This chat includes a discussion of topics of interest to K-8 teachers who teach and/or integrate computer science.The Computer Science Teachers Association is a membership organization that supports and promotes the teaching of computer science and other computing disciplines. CSTA provides opportunities for K–12 teachers and students to better understand the computing disciplines and to more successfully prepare themselves to teach and learn.
Welcome to tonight’s #csk8 Integration of Computer Science and Math in K-8 chat, the 3rd in our series of chats about cross-curricular integration of CS. Tonight’s chat is moderated by @Todd_Lash along with our guest moderator @stevenpfloyd.
#csk8 is a structured chat. Questions are numbered Q1 for Question 1, Q2 for Question 2. Your answers should start with A1 for the answer to Q1, A2 to answer Q2, etc.
I am Sheena, K-8 Computer Science teacher in California. Teaching Python, Scratch, micro:bit, Arduino & more. CS Integration specialist for the district #csk8
A1: I think this would be beneficial in not limiting students to any device that would enhance their learning and progression within the technological period. #csk8
#csk8 A1: Many reasons to integrate: Authentic application of CS/CT in natural contexts, finding "stand alone time" for CS/CT is difficult, equity as all kids usually get the core subjects.
#csk8 A1: Many reasons to integrate: Authentic application of CS/CT in natural contexts, finding "stand alone time" for CS/CT is difficult, equity as all kids usually get the core subjects.
A1: I think integration with CS provides new ways for students to invent and test math procedures, rather than just follow them! It also provides new modes for expressing understanding. #csk8
A1: I think integration with CS provides new ways for students to invent and test math procedures, rather than just follow them! It also provides new modes for expressing understanding. #csk8
A1: CS & Math has a natural chemistry btw them and offers something for everyone. Low floor/high ceiling activities in meaningful contexts, something for everyone #csk8
#csk8 A1 To me adding the integration is the equivalent of a shopping BOGO:) In any subject area you are teaching and exploring the content - plus gaining the value and thought processes of CS.
#csk8 Especially in today's society where technology drives everything, exposing students to computer science and math at an early age is so important. This can foster a passion rather than a fear for STEM topics later in education.
A1: #csk8 Both computer science and math connect closely with the thinking skills of abstracting, generalizing, organizing info. Also, computers can do routine calculations to free up students to engage with higher order math concepts.
A1: I also think the new wave of CT work has the potential to reinvigorate use of reasoning and deep thinking in elem. math classrooms! In the #CT4EDU project, we saw Ts really take up CT ideas as good goals and strategies for framing their math lessons. #csk8
Well said! And connecting math concepts to another area, a new context. Cross-curricular and connecting to other areas of our lives seems like an important skill right now. #csk8
A1 One advantage is that students look at the math from a new perspective. @georgegadanidis talks about #coding enhancing understanding of #math ideas and giving abstract concepts a more tangible feel #csk8
A1 - This paper outlines how teachers and students felt about CS and Math being taught as an integrated course in grade 10 https://t.co/Ok1CJWwMHh#csk8
All kids take math - so when we add any type of CS into a math class, they see what it is all about. All kids get access to CS. When they have to set x and y coordinates to reset a sprite, or fix angle of rotated sprite, they are playing with math #csk8
I suppose the class landscape would vary but I’m thinking unplugged Cartesian plane activities (low floor) others begin to scaffold into coding platform and high ceiling for my Ss is to manipulate the relationships, find patterns, use abstraction to prove given concept #csk8
Jumping in late...Hello from Louisiana:)
A1: Integrate Computer Science and Math for 5-14 year old students increases computational thinking ... teaches them to think! #STEM4all#csk8
A2: One challenge is making sure integration results in an enriched experience, not a shallower treatment of each topic! I think this challenge is address through careful selection of contexts and tasks that aren't contrived for the sake of serving both disciplines. #csk8
#csk8 A2: A challenge educators might face while trying to integrate computer science in curriculum at such a young age is the engagement part. Especially if kids don't know basic mathematic principles, many concepts in computer science might be difficult to express and make fun
yes, and allow students to explore this important area at a young age! They might find their niche, and would never have known it until much later #csk8
#csk8 A2 convincing teachers and other educators of the aforementioned advantages and answering the age old question of "where will I find the time to add something" with integration is not adding in the traditional sense
I find using a computer program to collect data can help students with looking for structure (SMP7). It's a lot easier to see a pattern in multiples of 5 if I can have the computer generate a hundred of them. #csk8#iteachmath#mtbos
A2: Biggest challenge is getting into a math classroom. Math teachers have so much curriculum to cover, assessments to give and grade, they are overwhelmed and not ready for something new. Math is very closely tracked, and often teachers want to just keep what is working. #csk8
A2: Finding opportunities in the curriculum for authentic integration is challenging! Often teachers don't have resources or expertise. Only innovators/high adopters end up creating these authentic activities. We need more resources to help novice CS teachers. #csk8
A2: Biggest challenge is getting into a math classroom. Math teachers have so much curriculum to cover, assessments to give and grade, they are overwhelmed and not ready for something new. Math is very closely tracked, and often teachers want to just keep what is working. #csk8
Yes - In Ontario, we have math processes - here is an example of grade 3 processes (last updated in 2005) I find coding and CT helps with focusing on these processes #csk8
A few years ago while using @gotynker , one of my girls wanted to learn about degrees to control one of her characters. We did a mini-lesson on angles in a circle, and she got it and shared it with the rest of the group.
https://t.co/cd4xSl3Zs6#csk8@codeequity#mathchat
A2: #csk8 Budgeting hurdles, such as money for workshops that teachers may attend to learn. Also, they need proper tech to create the environment to enrich this course if integrated into the curriculum
Time is certainly an issue, but integrating CS and other core curriculum can have advantages in the way of not having a totally separate computing class. #csk8
A2: one obstacle can be ensuring that the intended outcomes aren’t blurred by CS/technological integration. Striving for enriching learning opportunities which are extended and differentiated through CS #csk8
A2: The first challenge is to empower teachers with avenues to integrate Computer Science and Math and raise awareness that they don't need to know "everything" about CS to integrate it in their classroom #STEM4all#csk8
@TaraLinney Also, SMP4, modeling with mathematics is easier if the computer can do the calculation, allowing students to focus on developing and evaluating the model. Representing a mathematical model as a computer program brings the model to life. #csk8#iteachmath#mtbos
Agree. However just providing good integration resources and support is not enough, math teachers need to make the time to understand and appreciate why it will make a difference and then assign a bit of class time to a CS activity. #csk8
All of these are great "real world" points Sheena. Showing the value of integration beyond just getting a chance to do more CS is important if it is to ever be widely adopted in core courses such as math. #csk8
Q3: Are there math concepts that are easier or better to integrate with CS? Are there math concepts that are difficult to integrate with CS? Why? #csk8
I like this emphasis. As a future educator, this idea does scary me but that reassurance is good in not knowing everything just enough to give students the advantage that we did not necessarily grow up with in primary school. #csk8
Another great point. For authentic integration b/t CT and math, we need systemic change, time for teachers to "sit in the content", resources, and administrative buy-in. Are we asking too much? #csk8
Agree. However just providing good integration resources and support is not enough, math teachers need to make the time to understand and appreciate why it will make a difference and then assign a bit of class time to a CS activity. #csk8
Anne, that is a great point! Elementary teachers are generalists and often scare easily when asked to do something deep especially in STEM topics. #csk8
A1: CS and math share a ton of the same practices: algorithmic thinking, persisting until a problem is solved, using logic to deduce the answer... it’s really powerful to share this with students because many find power in knowing they are good at something that’s LIKE math #csk8
Certainly a big challenge, I wonder what's required to empower teachers to eventually create their own, valuable resources: good exemplars? design strategies? criteria for effective lessons? #CSK8
A2: Teachers may be uncomfortable with CS. Providing supports for learning programming, more time in school days for collaboration between tech specialist and math/classroom teachers. #csk8
"spark" is a great word! Communicating the excitement and creativity that goes along with #computerScience is important! It is a fun and exciting thing to do, students often celebrate, etc. This needs to be ceommunicated. #csk8
A3: Such an interesting question! I think a lot of the compatibility depends on the CS tools you are using. Scratch is a great fit for visual modeling of work with geometry, number lines, etc. Is the fit the same for other environments? Not sure. #csk8
Yes we are asking a lot, especially if there is no support from the administration/buy in from parents, who are still evaluating mastery with only a specific type of math assessment. Teachers may just teach to that test, not spend time letting kids play with math! #csk8
Totally agree! Many times they are so overwhelmed with core curriculum that the idea of learning something new is off putting- add the feelings of "I'm no good at technology" and no wonder they don't #csk8
A2 - Supporting teachers to ensure they feel empowered to create and develop these skills in their students. Low efficacy is a barrier and this impacts student efficacy. Effective Professional Learning is the key, imo. #csk8
I don't think it's realistic to ask novice CS teachers to create large-scale integrated experiences/units. We should give them resources and support incremental development of their own professional growth. We can think of Use/modify/create as a growth trajectory for them. #csk8
Certainly a big challenge, I wonder what's required to empower teachers to eventually create their own, valuable resources: good exemplars? design strategies? criteria for effective lessons? #CSK8
A3: Such an interesting question! I think a lot of the compatibility depends on the CS tools you are using. Scratch is a great fit for visual modeling of work with geometry, number lines, etc. Is the fit the same for other environments? Not sure. #csk8
A2: One challenge that stands out to me is that in math, there is typically one right answer, whereas in CS, there are many right ways to solve the same problem. Not sure how to solve it, other than to be aware and help kids see (and appreciate) the difference #csk8
I see a lot of students starting to learn about negative numbers in CS classes using #Scratch. They see the negative numbers in coordinate grids, and the setting really shows "changing by a negative means moving in the opposite direction". #csk8
A2: I’ve also run into challenges with vocabulary: a variable is two different things for math/CS. We have to be really specific and note the difference when teaching kids, especially when some are in both algebra and our classes at the same time. #csk8
#csk8 A3 I find that some of the best math learning, including for myself, is by using the math-based menus for "non-math" game making, eg <, >, variables, etc. It then seems more intuitive.
A3- Geometry is my favourite! Also beneficial to develop spatial reasoning skills while we are at it:) Probability and data management also work well. Love the Cartesian plane in Scratch and turtle like geometry as inspired by Papert. #csk8
A3: Great question. I think we are still learning. Natural synergy with geometry. Students can demonstrate mathematical understanding of broad areas such as number lines, etc. since they can animate their own story problems. #csk8
Q3: Are there math concepts that are easier or better to integrate with CS? Are there math concepts that are difficult to integrate with CS? Why? #csk8
I think that depends on the kinds of questions we are asking in math and even though there may be one "right" answer, there are often multiple ways of getting there. #csk8
YES!! And resources from classroom teachers, not just from larger non-profits/companies. What is actually being used in the classroom, and how does it work? #csk8
A3- Geometry is my favourite! Also beneficial to develop spatial reasoning skills while we are at it:) Probability and data management also work well. Love the Cartesian plane in Scratch and turtle like geometry as inspired by Papert. #csk8
I like this as a perfect opportunity to show that there are many ways to solve problems and to take the opportunity to compare and contrast algorithms.... also can discuss similarities and efficiency. #csk8
Scratch can be a very good tool to teach the abstraction needed to understand algebra - learning when/how to use variables - how to take a word problem and turn it into an equation for example. That is what is needed to code any open ended problem- abstraction/ variables #csk8
It's a fine line. We want to empower teachers to create and we don't want to deprofessionalize by giving too much. At the same time, we need to be realistic ab their needs, time, and developing expertise. #CSK8
I completely agree, as a person with very little knowledge of anything CS based, it is intimidating wanting to go into the field of elementary eduction with expectations to create the system.
A3: Algorithmic thinking is easy, of course, and variables are challenging to integrate because they mean something different in CS than math. In CS, a variable is always changing, whereas in math, a variable has one (maybe two) values. #csk8
A3: Several great geometry, probability, and data management opportunities. I love having students become creators and obtaining data, utilizing it, & making informed decisions in order to draw relationships & manipulate it to achieve desired outcome #csk8
I do find that I can use variables to make them come alive for students when coding. I feel like we end up shifting from procedural to conceptual mathematics. #csk8
We struggle with language issues, too, with Ss and Ts both. Algorithm, for example, carries a connotation of something to be followed in math, and in CS it tends to be something developed or invented! (I'm hoping to carry that invention idea from CS to math for Ss and Ts!) #csk8
Great point ab variables. It is confusing for Ss to see this term used differently in math and CS. It makes me think of the academic language dev't we are trying to integrate in the integrated activities. It's important to be clear! #csk8
A3: Algorithmic thinking is easy, of course, and variables are challenging to integrate because they mean something different in CS than math. In CS, a variable is always changing, whereas in math, a variable has one (maybe two) values. #csk8
A3: Absolutely. In K-8, Negative number addition, coordinate grids, iteration, functions, linear movement, angles, probability, statistics, math modeling, writing equations, factoring, prime numbers. #csk8
#csk8 Integrating basic mathematic functions and variables serve as the foundation of Computer Science and straight math topics. Teaching surface level material in an engaging and effective manner would be my primary focus. I want my kids to be motivated by the curriculum
#csk8 A4 I will say yes. Looking at the younger end of the hashtag:) In a Grade 1/2 class students used Scratch Jr to make number fact flashcards using multiple sprites and multiple levels.
#csk8 A4. Integrating basic mathematic functions and variables serve as the foundation of Computer Science and straight math topics. Teaching surface level material in an engaging and effective manner would be my primary focus. I want my kids to be motivated by the curriculum
Great point. It’s tough, though, when kids are taught and tested on specific strategies in their math classes. While it’s true that there are many ways to solve the same problem, that’s not always reflected in math assessment. #csk8
A4: Yes, it possible to teach a new concept in both at the same time. For example, working with Distance Rate and Time while integrating @sphero for application of a concept to complete a challenge...Learn through doing #csk8
This is great example of carrying over practices or conventions from one subject to another! very interesting, I believe @lisaannefloyd told me once about the idea of having Ss answer math questions in pen so they can see their errors and debug.. #csk8
In reply to
@KatietheCurious, @Jennifer_Manly, @Todd_Lash, @lisaannefloyd
Time! I know a lot of teachers who are doing really innovative integrations in their classroom and don't have the time to put that work into a shareable form because they are with students 6 hours a day, and prepping for another 3+. #csk8
yes, assessment is an interesting area of focus. #computerScience classes often sometimes use alternative methods such as larger projects, portfolios, etc... I wonder if there's use for these in mathematics assessment? #CSK8
A4: I think kids can really dig into both at the same time, but ideas from each can't both be brand new. Kids can use loops to think about equal groups & multiplication, but only if they have some understanding of groups first! Need not be fleshed out understanding, tho. #csk8
ScratchJr is interesting, I had never heard it used that way before, sounds very interesting! I've often seen the grid used, and Ss quickly learn to use x-y points. #csk8
#csk8 A5: Cultivating a passion for STEM topics by teaching in unconventional manners. Going beyond curriculum standards and generating a passion for math and computer science through games and activities can greatly improve student response
A5: We've had good traction in #CT4EDU project integrating four big CT ideas into math & science in unplugged lessons: Decomposition, Abstraction, Patterns, and Debugging! #csk8
I always like looking at optimization: calculating the quickest path for a beebot, or most efficient algorithm with some type of mathematical analysis. #csk8
This is a key concept behind data science. Data is an important part of CS often ignored at K-8 (especially at K-5). Writing programs to process data, using spreadsheet formulas, are was to integrate cs and statistics. #csk8
A5- As educators we can use what we learn from teaching CS in other classes. I feel like teaching CS has made me a better math teacher. The mindset is important -errors are opportunities for learning, I'm more attentive to zone of proximal development for each student #csk8
A4: I think if they naturally fit with each other and kids are learning about things that matter to them, yes! Every time I’ve done it, we use programming as a means for them to apply math concepts, so neither is entirely new. They do access higher lvls of thinking, though #csk8
A5: CS concepts other than programming that could be integrated in math could be terms such as pixels which connects to concepts such as area, proportions, etc #csk8
#csk8 A6 I highly recommend the resource materials available through @TLPCanada. For Scratch and Scratch Jr. Not as well known, but well worth looking at.
Yes! We had students obtain data within various fields that were meaningful to their interests and draw comparisons & causations from their research. Compared data locally w global connection & presented via data visualization with a variety of tools including infographics #csk8
A5: Binary and hexadecimal number systems tie in with place value in grade 2-3. The idea of exponential growth connects exponents to big O, P vs NP, computational complexity. Organizing mathematical work or observations connects to data structures. #csk8
Good one! Optimization problems - these can be great minds on activities (handshake problem, etc.). Also an opportunity to connect to nature, as there are many examples in animal behaviour (used Canadian spelling for an American chat😀) #csk8
Here is a great resource for those of us interested in math/CT integration: Lisa Floyd’s Blog: Lisa is a longtime enthusiast of integrating math and CT. Her blog is full of ideas, projects and resources. #csk8
These are great. I had the privilege to hear from Noss and Hoyles in 2014 when they were in the early stages of this project at a CT and math symposium at Western. #csk8
A6: Follow @everydaycs and check out https://t.co/a80RYzsHAw for learning trajectories for CT topics and sample integrated math+CT activities for upper el! #csk8
The #CT4EDU team will also soon be sharing posters for elem. classrooms created by our awesome partner teacher @mrsfelts4, and a "toolkit" we developed for helping elem. Ts think about how to bring CT into their teaching! #csk8 (Let's get on that, @yadavaman!)
A6: Easy project: have kids create a math teaching tool in Scratch. Leave it open ended enough, but work with the math teachers to identify challenging standards and help kids pick one they struggle with. Then, share links w/ math teachers and use them for review. #csk8
Q7: Is there anything else that you would like to ask or share about integrating CS into Math or integrating Math into CS for 5-14 year old students? #csk8
A7: I'd just like to share that I've noticed lots of CT happening in elem. classrooms, when I'm looking for it! Kids naturally use decomposition, patterns, & abstraction, even though they don't realize it. Helping Ts recognize this could be a good first step in teacher ed! #csk8
A7: I often think about how much I LOVED my post-calculus math courses, where you really dive into symbolic logic. I enjoyed math before that, but it wasn’t love. CS allows us to give kids a glimpse into that, and I think we owe it to them to make the connection. #csk8
Q7: Is there anything else that you would like to ask or share about integrating CS into Math or integrating Math into CS for 5-14 year old students? #csk8
A7 I've been teaching #computationalthinking in math and science education at @westernuEdu to preservice teachers (who are so inspiring) for a few years now and always love to connect with others to explore new ideas #csk8
A7: I've gotten a lot of out of talking to programmers about the math they use in their jobs. Broad understanding of what math is and what cs is show more connections. #csk8
Thank you for joining us tonight for the #csk8 Integration of Computer Science and Math in K-8 chat ! Special thanks to @stevenpfloyd for joining us as a guest moderator.
An archive of this chat will be posted in our CSTAK8 Facebook Group at https://t.co/GdzQw5520V Continue the conversation there or on Twitter using the #csk8 hashtag.
The next #csk8 chat will be on Wed, 11/7, at 5pm PT/8pm ET when we will be continuing our series of chats about cross curricular integration of CS in K-8. Please plan to join us!
