students.

This 1.5-hour workshop is open to science and math teachers of all grade levels and is particularly relevant for teachers of AP or IB science courses and any class that includes independent research.

Parts 5-8 continue the Statistics for Science series to include the skills required in high school Advanced Placement (AP) and International Baccalaureate (IB) science courses. In these workshops, we will learn how and when to use each of the most common statistical tests that are used to test hypotheses. A hand-calculation will be done using a very small data set so participants can see how the outcome is impacted by common issues such as a small sample size, variation, and outliers. Participants will learn how to write the spreadsheet formulas for each equation, how to interpret the calculated values using tables, and the significance of the p-values obtained in their results. I invite you to join us even if you are math-phobic or do not have a background in statistics, this series of workshops is tailored to science teachers who need some help providing context and explaining these concepts to their students.

This 1.5-hour workshop is open to science and math teachers of all grade levels and is particularly relevant for teachers of AP or IB science courses and any class that includes independent research.

This is the culminating workshop for the Statistics for Advanced Level Science series. In this session, we will compare the application of different hypothesis tests and discuss how more than one type of statistical analysis may be appropriate for the same set of data. We will look for the key components of research questions or data sets that indicate choices for analysis and discuss the strengths and weaknesses of each. In teams, we will collaborate to create a dichotomous key for choosing an appropriate method so you have a guiding diagram to consult when you are advising your own students. It is suggested that you take the Part 5-7 workshops or are comfortable with the methods of hypothesis testing covered in the previous workshops so you can participate fully.

This 1.5-hour workshop is open to science and math teachers of all grade levels and is particularly relevant for teachers of AP or IB science courses and any class that includes independent research.