This course will become read-only in the near future. Tell us at community.p2pu.org if that is a problem.

This is our mini-forum for general conversations about the course. Got an idea? A question? Want to add thoughts to the past topic? Found a cool math video? Put it all here!

For my part, I am going to place recordings of the weekly meetings into comments to this thread. And probably some XKCD comics

• Week 5 meeting February 13, 2013.

If you missed it, here are two questions...

Question 1

Find some examples of computer games for learning mathematics. Do the players do math content with/on/inside the computer? Or does the computer just makes submitting the answers fun, manages tasks, and does other important but non-mathematical services?

Question 2

What is a good example of an activity where the computer helps learners do math they have not done before, as opposed to quizzing them on things they are supposed to know already?

Text chat transcript:

Joined on February 13, 2013 at 10:01 AM

Lisa Rittler: yes I can hear you

Moderator: Show us the pictures or videos when the musical plays!

Moderator: Prezis were amazing

Lisa Rittler: Its always neat to see the direction we all take!

Lisa Rittler: Im look for a videography guy!

Moderator (Maria Droujkova): Sue has a bit of lag

Moderator (Maria Droujkova): I hear my voice as a chipmunk (high)

Moderator (Maria Droujkova): go ahead Sue

Moderator (Lisa Rittler): helium balloon voice

Moderator (Sue Sullivan): whoops had nothing to say!

Moderator (Lisa Rittler): can you repeat those terms again please?

Moderator (Maria Droujkova): What sense does "computer-based" vs. "computer-delivered" means?

Moderator (Lisa Rittler): yes--me too!

Moderator (Maria Droujkova): Katherine: The material is given through a computer (delivered, like a test).

Moderator (Maria Droujkova): Sue: I wonder if "computer-based" refers to math that is primarily a part of programming, like Discrete Mathematics (e.g. converting to hexadecimals and binary)?

Moderator (Maria Droujkova): Lisa: Quizzes or problems - computer-delivered

Moderator (Maria Droujkova): My contribution: Timez Attack http://www.bigbrainz.com/

Moderator (Sue Sullivan): I'm not familiar with games designed specifically for mathematics instruction (yet!)

Moderator (Lisa Rittler): I'm not sure of the name but the game where the kids have groups of numbers and they have to grab the group that is the correct answer to addition & subtractions problem...i'll search for it

Moderator (Maria Droujkova): done watching?

Moderator (Katherine): wow, the example I was going to give is not nearly as exciting as this game!

Moderator (Sue Sullivan): yes

Moderator (Maria Droujkova): please give it, though

Moderator (Lisa Rittler): here is mine:

Moderator (Maria Droujkova): http://www.bigbrainz.com/

Moderator (Lisa Rittler): here is mine:http://www.coolmath-games.com/0-math-man/index.html

Moderator (Lisa Rittler): not the same as the one I was thinking of though...but fun pacman game

Moderator (Maria Droujkova): Tools - Web Tour - Start Web Tour

Moderator (Maria Droujkova): it shows for me

Moderator (Maria Droujkova): if you can't see it, minimize Elluminate and bring it back up

Moderator (Maria Droujkova): (a lot of people object to Timez Attack - kids get scared of violence even)

Moderator (Maria Droujkova): others like it

Moderator (Lisa Rittler): yes...I see it!

Moderator (Maria Droujkova): yes, we can see

Moderator (Sue Sullivan): yes

Moderator (Maria Droujkova): you have to paste into here

Moderator (Maria Droujkova): "The car goes a bit faster if you give right answers"

Moderator (Maria Droujkova): Violence is an issue

Moderator (Maria Droujkova): Do kids perform their math content within the computer, or in their heads, or on paper, etc.?

Moderator (Maria Droujkova): Katherine: there is no higher thinking in these operations, just memorization. The computer gives it the interface that makes it exciting. I did not know I liked math till later - arithmetic was tedious.

Moderator (Maria Droujkova): (cont) the kids are doing it the same way as I was, but it's more fun.

Moderator (Maria Droujkova): Lisa: To tie this with my topic of SMART Board. Memorization and repetition may be boring, but it's important. I picture these games on the projector, with kids in teams, competing and supporting each other. The kids enjoy the technology piece very much, even learning to manipulate mouse/buttons/touchscreens, and it's easier for them.

Moderator (Maria Droujkova): Sue: Student's attention is paramount. Computers give opportunity to create stimulating and visually pleasing environment - just makes it more fun, less tedious.

Moderator (Maria Droujkova): Lisa: Computers help students find common ground with other students (with whom they would not otherwise connect), create the community, share with the family, tell cool things to friends and others.

Moderator (Maria Droujkova): Sue: Using computers reinforces the idea that computers are just tools humans use to make tasks easier.

Moderator (Maria Droujkova): Katherine: Computers are much more part of the reality of kids today than it was for us. They are going to use computers everywhere, on every job. Using tech responsibly, as a tool, prepares them - it's not something to get around work, it's a tool FOR work.

Moderator (Maria Droujkova): Have you seen software where the computer provides MATH CONENT tools? Not motivation, no time and task management, but content?

Moderator (Maria Droujkova): GeoGebra

Moderator (Maria Droujkova): Katherine: The mathematical content is embedded in the tools like GeoGebra itself. They are for creation of math objects like shapes.

Moderator (Lisa Rittler): see this link:

Moderator (Lisa Rittler): http://illuminations.nctm.org/ActivityDetail.aspx?ID=205

Moderator (Maria Droujkova): Illuminations is a neat project

Moderator (Maria Droujkova): Lisa: Kids are creating different shapes, literally starting from nothing and creating. You can make a 3D shape... They are literally doing the math through this.

Moderator (Maria Droujkova): Sue: To me, what I found most helpful in my personal math experience is computer software that provide modeling, like the relationship between the sine function and the circle.

Moderator (Maria Droujkova): Games is not where math is at... And math content software is very different. Why? How?

Moderator (Maria Droujkova): Katherine: If you are in the game-playing zone, you are not doing higher thinking, and they just give you motivation, but not much math. But my brain is in a different mindset when I am using other math tools (like modeling - MD). Bigger thinking would requite an RPG game, strategy, that sort of thing.

Moderator (Maria Droujkova): Sue: In a way, all games that we would play, by extension, apply math and physics. Minecraft, for example, involves a lot of strategic planning, probability, other math.

Moderator (Maria Droujkova): http://en.wikipedia.org/wiki/Logical_Journey_of_the_Zoombinis

Moderator (Maria Droujkova): Lisa: My brain is going a mile a minute thinking about game scenarios. My kids at home use their imagination to become real people in the world. Maybe you can use computer to be a pharmacist, figuring out percentages and so on to help a patient get better. It would be amazing

Moderator (Maria Droujkova): http://www.kosjourney.com/

Moderator (Maria Droujkova): Katherine: NASA game where you are working at an airport as an air traffic controller. The computer gives you exciting interface and motivation, and you can incorporate modeling into the game itself, not just as a fun exciting interface. You are modeling equations, graphs, etc. You can change your inputs, see what happens to the outputs - but within the fun aspect of the game itself.

Moderator (Maria Droujkova): http://www.nasa.gov/centers/ames/Sector33/iOS/index.html

Moderator (Maria Droujkova): Sue: These games give us opportunities to customize the learning experience of students, so we can give them optimal learning experience.

Moderator (Maria Droujkova): Katherine: We can make it relevant to kids in many different ways.

Moderator (Maria Droujkova): Katherine: They can meaningfully get to that AHA moment on their own, and it's very meaningful.

Moderator (Lisa Rittler): Thank you guys! I always learn something from every person involved!

Left on February 13, 2013 at 11:02 AM

Text chat transcript from the February 11 meeting (Gina, Maria):

Joined on February 11, 2013 at 8:15 PM

Moderator: http://derp.co.uk/xkcd/comics/sierpinski_valentine.png

Gina Mulranen: I love that!

Moderator: https://moodle.org/

Gina Mulranen: I can show you my moodle page if you like.

Moderator (Maria Droujkova): http://moodle.palcs.org/We

Moderator (Maria Droujkova): it won't go beyond the password

Moderator (Maria Droujkova): yes!

Moderator (Maria Droujkova): Awesome

Moderator (Maria Droujkova): Scratch is a very lovely and rich program for math

Moderator (Gina Mulranen): Wow!

Moderator (Maria Droujkova): Right, involved parents are a blessing, but also present certain challenges

Moderator (Maria Droujkova): Computer-based vs. computer-delivered

Moderator (Maria Droujkova): http://csunplugged.org/

Moderator (Maria Droujkova): http://wolframalpha.com/

Moderator (Gina Mulranen): Wow!

Moderator (Maria Droujkova): self-check is an interesting case...

Moderator (Maria Droujkova): students like them a lot for learning

Moderator (Maria Droujkova): for skill training

Moderator (Maria Droujkova): http://hotmath.com/

Moderator (Maria Droujkova): http://www.wolframalpha.com/input/?i=y%3D2x%2B3

Moderator (Gina Mulranen): I get excited easily =)

Moderator (Gina Mulranen): Yep!

Moderator (Gina Mulranen): Especially about math

Moderator (Gina Mulranen): Sure!

Moderator (Gina Mulranen): Yes

Moderator (Gina Mulranen): lol

Moderator (Gina Mulranen): Sure! Thank you!

Left on February 11, 2013 at 8:58 PM

• Q1: http://www.funbrain.com/brain/MathBrain/MathBrain.html This math arcade is pretty fun. I only did the first couple games. Basic skills, most computation can be done in the students head. It is a board game set up where the student must complete one game before moving onto the next. This is more for fun type of game versus a drill type game. Each game is different and requires different skills.

Q2: I think a site like Wolfram Alpha is a good example here. It can help students go through new ideas step by step. They may have already been taught the material but the step by step break down of how to solve problems would be helpful after the student left the classroom.

• Question 1

I have used FunBrain activities like Katherine mentioned in the recording. I actually just used the line jumper recently to help my student practice adding and subtracting negative and positive numbers while using the number line to verify that their answer makes sense. Here is the link: http://www.funbrain.com/cgi-bin/nl.cgi?A1=a&A2=3&A11=1&A12=1

I also find a lot of great games on Quia. This is a site where teachers can make games and post them for other teachers to use as well. It is very easy to search for games based on subject area and concept. Here is a link to the exponents battleship game I recently used with my Algebra 1 students for their test review day: http://www.quia.com/ba/53930.html

I agree with Katherine that a lot of math games are just giving students the motivation to do practice problems on specific concepts. However, I also have to agree with what Sue mentioned on the different gaming pieces that the students use when playing games - strategy and problem solving. So I do think there is value to incorporating these games into the classroom.

As for the math content, I do think some online manipulatives like GeoGebra allow students to expand and discover mathematical concepts. However, most of the games I have seen online are used for skill practice.

Question 2

I found this website when searching for more depth to math games. http://mathsnacks.com/snacks.php The games in the website provide ways for students to challenge themselves based on their skill level and relate the concepts to real-life situation, like ratios in dogdeball! I think this is a great way for students to extend their basic skills with a concept by seeing it in a different context with these very detailed gaming situations.

I have also just implemented Descartes Cove for one of my Pre-Algebra students from last year that is not quite ready for my Honors Algebra 1 yet. It looks kind of like the resource that was mentioned in the recording (http://www.kosjourney.com/). I just assigned this program last week so I will ask the student for an update to see if she is learning a new way to solve these problems, or if it is just skill practice.

Check it out! I found a virtual field trip today when I was researching discovery learning activities! http://www.discoveryeducation.com/doodle4google/

• Hey classmates. Sorry I was not there yesterday. I look forward to hearing everyone's ideas and commenting on them here. "see" you all next week!

• Here is a link to my cyber charter school's Moodle page: moodle.palcs.org

You need to be a student to access my specific web pages, but this gives you a general idea of the layout and the components to the Moodle server. This is where I post assignments, message my students, email parents, and post lessons. Let me know if you have any questions on this online server or what I do as a cyber teacher.

• Here is a cool link to help kids learn ratios (which is what the teacher I'm working with started this week in Phila 7th grade class)

http://www.mathgametime.com/games/ratio-blaster-math-game

The kids play a game similar to the "old school" video game asteroids which I happen to LOVE :)

Also, pinterest which is sweping the MOM nation these days it seems also has lots of folks showcasing different websites, here is a link to what someone thinks are the top 100 teacher websites to check out:

http://pinterest.com/pin/128915608053503792/

this link was one of the links from above...its this cool YouTube video showing "dragoncurve-numberphile"...I'll let you guys check it out...pretty cool reference from Jurassic Park book

• As someone who loves dragons and fractal-ly ideas both... Thumbs up! Thanks for the link - I have not seen the vid before!

• This is the recording and the chat log of the February 6 meeting. If you missed it, please see what we did, and comment on the following questions.

Question 1

Question 2

What do you think students would learn from that topic?

Question 3

What do you think your peers (teachers) would learn from exploring the topic with you? What is some deep, global issue about teaching and learning mathematics that your topic could bring up?

Recording

Chat log

Joined on February 6, 2013 at 10:02 AM

meagan: you froze

Moderator: lag

Sue Sullivan: I can still hear you.

meagan: it kicked me out!

meagan: sorry

Moderator: Get the mice, press the video

Moderator: there we go

Moderator: yay

Moderator: Show us your other Prezis!

Moderator: Hi Lisa

Moderator: I can hear you

Moderator: taking notes here

lisa rittler 1: Megan I can hear you also!-Lisa

Sue Sullivan: I can hear you

Moderator: Meagan: I am really intersted in blended learning. I found a site online where you can pose assignments, so I would assign that

Moderator (meagan): sorry you are breaking up not sure if it is my computer

Moderator (lisa rittler 1): sorry guys...trying to figure out how to how can I speak...sorry...having trouble gettting into conversation...conversation cutting in and out

Moderator (Maria Droujkova): Tools - Web Tour - Start web tour

Moderator (meagan): i can hear you know

Moderator (lisa rittler 1): I can hear now

Moderator (Maria Droujkova): yay

Moderator (Maria Droujkova): we can hear

Moderator (meagan): yes

Moderator (Katherine): yes

Moderator (Sue Sullivan): yes

Moderator (lisa rittler 1): now I can't hear you guys??? ugg I am so novice

Moderator (meagan): yeah astronomy!!!!!!

Moderator (lisa rittler 1): this sounds really great for astronomy!

Moderator (Maria Droujkova): Katherine: I am really interested in space exploration and how they are using social media. NASA is really trying to reach out to young people. The Rover is Tweeting - in smart, casual style approachable to kids. I am not sure how, but there should be opportunities to use data in some way, with students.

Moderator (Maria Droujkova): it works

Moderator (Maria Droujkova): Lisa: Any time kids watch something having to do with space travel, there is always a lot of interest. The Franklin Institute has a lot of good programs.

Moderator (meagan): the site I was talking about is http://poster.4teachers.org/

Moderator (Maria Droujkova): Tools - web tour - start web tour

Moderator (Maria Droujkova): So Meagan is taking us on a little field trip now

Moderator (lisa rittler 1): thanks Meagan

Moderator (Maria Droujkova): Tools - application sharing

Moderator (lisa rittler 1): lovely flower

Moderator (Maria Droujkova): we can

Moderator (Sue Sullivan): I can hear you

Moderator (meagan): I did include the link to what I created on our p2pu site if anyone wants to check it out

Moderator (Maria Droujkova): Lisa: Many teachers have smart boards, but not using them. It's something that you should be able to use on many different levels - show examples, do applications... I would like to become an expert, maybe even come up with simple training for that, help overwhelmed teachers.

Moderator (Maria Droujkova): Meagan: Maybe you can have students make presentations to use with smartboard.

Moderator (lisa rittler 1): yes--thats great...any suggestions for websites already out there for smartboards

Moderator (Maria Droujkova): Sue: It's hard to make up my mind. I am inrigued with the idea of a virtual field trip. Maybe we can have a math trip?

Moderator (Katherine): sorry, my daughter saw the drawings on the screen and has taken over!

Moderator (Maria Droujkova): Meagan: We can't physically go to the pyramids, but can do it virtually

Moderator (Maria Droujkova): (kids are participating - grand! always makes me happy)

Moderator (meagan): like the idea of students planning and finding out what it would cost

Moderator (Maria Droujkova): Lisa: There are so many resorts, and well-established ones already have virtual tours set up. They can plan the tour, where to stay, research activities in that town, finances, statistics about what different class members want to do -- you can throw a lot of math in there as well.

Moderator (Katherine): yes, it is!

Moderator (lisa rittler 1): right...oh gosh..teaching teachers

Moderator (lisa rittler 1): lol

Moderator (Maria Droujkova): What are some big ideas about math ed you can investigate in connection to your topic?

Moderator (Maria Droujkova): Katherine: Obviously, having teachers learn about different information about space travel, what is available. "How do you learn about something if you don't already know about the topic? How will you bring it into the classroom if it's really motivating to students?"

Moderator (meagan): love that game!

Moderator (Maria Droujkova): Lisa: We were doing a great exercise in another class, "Community builders." All of us can  enjoy a little game to introduce a concept. Maybe coming up with three facts (true, true, untrue) is something to try.

Moderator (lisa rittler 1): more board games

Moderator (Maria Droujkova): A bit more open question: "How can we use games or design games to teach these concepts?"

Moderator (Maria Droujkova): Meagan: Maybe take the idea of Monopoly or such, and create a virtual game for our students to use. Maybe something for Smart Board.

Moderator (lisa rittler 1): creating a game to learn smart board...I think I'll try to go in that direction

Moderator (lisa rittler 1): thanks!

Moderator (Maria Droujkova):

Moderator (Maria Droujkova):

Moderator (lisa rittler 1): hmmmm

Moderator (Maria Droujkova): Meagan: maybe comparing different sites for tours

Moderator (Maria Droujkova): Meagan: Teachers need to be aware about questions they pose. What are questions that are thought-provoking enough?

Moderator (meagan): yes

Moderator (Sue Sullivan): yes

Moderator (Maria Droujkova): Two-part: something to explore; and then a bigger open-ended question for teachers.

Moderator (lisa rittler 1): can you guys all see each other?

Moderator (lisa rittler 1): yes

Moderator (lisa rittler 1): pretty cool!

Moderator (meagan): I have never used this before but i like it

Moderator (lisa rittler 1): I used once for a very boring mortgage training course

Moderator (meagan): we plan our week after spring break correct?

Moderator (Maria Droujkova): right

Moderator (Maria Droujkova): Challenging!

Moderator (lisa rittler 1): yes--mind as well!

Moderator (lisa rittler 1): mine as well I mean!

Moderator (lisa rittler 1): yes---this is definitely teaching me patience as well

Moderator (Maria Droujkova): Free and open - these are values in education and for educators...

Moderator (lisa rittler 1): wholly molly!

Moderator (lisa rittler 1): this is amazing!

Moderator (meagan): yes that woould be great!!!!!

Moderator (Sue Sullivan): wonderful!

Moderator (lisa rittler 1): thank you

Moderator (Maria Droujkova): Thank you

Moderator (Katherine): thanks everyone!

Moderator (Sue Sullivan): Have a good week, everyone!

Moderator (Maria Droujkova): You are inspirational

Moderator (meagan): thanks "see" you next week

Left on February 6, 2013 at 10:57 AM

• The first thing I wanted to comment on when listening to the recording was on the comment about how well the course is going. I am also impressed with the quality of the feedback from every one and how passionate everyone is on the technology and math education material. This is really my first course that has incorporated technology into specific math concepts and I am loving it! Since I teach in a cyber school and teach a cyber class through Adobe Community, all these different technology tools are SO helpful. I am loving this course!!!

I also wanted to comment on Meagan’s link for the poster for teachers site. This is a great tool, especially for my cyber students who usually have to scan in their homework and their posters lose the original quality when they do that. This software is fantastic and a lot easier for me to track and grade the assignments, since they are all in the same place.

Another topic I wanted to comment on from the recording is the idea of games. I use games a lot to review concepts, especially before a test when anxiety can be high. I think games are important for team building skills and experience. I also LOVE giving students the assignment of designing games. I had my Pre-Algebra students design a game that practices with operations with fractions. The students loved this assignment and enjoyed playing each other’s games.

Question 1

I relate a lot to Sue in the fact that I am indecisive. There are so many topics that I want to explore in more depth because my school is a cyber school and I really am trying to become more tech-savvy, especially for my cyber students who attend my virtual classroom. In the recording, I heard a lot on the virtual field trips, which I love. I actually am really interested in webquests, which I think can be thought of as a virtual field trip in terms of math concepts. I have been looking into these webquests to give students a different platform to learn new concepts in.

The other concept that I really loved was Scratch. I really enjoyed computer programming when I was in my under grad and I wish I had something like Scratch when I was younger. This is a really fantastic problem solving software that promotes a lot of creativity, which is where my gifted students thrive. I really do not know how I can incorporate the computer programming into my curriculum or an assignment for my students to do at home. I really would enjoy any feedback on how other teachers have done this!

Question 2

From the webquests and virtual field trips that I mentioned above, I agree with Katherine that these opportunities to think outside of the math curriculum are essential for students to relate math concepts to the real world. This is where they can get excited about the material and explore things they are interested in. As I mentioned above in question 1, I think Scratch would teach students advanced problem solving skills and give them the opportunity to build and create.

Question 3

I think other teachers would also benefit from exploring the topics of webquests and virtual field trips because I know there are a lot of different places out there that we want to take our students and that we want them to see. However, with budgets and time constraints, these ideal field trips may not be feasible. I think these virtual field trips is so appealing because it can bring a new experience to the classroom to get students interested in some material outside their textbooks. What teacher would not like to give their students that type of opportunity? =)

A global issue about teaching and learning mathematics that using Scratch in middle school could bring up is how young students can start with using the computer programming software. Another issue could definitely be how to incorporate the computer programming assignments into our curriculum. Do you really want students spending hours and hours trying to get a bumble bee to turn around, or should these students be practicing their fractions skills? I feel like parents might be upset about spending time teaching computer programming to a middle school audience because of the importance of the foundational math skills that are taught during those years and the practice of these concepts.

• I would like to say both issues are promising for discussion and investigation. Meanwhile, here's a tongue-in-cheek take on one of them, from XKCD:

• I love this comic! I definitely think it has value to it as well. I think the problem solving skills and the experience with computers is very valuable to the skills students will see in their future. However, I know there is plenty of conversations about students spending too much time playing with the computer and are still not able to divide fractions correctly. I think there needs to be a healthy balance. This is one of the reasons why I want to explore computer programming for my Tech Week topic.

• I am realy sorry I missed it too! Looking forward to chatting with all of you today.

I definitely feel MATH TEACH anxiety. I am so impressed with all of your knowledge & hope to be there one day. The most difficult part of starting this journey to being a teacher for me is feeling like I have all the tools to reach every student. This course is certainly preparing me for that. As I looked at your conversations, it made me think about how the structure of the lessons & the schedule each week is something the kids can rely on & also get excited when they know a change is coming if they were bored with a certain way of learning.

For ex:

M- review with individuals working on websites & then comparing with each other what they struggled with

T- Old school Chalkboard day...starting new lesson & having kids come to board & work on problems

W-groups choose technology...one on website...one of problem solving with visual aids using paper...one uses chalkboards...one uses computer program...etc

Th- Teacher reviews lesson with whole class on smartboard & goes through where struggles are

F- review & test with rewards avail...new roles in classroom with good behavior during test... & the thest formats can be different each week as well...some collaberative..some individual..some pairs, some paper & pencil, etc

• Interesting comment about routines. While kids fight certain types of routines and "the daily grind" - this is one of the major draws of computer games. Ironically, some kids only experience good workflow in computer games...

Setting up routines by days of the week seems like a good balance between predictability and some variety. I would add one thing to this type of planning, probably at a later stage. I would tie types of math to days, too. For example, Fridays are for puzzles and math jokes. You already have a type of math on Mondays (review exercises).

•

If you missed the meeting, check out the recording and the transcript. Please comment on the following three issues related to Bloom's Taxonomy and this course.

Question 1

Describe a situation you've seen (or can imagine) when higher-order tasks can help to deal with math anxiety, and when low-order tasks can help to deal with math anxiety.

Question 2

In your experience and in your opinion, what types of people especially benefit from higher-order tasks? Why?

Question 3

What would make this course better for you?

Chat transcript

Joined on January 30, 2013 at 10:02 AM

Moderator: Grab the mic and introduce yourself!

Moderator: Hi Sue!

Moderator: You need to click the transmit button on the video

Moderator: there!

Moderator: Good to see your smile

Moderator: /wave

Moderator: you are!

Moderator: I can hear

Sue Sullivan: i can hear

Moderator: thanks!

Moderator: I can hear

Sue Sullivan: i can hear

meagan: I can hear you

meagan: I am at home

Sue Sullivan: I am at home, my boys are at school

Moderator: I will be taking notes in chat

Moderator: Levels can be incorporated into one task, not just one or two, but multiple.

Moderator: Anxious students believe they can't be good at math, especially with new topics. It helps them to start at something too easy - it's not for learning, but for preparing, exploring and feeling successful.

Moderator: (First comment from Meagan, second from Katherine)

meagan: I like that idea. It makes it easier to get into a new topic.

Moderator: Sue: Either is possible. Some take things apart to discover what they are, others create right away, like a small child with playdough. You need to stay within the zone of proximal development to address anxiety.

Moderator: Maria: What events led to that past anxiety? How does it relate to the order of tasks?

Moderator: Sue: Failure is the necessary part of learning, for all orders of tasks. The culture has a huge fear of failure, and stigma of shame that becomes a self-fulfilling prophecy.

Moderator: Meagan: I purposefully make mistakes, and kids call me out on it, and I show it's not that big of a deal. Modeling how to deal with mistakes.

Moderator: Katherine: Students who are strong overall, may still struggle with math. Students with math anxiety may be good overall students - they struggle, they work on it, but for math, it does not work, and they don't know what to do to fix it. Students who struggle overall don't have the same sort of panicky anxiety.

Moderator: Maria: if you designed curriculum long-term, could you choose low-level or high-level tasks to lower that anxiety?

Moderator: Meagan: Creative tasks can become a second nature and students won't be as anxious.

Moderator: Katherine: Low-order tasks don't give you much room, but with high-order tasks are open to you making your own sense of them (e.g. some learn easier from the book). You can design tasks so students can take different approaches, in their own ways I don't even think of. Designing curriculum with low-level tasks can give low-risk practice setting, safe practice. Instant feedback from a computer, in private, for example - 50 problems, never have to be wrong in front of others.

Moderator: Sue: I would design my curriculum to include all levels, like differentiating instruction. Toolbox approach: giving them things, seeing what they prefer.

Moderator: Katherine: Choice gives students control, if you can design curriculum this way. Say, four different approaches - this lowers anxiety if they can choose. Just the choice itself gives control.

Moderator: Meagan: Today I can practice, but next day I can be creative - it gives some variety, which helps.

Moderator: Sue: There are problems other than anxiety: students can be bored, or not see the need. The motivation is important.

Moderator: Maria: What type of students would benefit from starting from high-order tasks?

Moderator: Sue: My older son. He has the tendency to not care about math, but his passion is photography, design, videography. If he has freedom to use those mediums, he works much, much better in mathematics!

Moderator: Meagan: People who get bored (e.g. with flashcards). If you give them an opportunity to go beyond, they may think math isn't so bad.

Moderator: Katherine: A points about social issues, people who don't do math because their friends don't do math. This sort of person (and friends) may be drawn into an interesting task: "Wow, this is more alluring!"

meagan: The all time question!

Moderator: Katherine: Students who ask, "Why do I have to learn it?" - So higher-order tasks address concerns that math is pointless and stupid. But you can relate it to sports, architecture, business, science and this benefits such students.

Moderator: Sue: "The wire" - probability of rolling dice, for inner-city students. If a culture sees success at school as "uncool" may remove the stigma.

Moderator: *Higher-order tasks may remove the stigma.

Moderator: Geogebra as a community

Moderator: Maria: what would make this course work better for you?

Moderator: Katherine: Discussions, following up on threads. An online discussion forum.

meagan: We could set one up on blackboard

Sue Sullivan: wonderful idea

meagan: nothing at the moment

Sue Sullivan: I don't have anything right now

Katherine #2: No more to add right now

Left on January 30, 2013 at 10:55 AM

• I am really sorry that I am not able to attend these meetings! I really enjoyed hearing from Sue, Katherine, and Meagan. I am actually not a parent like you ladies are, but I am a full time middle school math teacher. That is why I am not able to attend the Wednesday morning meetings.

One of the questions that was posed in the recording was can the different levels of Blooms Taxonomy be incorporated into one activity. I think it really depends on the types of students. Since I teach gifted students, I can lose them easily in a lesson if I do not incorporate higher level thinking questions or an activity where they create with what they have learned. I also agree with Katherine when she talked about her experience as a tutor. I am a tutor as well as I also start at the bottom to gain students confidence level with math. Then as they gain more confidence, they are more likely to attempt the higher order thinking questions.

Question 1: Math Anxiety

I actually did research on math anxiety with gifted students in a previous grad level course. One of a characteristics of gifted students is a fear of failure and I found that even my brightest students were so fearful to raise their hand because if they got the question wrong, then they think that other students or myself will question their giftedness. The questions that cause the most anxiety was the questions I posed that did not have one right answer. For example, "What do you think a function is by looking at this example (point), which is a function, and these two non-examples (point), that are not functions." I got maybe one shaky hand raised for this question. Because the students had not learned what a function was, they were not willing to offer ideas, for fear they would be incorrect. I get more student hands when we are solving for x or doing practice problems because they have been taught the material.

I really like that Meagan mentioned the importance of making mistakes as a teacher and noting how we learn from it and not let it effect the rest of the lesson. I actually do the same thing when I teach as well. I think it is really important for the students to see someone they look up to and respect to learn and move on when making mistakes.

I think that the higher order tasks can be applied to learners who have mastered the basic understanding of the concepts. I think frustration and anxiety could surface if the students have not mastered the foundational skills needed in order to even begin to think beyond the concept. I also think that the higher-ordered tasks are important in order to get students to THINK about the math. Students can become like robots, crunching out algorithms to solve problems, and can lose the sense of the "how" and "why" it works. Then they won't be able to apply the concept to different types of problems. Students need the opportunity to problem solving and creating in order to enhance and deepen the understanding of the concept. I think that even the lower-level students can still be given these opportunities with guidance and step-by-step. You, as the teacher, need to be careful with the approach and deliverly of the higher-ordered tasks to meet the student skill level and challenge them without causing any frustration. It is hard! I know!

I also agree with Katherine's point that these higher-ordered tasks can help students relate math to real-life, which is important for a lot of these students.

Question 3: The Course

I am LOVING this course! The feedback is so quick and so, so valuable. There is nothing that I can think of right now that would make this course better for me, besides a different time for the live sessions. =)

• I'd like to follow up on Sue's comment with some terms I found useful for the topic:

vs

The definition of giftedness as ability leads kids to attribute success to "something innate" - and that, in fact, produces anxiety. In contrast, attributing success to hard work means you can always DO something in case of a failure (work harder) - rather than conclude that you just aren't as gifted as you thought, and give up. At least that's how one theory goes.

Some study results confirm that seeing yourself is gifted is a risk (as explained above) and other results do not, for example, this: http://www.ernweb.com/public/921.cfm

What everybody agrees is that praising ability should be done carefully (if at all).

• Thank you for your story about a refugee girl, Sue. Sometimes more unusual cases make us notice something deep. And then we start seeing similar things all around - like kids puncihing numbers into calculators without any idea what happens.

• Hi Sue!

I have worked with the term "mindset" before. In my program, we have incorporated a period during the day on Fridays called Gifted Seminar, where a teacher and a small group of students talk about characterisitics of gifted students within their cohort and talk about how to deal with the joys and challenges that come from those characterisitics. One of our seminars was on a fixed mindset and a growth mindset. It was a really great topic because a lot of the students could relate to times where they used a growth mindset and a fixed mindset. Then I talked about how famous people used the growth mindset model to develop things like the lightbulb. I uploaded the PowerPoint I used to teach this concept into my online locker so you all can view it too. Enjoy! http://locker.palcs.org/~gmulranen/mindset.pptx

• Gina - loved the powerpoint and have saved it for future use - thanks so much!

• Gina Thank you so much for the presentation. I was always in gifted programs and remember having conversations like the one in your cartoon. I always wanted to do better and worked hard. I will keep this presentation to show future classes.