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Course Descriptions

Wondering what to expect in your WVUteach classes? Read the descriptions below and learn more about your journey to become a certified math or science teacher.

Introductory Courses

Step 1

ARSC 120-Step 1: Inquiry Approaches to Teaching (1 credit hour)

This 1-credit-hour class meets once a week and includes five visits to a local public school. In this course, students will learn the elements of an inquiry-based lesson. Two to three students will be paired and matched with a mentor teacher in a 3rd - 6th grade class for student teaching at a time that fits the students' schedules.

Step 1 Printable PDF

Step 1: Inquiry Approaches to Teaching

Pigs and Chickens Sample Lesson Plan

Contributed by Jason Ermer and Chris Costello

Engagement

Estimated time: 3 minutes

Table 1: Engagement
Teacher and Student Activity Probing Questions (Questions that make student thinking visible), Predicted Student Answers (to a few questions), Misconceptions

1. Ask students about their favorite animals, and guide the conversation toward barnyard animals.

Note: To increase participation, the teacher can ask students to write down three examples of their favorite animal.

1. "What is your favorite animal? Why do you like that animal?"

“Write down your three favorite animals.”

“I heard someone mention ______, did anyone else list a farm animal?” “What is your favorite farm animal?”

(Accept all responses.)

2. Teachers with a high threshold for noise and chaos may wish to have students imitate the sounds their favorite animals make.

3. Transition to the problem:

Teacher will transition from the initial questioning to focus on the context of pigs and chickens. 

3. “Speaking of barnyard animals, my friend Fred, the farmer, has a problem about the number of animals in his barnyard… and he would like our help. Do you think you could help him out?”

4. Project and read the story shown at right.

The teacher should answer any questions about the problem prompt. 

Note: The teacher should make sure that the students understand that a pig has 4 legs and a chicken has 2 legs.

4. "Once upon a time, there was a farmer who raised pigs and chickens. One morning, the farmer looked into the barnyard and counted 24 heads and 80 feet. How many pigs and how many chickens are in the barnyard?"

Note: This kind of problem usually appears around the time that students are learning about systems of equations. In that context, solving such problems becomes a fairly formulaic exercise. This lesson presents the problem to much younger students, however, which can provide an opportunity for them to be creative in how they approach a solution.
Transition

“I'd like you to work with your partner for about 5 (or 10) minutes to see if you can figure out how many pigs and how many chickens are in the barnyard.”

Exploration

Estimated time: 10 minutes

Table 2: Exploration
Teacher and Student Activity Probing Questions (Questions that make student thinking visible), Predicted Student Answers (to a few questions), Misconceptions

1. Materials management:

The teacher will assign 1 person from each group to come pick up a white board, marker, and eraser.

1. “With the members of your group, determine who has the most (or least) number of siblings. This person will be the materials manager for today’s lesson. The materials manager should come pick up one white board, one marker, and one eraser.”

2. Teacher circulates and guides student groups using the questions at right.

Note: In addition to circulating the room and asking probing questions, the teacher should be identifying potential methods or strategies used (to help facilitate the explanation section.)

2. "How did/will you begin?"

Some students may be stuck about how to get started. Consider prompting students with one or more of the following questions:

"Do you suppose the barnyard could contain one pig and one chicken? Why or why not?"
No, because the farmer counted 24 heads. If there were just one pig and one chicken, that would be only 2 heads.

"If there were only one pig and one chicken in the barnyard, how many feet would there be?"
Six feet, since the pig has four feet and the chicken has two feet.

"What is one combination of pigs and chickens that would give us the right number of heads? How many feet would there be in that case?"

“Do you think it is possible to have all pigs? What about all chickens?” No, that would not be possible because we would have too few/many legs.”

There are many possible combinations that will give the correct number of heads. In any case, guide students to see that each pig has four feet and each chicken has two feet.

Suppose students guess 12 pigs and 12 chickens, which would result in (12 × 4) + (12 × 2) = 48 + 24 = 72 feet. Follow up with:

"So, have we found the answer yet? How do you know?"

No, we need 80 feet but we only have 72 feet.

"What should we try next?"

Students might make another random guess, or might notice that since we currently have too few feet, we need to add pigs and take away chickens.

The questions above suggest a guess-and-check approach. Students might need some help in organizing their data.

"How might we organize our guesses?"
Suggest may suggest an organized list or a table like the one shown below, but don't force students into a particular representation.

"What patterns can you see in your data?"

The number of pigs plus the number of chickens always equals 24. When we trade one pig for one chicken, the number of feet goes down by 2 because we take away four feet (from the pig), but add two feet (from the chicken). So, in the end, we lose two feet.

Encourage students to work forward and answer the question based on the pattern they have discovered: "Can we use this pattern to answer the question? How will we know when we have arrived at the answer?"

As an alternative to guess-and-check, students might solve this problem by drawing a picture.

"Can we draw a picture to represent this situation? How could we represent the 24 heads?"

We could draw 24 circles (or some other representation).

"How could we represent the feet?"

We could add lines to the circles (or some other representation).

"How will we know when we're done?"

We will have a total of 80 lines (for the feet).

Students can proceed down a number of paths here. Some possible paths include:

Adding two lines to each circle (since each animal as at least two feet), for a total of 48 feet. Follow-up question:
"What does this picture represent?" This picture represents a barnyard with only chickens. 

Then, adding two feet at a time to some animals and counting up by twos until reaching 80 feet. 

Or, realizing that there are 80–48=32 feet yet to be drawn, and that we will add feet in pairs. So, we must add 32÷2 = 16 additional pairs of feet. 

In any case, in the end we will have a picture that shows 24 circles, some of which have two lines attached, and some with 4 lines attached. We can then count the number of two-line circles (this is the number of chickens) and the number of four-line circles (this is the number of pigs). 

Transition

While monitoring the groups, watch for the end of the Exploration and announce the one-minute mark. This could be either:

  1. When the allotted time is almost up, or... 
  2. When most of the student groups have found a productive strategy (whether or not they have solved the problem completely). Groups that finish early can be presented with the Extension Problems below. 

After an additional minute, call the group back to order.

Explanation

Estimated time: 10 minutes

Table 3: Explanation
Teacher and Student Activity Probing Questions (Questions that make student thinking visible), Predicted Student Answers (to a few questions), Misconceptions

1. Ask students to share their ideas – both for the answer to the problem and for their approaches.

Students can hold up their white boards to show their work and help facilitate the presentation.

Note: The focus here should be on the methods that students used to organize their data and solve the problem. The teacher should use the information gained while circulating to help call on students and/or highlight certain methods. (“I saw a couple of groups that tried ________. Would anyone like to show this method?”

1. “How did you approach the problem?”

We decided to start with the heads.

I just guess and checked different combinations.

We tried to do half chickens and half pigs, but that didn’t work so we then…”

"How many pigs and how many chickens are in the barnyard? "

There are 16 pigs and 8 chickens in the barnyard.

2. Focus students attention on specific points of each approach, and connect the different approaches with each other.

2. "Consider the guess where we have 12 pigs and 12 chickens. That makes 72 feet. What should our next guess be? Why?

We should make a guess that includes more pigs and fewer chickens because we need to increase the total number of feet. Increasing by one pig (and decreasing by one chicken) will give us an increase of two feet.

"How is this reflected in the table?"

If we increase in the "pigs" column, the "chickens" column decreases and the total number of feet goes up by 2.

"How is this reflected in the drawing?"

We can change a "chicken" into a "pig" by adding two lines/feet to one of the circles/heads. This means the total number of feet goes up by 2 (because we added two feet to the drawing).

3. Once the students have the opportunity to share, the teacher will address any misconceptions and fill in any missing vocabulary.

3. “What are the various strategies that we saw?”

“How did this help us reach the correct solution?”

Transition

“You did a fantastic job! I can not wait to tell my friend, Fred the farmer, the answer to his problem!”

“Now, I have another problem that I need your help with!”

Elaboration

Estimated time:

Teacher and Student Activity Probing Questions (Questions that make student thinking visible), Predicted Student Answers (to a few questions), Misconceptions

Depending on the background knowledge of the students, their success on the previous problem, and the amount of time remaining in the lesson, the teacher can choose one of the following options below.

(Problem 1, about strategies, could be included as an extension to the Explanation section given above or as an Elaboration. Problems 2 and 3 are more clearly Elaboration: they introduce story problems with "too little information" and open up the possibility of multiple correct answers.)

1. An extension about strategies:

1. In a terrarium of spiders and crickets, I counted 60 heads and 412 feet. How many of each animal are there? Which strategy would you choose to solve this problem? Why? Are there other strategies we haven't thought of yet? (Note for those who aren't bug fanciers: spiders have 8 feet and crickets have 6 feet.) 

2. An extension about a more ambiguous story:

2. In a barnyard that contains only pigs and chickens, a farmer counts 110 feet. How many pigs and how many chickens could there be? Is there more than one possible combination of animals? Find as many solutions as you can to this problem. Is there a pattern in these solutions? 

3. A really challenging ambiguous story:

3. A really challenging ambiguous story: A hobby shop sells model airplanes for 7 dollars each and model train sets for 18 dollars each. Yesterday they made 208 dollars selling only those two items. How many of each item could have been sold? Is there a solution? Is there more than one possible solution? 

Transition

“Remember the materials manager who picked up the materials? Well this time the other partner is in charge of returning the supplies to the back table.”

“I have been very impressed with the work you have done today! I have one more task where I would like you to show me all of the great things that you have learned today!”


Evaluation

Estimated time: 

Table 4: Evaluation

Teacher and Student Activity

Probing Questions (Questions that make student thinking visible), Predicted Student Answers (to a few questions), Misconceptions

Note: The majority of the evaluation occurs throughout the lesson.

*During Engagement: What animals are they interested in? Do they know about pigs and chickens? Do they know that a pig has 4 legs and a chicken 2?

*Before starting the Exploration: Do the students understand the task? Are the materials managed efficiently and safely?

*During the Exploration: Are students able to get started on the problem? What strategies are they using? How are they organizing data? Which groups are similar?

*During the Explanation: What explanations are provided? What strategies are used? What strategies are not used? What vocabulary are the students using? What are they not using? 

*During the Elaboration: Which elaboration problem best suits the students? Do the students understand the differences between this and the original problem? How are they attempting to solve this problem? Do the same strategies appear? Are these appropriate?

Formal evaluation (time permitting):

The teacher will pose a question for the students to answer individually (or in small groups)

Step 2

ARSC 220-Step 2: Inquiry – Based Lesson Design (1 credit hour)

This 1-credit-hour class meets once a week and includes five visits to a local public school. In this course, students will improve their teaching skills, develop lesson plans and gain experience teaching in grades 6th - 8th. In subsequent WVUteach courses, student experiences will be at the high school level.

Step 2 Printable PDF

Step 2: Inquiry-Based Lesson Design

Lesson Plan Template, Version 1

Engagement

Estimated time: 3 minutes

Author: Nancy Spillane
Team Members: Vanessa Licwov-Channell

Title of lesson: Mystery Box
Technology lesson? No
Lesson source: Jana McFarland, Lynn Kirby, Daniel Fitzpatrick


Lesson#:
Date lesson will be taught: 8/16/17
Length of lesson: 30 minutes

Mentor’s name:
Mentor’s school:
Subject/Grade level: undergraduate


Concept statement/Main idea: 

In paragraph form, write the concepts and vocabulary of this activity. 

Differentiating observations, inferences, and hypotheses, and introducing the idea of a theory (and differentiating from law).

Scientific inquiry requires using your senses to make observations that lead to inferences about the area of investigation. Scientists compile inferences to make a hypothesis to try to solve the question of the investigation.

Observation: an act or instance of viewing or noting a fact or occurrence for some scientific or other special purpose.

Inference: the act or process of deriving logical conclusions from premises known or assumed to be true.

Hypothesis: a suggested solution for an unexplained occurrence that does not fit into current accepted scientific theory.

Theory: a well-established explanation for a phenomenon in the natural world based on repeated verification through observation and experimentation.

Law: a statement based on repeated experimentation and observation that describes an aspect of the natural world.


Standards

List the appropriate process and content standards for your lesson.

CCMS – Common Core Mathematics Standards

NGSS – Next Generation Science Standards

  • Practice 1: Asking questions and defining problems.
  • Practice 3: Planning and carrying out investigations
  • Practice 4: Analyzing and interpreting data

WV NextGen CSOs Mathematical Process Goals

  • Make sense of problems and persevere in solving them
  • Construct viable arguments and critique the reasoning of others

Objective/s– Write objective/s in SWBAT form. 

The Students Will Be Able to:

Evaluation

Based on your objectives, draft the content of the questions you will ask on your pre- and post- assessments; at least one question for each objective. Questions do not have to be multiple choice. The actual pre- and post- assessments are required at the end of this lesson plan.

SWBAT:

  • Make observations.
  • Draw inferences.
  • Develop a hypothesis.
  • Differentiate observations, inferences, and hypotheses.

What do you hear or feel when you move the box?

Are there different ways to move the box that might give you different information?

Since you hear that one sound is louder than another, what can you infer about the objects?

Write a hypothesis that you can answer through experimentation.

What is in the Mystery Box?


Materials list (BE SPECIFIC about quantities)

For whole class:

Per group:

  • Mystery Box
  • Magnet

Per student:

  • Pencil and paper OR Whiteboard for team
  • Mystery Box Activity Sheet (see attached)

Advance preparation:

  • Enough identical boxes for all groups – groups should be 4 students or fewer
  • Put objects in boxes and seal them: nail, washer, marbles, pencils, etc. – different physical properties. All boxes should have the same contents.

Accommodations: Include a general statement and any specific student needs.

For students with physical limitations, allow others to move/shake the box so all students can observations and inferences. Students hard-of-hearing or with vision limitations may use touch to feel different sensations when moving the box.

Safety: Include a general statement and any specific safety concerns.

There are no safety concerns for this lesson.


Engagement

Estimated time: 2 minutes

What the teacher does and how the teacher will direct students (directions):

Probing Questions: Critical questions that will connect prior knowledge and create a “Need to Know”
Expected Student Responses and Misconceptions – think like a student to consider student responses INCLUDING misconceptions (write these in italics)

Ask the students how scientists come up with things to study.

“Please raise your hand if you have a thought to share.”

“How do scientists come up with things to study?”

They make observations about natural phenomena.

They are curious about something and want to know the answer.

They want to improve the world somehow.

It depends on what they are funded to study.

Transition

“Today you will all be scientists, and you are tasked with determining what is inside of this box.”


Exploration (I)

Estimated time: 5 minutes for short exploration (Exploration 1) to give students the opportunity to make observations and then to clarify their ability to differentiate observations and inferences.

What the teacher does and how the teacher will direct students (directions):

Probing Questions: Critical questions that will guide students to a “common set of experiences.”
Expected Student Responses and Misconceptions – think like a student to consider student responses INCLUDING misconceptions (italics)

“Each group will receive a Mystery Box.

You should not open or otherwise damage the box.

Your first task will be to take five minutes to write two or three observations on the white board on your table.”

Have the students write down one question that they will try to answer.

Before you begin your observations, write down a question that you will try to a through your observations.

How can you make observations about something you cannot see?

What other senses do you have? “ Smell, touch, sound, taste.”

How can you manipulate the box to gather data? ” Shake it, listen closely to how things move inside, tip it slowly from side to side.”

Transition

Take a few seconds to make sure you have written your observations on your whiteboard. Decide on one member of your group and one observation you would like to share.


Explanation (I)

Estimated time: 5 minutes

This explanation is designed to help differentiate the terms: observation, inference, and hypothesis, which students then use to continue investigating the Mystery Box.

What the teacher does and how the teacher will direct students (directions):

Probing Questions : Critical questions that will help students “clarify their understanding” and introduce information related to the lesson concepts and vocabulary
Expected Student Responses and Misconceptions – think like a student to consider student responses INCLUDING misconceptions (italics)

Please share your observation while I write it on the board.

What do we notice about these observations?

Can we group them into different types?

“There seem to be some that are based on what I can hear or feel, but others where I’m guessing what is making that sound or sensation.”

Are they all observations?

“Yes! (but no…)”

What is an observation? Can we come up with a definition of an observation?

“It’s something based on what I can see, hear, feel, smell…using my senses. It’s a description with which all of us in our group would agree.”

What do we call something that takes an observation and adds our suspicions about what is going on?

“A n inference, perhaps a hypothesis.”

Transition

“This time, using the Activity Sheet to write down your group’s data, let’s see if we can differentiate observations and inferences as we explore the Mystery Boxes.”


Exploration (2)

Estimated time: 5 minutes for short continuation of exploration (Exploration 2) during which students will make a certain number of observations, turn them into inferences, and write a hypothesis in response to their question.

What the teacher does and how the teacher will direct students (directions):

Probing Questions: Critical questions that will guide students to a “common set of experiences.”
Expected Student Responses and Misconceptions – think like a student to consider student responses INCLUDING misconceptions (italics)

Using your Activity Sheet as a guide, first write down one question you are going to try to answer.


Write down 10 observations of your box.


From your observations, write 5 inferences.


And finally, write down one hypothesis that responds to your question.

How can you make observations about something you cannot see?

What other senses do you have? ” Feeling, tasting, smelling, hearing.”

How can you manipulate the box to gather data?

“ I can move the box, shake it, listen carefully as things move about.”

How are your inferences different from your observations?

Transition

“Make sure you have completed your Activity Sheet. Choose a different member of your group to report out one observation, one inference, and your hypothesis.”


Explanation (II)

Estimated time: 5 minutes

Student groups will report out their question, one observation, one inference, and their hypothesis. Other groups will evaluate whether each statement fits the description identified.

What the teacher does and how the teacher will direct students (directions):

Probing Questions: Critical questions that will help students “clarify their understanding” and introduce information related to the lesson concepts and vocabulary
Expected Student Responses and Misconceptions – think like a student to consider student responses INCLUDING misconceptions (italics)

Each group, please share one observation, one inference, and one hypothesis.

After sharing out, assign different groups to define each the three terms on their white boards.

After all groups report out:

How might you define observation, inference, and hypothesis?

”An observation can be made using one of our senses.”

An observation is statement that others would agree with. It’s data.”

How are inference and hypothesis different?

“An inference is a statement based directly on observations; a hypothesis is a testable prediction based on all data collected.”

Transition

Does the hypothesis represent fact? A hypothesis must be testable. Are there tools that might help us figure out what is in the box? What might help you answer whether this hypothesis is correct?


Elaboration

Estimated time: 5 minutes

What the teacher does and how the teacher will direct students (directions):

Probing Questions: Critical questions that will help students “extend or apply” their newly acquired concepts/skills in new situations
Expected Student Responses and Misconceptions – think like a student to consider student responses INCLUDING misconceptions (italics)

“Scientists use tools to make more sophisticated observations and collect more data about whatever they are studying. What are some tools that might allow you to discover more about your Mystery Box?

For example, how might a magnet (or an X-ray machine) be a useful tool to help us refine our observations, inferences, and hypothesis about the Mystery Box.”

“Each group will receive a magnet. You may refine your observations, inferences, and hypothesis after using this tool.”

How might a magnet be helpful?

With the magnet, we can better differentiate metallic from non-metallic objects in the Mystery Box.

If you could choose another tool, what might it be?

An x-ray would be useful, since we could get a better picture of the objects inside.


OR help students engage in a discussion of hypothesis in comparison with theory, and the differentiation of theory and law. This is less of a direct elaboration, but is a continuation of ideas behind scientific exploration and discovery that are important to delineate.

Transition

“The magnet was helpful, but ultimately it did not tell us everything about the Mystery Boxes. In science, we can refine our tools and procedures to allow our investigations to go further, but we don’t always get to look inside the box.”


Evaluation:

Estimated time: 3 minutes

Students are given an exit ticket to define and to provide an example of an observation, inference, and hypothesis.

Critical questions that ask students to demonstrate their understanding of the lesson’s performance objectives.

Formative Assessment(s): In addition to the pre and post assessments, how will you determine the student’s learning within this lesson (i.e., observations, student responses/elaborations, white boards, student questions, etc.)?

The teacher will collect the students’ papers with observations, inferences, and hypothesis.

Formative assessment occurs in both the Explore and Explain phases of the lesson plan.

“In summary, let’s review our learning objectives.”

Call on specific students to answer the following questions:

What is an observation?

What is an inference?

What is a hypothesis?

Summative Assessment: Provide a student copy of the exit questions or post assessment (attach extra pages to this document).

Exit questions for students to respond to. What is an observation? Give an example. What is an inference? Give an example. What is a hypothesis? Give an example.

Follow on:

Definitions to address:

  • Observation: information gathered through the senses. An observation is typified by statements like the following: I saw . . . I heard . . . it tasted . . .
  • Inference: an interpretation or conclusion derived from observation, fact, prior knowledge and/or other premises. An inference is typified by statements like: I think . . . I believe . .
  • Bias: a personal and sometimes unreasoned judgment. We all have bias as scientists despite our efforts to limit it. Our prior experiences and knowledge bias our observations.
  • Preconceive (as in preconceived notions): to form (as in opinion) prior to actual knowledge or experience.
  • Assume: to take as granted or true.
  • A scientific question: a good scientific question should be specific and you must be able to answer it using the tools available to you.

What do we know about the terms: hypothesis and theory? Are they the same? A hypothesis is a guess; a theory is an explanation based on repeated experimentation that has yet to be demonstrated to not be substantiated.

Theory and Law: A theory is an explanation of a phenomenon; it attempts to describe why something happens. A law only describes a phenomenon (again based on experimentation); it does not attempt to explain why.


WVUTeach Courses Following Step 1 and Step 2

UTCH 221: Knowing and Learning in Science and Mathematics (3 credit hours)

This course draws on scholarship in educational psychology to provide a firm foundation for the teaching of science and mathematics by exploring what it means to know and understand in these disciplines, and how that influences instructional methods and assessment.

Prerequisite: ARSC 120 or instructor consent. 


UTCH 222: Classroom Interactions (3 credit hours)

This course examines the interplay between teachers, students, and content, and how such interactions enable students to develop deep conceptual understanding of science and mathematics in secondary schools. Students learn a variety of instructional strategies to engage students of diverse backgrounds, acknowledging that quality instruction should reach all learners.

Prerequisite: ARSC 120 and ARSC 220 (Step 1 and Step 2 courses) or instructor consent.


UTCH 420: Project-Based Instruction in Science and Mathematics Classrooms (3 credit hours)

This capstone teacher preparation course focuses on the integration of mathematics and science content, infusion of technology and the design of equitable learning environments in project-based lessons that model the ways scientists, applied mathematicians, and engineers address real world problems. Each student team will design and teach a project-based unit and evaluate its effectiveness in a secondary classroom.

Prerequisite: UTCH 221 or instructor consent.


BIOL/CHEM/GEOL/PHYS 376: Research Methods (3 credit hours)

This project-based course for prospective science and mathematics teachers provides WVUteach students with the tools that scientists use to solve scientific problems and gives them the opportunity to use these tools in a laboratory setting and practice in how scientists communicate with each other through peer-reviewed scientific literature.

Prerequisite: ARSC 120 and ARSC 220, junior standing.


MATH 376: Foundations, Function and Regression Models (for math licensure students only) (3 credit hours)

In-depth study of topics taught by teachers of secondary school mathematics. Emphasizes development of the concept of function, exploring function patterns in data sets, and connections between these topics and topics of mathematics associated with the secondary school curriculum. Integrates use of appropriate technology in developing lessons that help students master the concepts of functions, data, and real world applications.

Pre-or Co-requisite: MATH 156


MATH 318: Perspectives on Mathematics and Science (3 credit hours)

Perspectives on Mathematics and Science explores knowledge generation in the sciences along with consideration of mathematics by referencing the philosophy, history and methods of these disciplines. The course is designed to prepare future teachers with the background, rationales and strategies necessary to enhance student knowledge and interest in these areas, providing deeper understanding of the underlying mathematics in science, and of mathematics in general.


UTCH 430: Apprentice Teaching (10 credit hours)

Final semester Supervised Clinical Teaching is the apprenticeship experience for WVUteach students preparing for careers as mathematics and science teachers. Student interns will teach at the secondary level with mentoring provided by university supervisors and experienced classroom educators. The required seminar will address experiences, questions and problems encountered in the field. 

Prerequisite: ARSC 120, ARSC 220, UTCH 221, UTCH 222 and UTCH 420.