3-15-12 I'm working on a math continuum to help me guide my instruction in the most meaningful way possible for my small groups. This is my extremely rough draft.
3-6-12 Reflections: Earlier in the year, math instruction occured in small groups (like guided reading for math) while the rest of the students explored math concepts in corners. This was incredibly problematic as it left little time for me to see what my kids were interested in mathmaticaly. I found myself focusing on increasing skills and developing student processes with no inquiry for the students. I tried improving this by creating more inquiry by asking students to solve meaningful problems and doing lots of conferring with students as they tried to solve these problems. I felt that only presenting students with number problems was still not giving students much opportunity to explore how numbers work.
Current Actions: After collaborating with teachers and reflecting on my practices, I have decided to re-assess my students and split them into two groups. Now each group is able to explore a concept that meets their needs through a hands on game/problem solving activity. This has allowed Mrs. J and I to observe students and see how they approach problems and allows students to investigate numbers more openly instead of only solving number problems.
Future Action Plans: After reading some inquiry blog posts from Lara (http://inquiryblog.wordpress.com/2012/01/21/counting-large-numbers-a-kindergarten-counting-inquiry/) and thinking about how to make our teaching/exploring time even better, I feel that we need to open our minds to more conceptual understandings that our students might be interested in exploring. I plan to investigate this and develop/discover a list of concepts worth exploring to expand our math workshop and meet more students' needs.
Hey Krista,
I stumbled upon this website that has a great example of collabration and how the students used strategies in counting. You can check it out and see if it is helpful! :) http://inquiryblog.wordpress.com/2012/01/21/counting-large-numbers-a-kindergarten-counting-inquiry/
Check out the video towards the end of the page.
Hope it helps,
Lara
Krista:
Focus: Constructivism in Math workshop Actions to take:
1-8-11 1. Incorporate math share time into 3 math workshops a week - use the format from writing workshop 2. Do a 'problem solving' corner at least once a week & meet with groups about their thinking - have them apply the skills they've learned in authentic, constructivist ways 3. Continue using key concepts and corresponding questions in each unit 12-9-11 * Use key concepts and corresponding questions in each math unit. Create learning experiences that fit the concept I'm teaching within the math curriculum.
1. Fosnot's math inquiry CD (where they show classrooms who are enacting inquiry-based instruction)
2. The book Guided math
3. http://www.10bomb.com/doc/contexts-for-learning-math-by-fosnot/- lots of articles;
4. From Lara: Really awesome website full of PYP and inquiry resources!!!! http://sites.google.com/site/pypresources/home/inquiry
Maybe look into: Borasi, R.(1992). Learning Mathematics Through Inquiry. Portsmouth, NH:Heinemann. Borasi, R.& Fonzi, J. (under review). Introducing Math Teachers to Inquiry: Framework and Supporting Materials to Design Professional Development. Borasi, R., Fonzi, J. & Smith, F.F. (in press).Beginning the process of rethinking mathematics instruction:A professional development program. Journal of Mathematics Teacher Education. Explored Resources to keep handy for future use: http://www.thirteen.org/edonline/concept2class/constructivism/index.html -this is an interactive site for all teachers · http://blogs.ibo.org/sharingpyp/ -This site is a PYP Blog focusing on sharing examples of what PYP implementation looks like in IB World schools.
On Facebook, there is an IB group that you can belong to, but it doesn’t really focus on teaching practices. Do a search and check out the group “PYP teachers lets share some ideas”. This is a fun and informal way to make connections with other PYP teachers in the world. Really cool! The site is growing every week.
1-8-12 - Thinking about inquiry and questioning
As I met with Jamie and Lara during planning time this week, we had a good conversation about what inquiry really is and I discovered that what I'm really researching here, is how to be a constructivist teacher in general. I want to make sure that I'm not encouraging students to learn skills, but instead facilitating authentic problem solving - which luckily leads to the development of some critical concepts AND skills they'll need for the rest of their lives. I read the constructivist site (http://www.thirteen.org/edonline/concept2class/constructivism/index.html) that Jamie suggested and realized that a 'math workshop' set up was only the beginning. Yes, I know where my kids are developmentally and what they need to learn, but I'm still teaching them in a way that focuses heavily on the development of the 'basic skills' they need in Kindergarten. I think that a combination of math workshop (where I meet with small groups), the presentation of authentic problems, and incorporating math sharing time will get our class on a better track to constructivist/concept-based/inquiry math!
What I discovered/learned from this article: It is better to provide students with meaningful problems in a guided inquiry approach allowing them to 'discover' concepts and ideas for themselves while providing the structure that leads them to 'discover' what is developmentally appropriate for them at the time.
What Lara & I discovered: It's crucial to use the key concepts and key concept questions in a math unit. We feel that we often teach form and function and then move on to something new with the idea that "students already get" the previously taught concept (ex: Patterns). We would now like to use form and function to help students understand the basic ideas behind a concept in math and then move them to a deeper understanding with more challenging concepts like connection, reflection, and causation.
For example: When teaching patterns, we focused on "what makes a pattern" and encouraged students to create and continue patterns. We never asked them to look at two different patterns and tell about the connections they saw. This discussion would lead to students labeling patterns and would enable them to have discussions about patterns more easily.
3-6-12 Reflections: Earlier in the year, math instruction occured in small groups (like guided reading for math) while the rest of the students explored math concepts in corners. This was incredibly problematic as it left little time for me to see what my kids were interested in mathmaticaly. I found myself focusing on increasing skills and developing student processes with no inquiry for the students. I tried improving this by creating more inquiry by asking students to solve meaningful problems and doing lots of conferring with students as they tried to solve these problems. I felt that only presenting students with number problems was still not giving students much opportunity to explore how numbers work.
Current Actions: After collaborating with teachers and reflecting on my practices, I have decided to re-assess my students and split them into two groups. Now each group is able to explore a concept that meets their needs through a hands on game/problem solving activity. This has allowed Mrs. J and I to observe students and see how they approach problems and allows students to investigate numbers more openly instead of only solving number problems.
Future Action Plans: After reading some inquiry blog posts from Lara (http://inquiryblog.wordpress.com/2012/01/21/counting-large-numbers-a-kindergarten-counting-inquiry/) and thinking about how to make our teaching/exploring time even better, I feel that we need to open our minds to more conceptual understandings that our students might be interested in exploring. I plan to investigate this and develop/discover a list of concepts worth exploring to expand our math workshop and meet more students' needs.
I stumbled upon this website that has a great example of collabration and how the students used strategies in counting. You can check it out and see if it is helpful! :)
http://inquiryblog.wordpress.com/2012/01/21/counting-large-numbers-a-kindergarten-counting-inquiry/
Check out the video towards the end of the page.
Hope it helps,
Lara
Krista:
Focus: Constructivism in Math workshop
Actions to take:
1. Incorporate math share time into 3 math workshops a week - use the format from writing workshop
2. Do a 'problem solving' corner at least once a week & meet with groups about their thinking - have them apply the skills they've learned in authentic, constructivist ways
3. Continue using key concepts and corresponding questions in each unit
12-9-11 * Use key concepts and corresponding questions in each math unit. Create learning experiences that fit the concept I'm teaching within the math curriculum.
- http://professionaldevelopment.ibo.org/ - planners, video, special class teachers
- http://www.epals.com/projects/info.aspx?divid=Resources_IB – IB on Epals – this is a must see site!!!
- PD360
- www.ibo.org
1. Fosnot's math inquiry CD (where they show classrooms who are enacting inquiry-based instruction)2. The book Guided math
3. http://www.10bomb.com/doc/contexts-for-learning-math-by-fosnot/- lots of articles;
4. From Lara: Really awesome website full of PYP and inquiry resources!!!! http://sites.google.com/site/pypresources/home/inquiry
Maybe look into:
Borasi, R.(1992). Learning Mathematics Through Inquiry. Portsmouth, NH:Heinemann.
Borasi, R.& Fonzi, J. (under review). Introducing Math Teachers to Inquiry: Framework and Supporting
Materials to Design Professional Development.
Borasi, R., Fonzi, J. & Smith, F.F. (in press).Beginning the process of rethinking mathematics
instruction:A professional development program. Journal of Mathematics Teacher Education.
Explored Resources to keep handy for future use:
http://www.thirteen.org/edonline/concept2class/constructivism/index.html -this is an interactive site for all teachers
· http://blogs.ibo.org/sharingpyp/ -This site is a PYP Blog focusing on sharing examples of what PYP implementation looks like in IB World schools.
On Facebook, there is an IB group that you can belong to, but it doesn’t really focus on teaching practices. Do a search and check out the group “PYP teachers lets share some ideas”. This is a fun and informal way to make connections with other PYP teachers in the world. Really cool! The site is growing every week.
Paul A. Kirschner; John Sweller; & Richard E. Clark suggest that open inquiry is not beneficial for students and goes against the apprentice/novice idea
http://www.tandfonline.com/doi/pdf/10.1207/s15326985ep4102_1
Inquiry in Patterns Video from Amsterdam:
http://www.pz.harvard.edu/vt/VisibleThinking_html_files/01_VisibleThinkingInAction/01c_VTPoP.html
- What Lara & I discovered: It's crucial to use the key concepts and key concept questions in a math unit. We feel that we often teach form and function and then move on to something new with the idea that "students already get" the previously taught concept (ex: Patterns). We would now like to use form and function to help students understand the basic ideas behind a concept in math and then move them to a deeper understanding with more challenging concepts like connection, reflection, and causation.
For example: When teaching patterns, we focused on "what makes a pattern" and encouraged students to create and continue patterns. We never asked them to look at two different patterns and tell about the connections they saw. This discussion would lead to students labeling patterns and would enable them to have discussions about patterns more easily.