# data[].attributes.body
You can also use scatter plots, the correlations, and the trend she you see to make predictions about the data or using the data.

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Measure of center is also sometimes called the "middle value"

# data[].attributes.subject
Measure of center is also sometimes called the "middle value"

# data[].attributes.body
Pros: We can see frequency, mode, median easily. You could recreate the data set with each individual piece of data.
Cons: Not very visual, does not show relative frequency

# data[].attributes.body
Pros: Shows relative frequency, often in percentages, very visual

Cons: Cannot see every individual piece of data, we could not recreate the data set

# data[].attributes.body
Correlation between data. We can tell if the correlation is positive, negative, strong, weak, etc. by examining scatter plots.

# data[].attributes.headline
What kinds of important information can we see from scatter plots?

# data[].attributes.subject
What kinds of important information can we see from scatter plots?

# data[].attributes.body
the measure of center is a summary we can use to describe where the "center" part of a distribution is. mean median or mode is not always used to describe this center, but rather it depends on the data and our interpretation of our data.

# data[].attributes.body
They do not always tell us the average. The average is just one thing that they can tell us.

# data[].attributes.body
No! Sometimes a "better" measure of center may be the median or mode. The average, or mean, can be greatly affected by outliers, which makes the average less representative of the data, or center.

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Circle graphs, box plots, stem and leaf plots, bar graphs, histograms, dot plots are all ways to display univariate data.

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Do measures of center always tell us the average?

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Do measures of center always tell us the average?

# data[].attributes.headline
Measures of center are different ways of finding the average of the data set. Different measures of center give us a new perspective of looking at the data.

# data[].attributes.subject
Measures of center are different ways of finding the average of the data set. Different measures of center give us a new perspective of looking at the data.

# data[].attributes.body
Through scatter plots

# data[].attributes.body
By "distributed" do you mean "spread"? (discriptions of distribution also include measures of center)

# data[].attributes.body
Univariate data examines characteristics of one variable. Bivariate data examines two pieces of data and their connection.

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What is an appropriate way to display bivariate data?

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What is an appropriate way to display bivariate data?

# data[].attributes.body
Measures of centers tell us information about our data's average.

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What are some appropriate ways to display univariate data?

# data[].attributes.subject
What are some appropriate ways to display univariate data?

# data[].attributes.body
Describe how data is distributed

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What is the difference between univariate data and bivariate data?

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What is the difference between univariate data and bivariate data?

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Measures of variability are numerical summaries that tell us how data varies within a set.

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Students developing a statistical question they have to answer through finding probabilities, finding measures of center or other analyses to best answer that question.

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The difference between a sample and a population

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The most learning occurs when students are able to learn hands on be in control of their own learning. The teacher can give students accountable talk sentence starters as a guide but students should be able to explain and justify their own thinking.

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The most learning occurs when students are able to learn hands on be in control of their own learning. The teacher can give students accountable talk sentence starters as a guide but students should be able to explain and justify their own thinking.

# data[].attributes.body
I learned that students might find that there is a difference from theoretical probability and experimental probability; and ways of facilitating discussions that cater to misconceptions surrounding that topic.

# data[].attributes.body
Teachers should know what their specific students know/ do not know through pre assessments. Not just what they should know based on common core.

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Teachers should know how to plan engaging meaningful lessons

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They should have students create, demonstrate, share, and justify how/why they make and use visual representations.

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Teachers should know how to organize the data collection process and help teach students the routines and procedures for working together. Then students can efficiently be active members in the data collection process and content!

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Oh yes, the data set could really make or break the entire problem!

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Oh yes, the data set could really make or break the entire problem!

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Teacher should know how or be open to learning how  to use technology for statistics and probability. This opens up many possibilities to expand students learning and gain interest.

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Teac

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The difference between mean, median and mode.

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By incorporating excel, like we used in this class, could also add an element of including technology to lessons catered around mean/median/mode/etc.

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The teacher should try practicing focusing questions more than the IRE and funneling when facilitating discussions

# data[].attributes.body
Teachers should understand the different types of data displays students can use to show data. Teachers should help students see and understand the differences between different types of graphs/displays of data.

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What are some things that you learned in this class (content-wise or teaching-wise) that you think would be important for all teachers to know when teaching prob or stats?

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What are some things that you learned in this class (content-wise or teaching-wise) that you think would be important for all teachers to know when teaching prob or stats?

# data[].attributes.body
Teachers should be able to create data sets that will accurately assess student understanding

# data[].attributes.body
Teachers should allow for student voice to take place in the classroom. Justifications and explanations should be made.

# data[].attributes.body
It might be basic but they should know which graphs or visual representations will best show what they are trying to get students to understand.

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Teachers need to know that each and every student comes in with different backgrounds and knowledge. Teacher can not expect because one student is familiar with a certain topic that the rest of the students will follow.

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Teachers should understand how numerical summaries are affected by data, and their significance. Teachers should understand how to show students mean and median are affected in different ways, and one may be a better representation of a data set.

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They should know how to facilitate productive rich discussion

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Teachers should address the concept of biases when collecting data, and discuss how that might change/alter/skew data when collecting statistical information.

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Teachers should know where students are coming from in understanding of previous math skills such as graphing, creating formulas and interpreting data. Even if the student understanding is nonexistent, teachers need to understand and determine where the students understanding of these concepts to be effective.

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Teachers need to know some of the content that students will be learning in prior classes, what they will learn in future classes, and what content aligns with their work from other content areas

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Aside from CCSS and the misconceptions listed earlier in the Padlet, what are the other things SPECIFICALLY that teachers should know/be able to do to be EFFECTIVE?

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Difference between a categorical variable and quantitative variable

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That one roll, coin toss, card draw etc. are dependent on each other.

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Some students may believe a certain piece of data might be an outlier - but there is a specific way to calculate this! (upper lower fences)

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Some students may believe a certain piece of data might be an outlier - but there is a specific way to calculate this! (upper lower fences)

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WHAT are some specific SKILLS students gain by learning about probability and statistics that they can use in the real world?

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WHAT are some specific SKILLS students gain by learning about probability and statistics that they can use in the real world?

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Not all graphs provide the same information for the same data set.

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Theoretical probability and experimental probability  are the same

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This is especially important so we can still reach and teach our higher level students.

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WHAT are some specific real-world connections in probability and statistics?

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WHAT are some specific real-world connections in probability and statistics?

# data[].attributes.body
I think another part of being able to anticipate student misconceptions is that the teacher should know her class and where her students stand. That would give the teacher a better idea of what the students might sa

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HOW MUCH do YOU feel you need to know about probability and statistics to feel CONFIDENT in yourself when teaching?

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HOW MUCH do YOU feel you need to know about probability and statistics to feel CONFIDENT in yourself when teaching?

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They should activate real-world experience prior knowledge, as well as academic prior knowledge when introducing probability/statistics, so that way students understand the relevance and applicability of their math.

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Misconception: "Gambler's fallacy" - a student might think an event is more likely to happen because it has not yet happened or not as frequently (ex. flipping a coin and getting heads four times, tails is most likely to be next).

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Misconception: "Gambler's fallacy" - a student might think an event is more likely to happen because it has not yet happened or not as frequently (ex. flipping a coin and getting heads four times, tails is most likely to be next).

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WHAT are some of the misconceptions we need to look out for in teaching probability and statistics?

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WHAT are some of the misconceptions we need to look out for in teaching probability and statistics?

# data[].attributes.body
Students will be able to see through any false confidence or any concepts you as a teacher struggle with and challenge you with those topics

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They need to be able to anticipate misconceptions, and think of multiple ways to address/clear them.

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Teachers can be experts with how to relate content to their students lives but they cannot do this without knowing the content they have to connect it to. I do not think a teacher can lead students to to understanding if they do not understand it themselves.

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I definitely think the grade levels below are just as important. Teachers must be able to help students make connections to prior knowledge and experiences.

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Teachers should know what students learn in elementary school that are the foundations of probability and statistics. This will help fill unforeseen gaps and build off of prior knowledge as well.

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Teachers should know what students learn in elementary school that are the foundations of probability and statistics. This will help fill unforeseen gaps and build off of prior knowledge as well.

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Teachers need to be able to use misconceptions from students along with real world applications to help students learn the concept

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I think it is also important to know the math covered in previous grades than you are teaching so that you can have a big picture when you teach new content to students. You know where they are coming from to your classroom and you know what you need to teach them so that they can be successful in higher grades.

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Some teachers might be "confident" knowing the bare minimum (student-level knowledge) while others may only feel "confident" if they have both BROAD and DEEP understandings of the topics that they teach.

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Creating real world applicability will help to promote engagement as well.

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What about the grade levels below?

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Some ways to do this is to anticipate and sequence student responses

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In addition to being able to answer students' questions teachers also need to be able to for see possible misconceptions that students might have with the subject matter.

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Maybe teaching enthusiastically means knowing enough to plan meaningful engaging lessons that you know your students will learn from.

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Since CCSS are just STUDENTS need to know, will it be enough for teachers to know only as much as their students?

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I agree with that. I do think it is better to know more than to little. That way teachers are prepared for those students that ask higher end questions.

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I think that teachers should know more than just above one grade level. It will be useful to know where the content students are learning will lead them as they continue into high school.

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Understanding the basics of probability can include concepts that you may not think relate directly to probability but relate indirectly. Students previous understandings may vary and knowing how to address misconception or misinformation on the fly will make an effective teacher in teaching probability/statistics. 

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Understanding the basics of probability can include concepts that you may not think relate directly to probability but relate indirectly. Students previous understandings may vary and knowing how to address misconception or misinformation on the fly will make an effective teacher in teaching probability/statistics. 

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Teachers also need to know a little more than the CCSS that they are teaching. For example, if teaching Middle School then the teacher needs to be knowledgeable in High School CCSS

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Teachers also need to know a little more than the CCSS that they are teaching. For example, if teaching Middle School then the teacher needs to be knowledgeable in High School CCSS

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Does that mean being enthusiastic while knowing the content well or just being enthusiastic like School of Rock?

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Teachers need to have full understanding to be able to address misconceptions!

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Teachers need to have full understanding to be able to address misconceptions!

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This is just to keep the Padlet from scrolling out of control!

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Enough to be confident and able to answer Qs!

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Enough to be confident and able to answer Qs!

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Teachers need to know enough to be able to make the content relatable for students.

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They need to be confident in the concepts they teach and understand why they work.

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Teachers need to know the concepts of probability and statistics, and have a strong understanding of the basic ideas of probability and statistics.

Teachers should know how probability and statistics apply to the real world. This way, teachers can make these concepts applicable to students, their lives, and their interests.

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I think that teachers need to have more knowledge of the topic than they expect their students to learn from the lesson. The teacher need to know what the students are going to be learning next about probability and statistics.

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Teachers need to be able to connect statistics or probability to students everyday lives. This may mean teachers know just a little and let students to the learning or teachers are experts with how to relate their teaching to students lives to help students understand what they need to know about probability or statistics

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Teachers need to know at least one grade level above what they are teaching. This is because they need to understand where their students are going with their future learning and the knowledge of what they need to know get there.

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Teachers need to know statistics and probability at a higher level than they are expected to teach their students.

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Enough to teach enthusiastically.