Using Mobile Technology to Promote K 2 Mathematical Reasoning and - - PowerPoint PPT Presentation

Using Mobile Technology to Promote K‐2 Mathematical Reasoning and Discourse

April 12, 2016 NCTM Research Conference San Francisco, CA

Presenters in speaking order: Pamela Buffington (EDC), Kelly McCormick (USM), Jo Louie (EDC), Patricia Moyer-Packenham (USU)

Session Format

• Overview of the EDC‐Maine research‐practice

partnership and 2‐year co‐investigation

• Emerging teacher and student outcomes

– Evidence from classroom video and artifacts – Evidence from teacher logs, surveys, and interviews

• Discussant’s reflections
• Session Q&A and discussion

Project Background

• Research + Practice Collaboratory: 5‐year NSF project to bridge

research and practice in STEM

– National network collaborations: Develop and distribute tools & products to researchers + practitioners – Focused, short‐term collaborations: Convene researchers + practitioners to jointly address STEM ed challenges – Ongoing local collaborations: Build local R+ P partnerships to promote STEM ed improvement

• Four themes: Cross‐setting learning, Formative assessment,

Interactive Technologies, STEM practices

• Partners: Exploratorium, U Washington, Education Development

Center, U Colorado‐Boulder

Local Collaboration Site: Auburn, ME

• District profile

‒ Northeast, small city, 3,627 students (NCES, 2013‐14)

• Mathematics context

‒ low achievement in early grades ‒ 1:1 iPad implementation K‐3 ‒ need for mathematics and technology professional learning

• EDC, Auburn School District, & Maine higher ed (math

educator) partnership formed to support district, build capacity of local researchers, and test conjectures of R+P project

Building an Equitable Research + Practice Partnership

• Assemble critical partners,

agreements, Design Team

• Jointly identify problem
• Create shared language & vision
• Collectively develop solutions &

research agenda

• Conduct ongoing cycles of

iterative co‐investigation

• Auburn participants:

‒ 9 administrators ‒ 8 teachers (Cohort 1) ‒ 9 teachers (Cohort 2) ‒ 2 mathematics coaches (1 per yr)

Context of iPad Use Prior to Project

• Primary focus on content‐related apps, skill and drill.

Use not well integrated with instruction

• Teachers lacked targeted PD to support math learning

integrating 1:1 iPads with instruction. Primary focus on literacy learning. Some K PD, less for Gr 1‐2

• District policy around math app use was not

centralized, little use data or analysis specific to math

• Little/no PD on specific mathematical practices

Exploration of Open Math Apps

• Example Apps1 –

Number Number Rack Frames

• These tools/apps were integrated

into the core instruction and provided in mathematics toolkit to students on their individual iPads Tools for Thinking and Representing

Note1: The apps shown here are created by The Math Learning Center. To find out more go to http://catalog.mathlearningcenter.org/apps

Tool Use Informed by Research

• Mathematics learning

progressions research

• Developmentally

appropriate use of technology

• Research – Practice Briefs

Video – Snapshot of Practice

YouTube

Exploration of Recording Apps

• Explain EverythingTM, Show Me, Use of iPad video

Selected by teachers, introduced in order to elicit and record student thinking and explanations

• Used to record students’ written and verbal

mathematical thinking

• Used to record use of physical and virtual models

Grade 2 Student ‐ Screencast

Co‐Development of Research Agenda

Sept – Dec 2014:

• Teachers tried new strategies & apps with students
• Monthly meetings to discuss, provide resources
• School‐based co‐investigation teams, with new math

coach, for teacher support and data collection

• Discuss possible interventions and

research questions

Co‐Investigation Plan

Jan 2014:

• Teachers’ hypothesis:

‒ When students record and review explanations of their own mathematical thinking, engagement and learning improve

• Proposed strategy:

‒ At least bi‐weekly, students record and review their thinking on the iPad when solving a mathematics problem

Co‐Investigation Research Questions

• How do teachers implement the recording strategy?
• What outcomes appear to emerge – for whom and

under what conditions?

• What are the critical components of the strategy that

may contribute to positive outcomes?

Co‐Investigation Process

Feb – present:

• 30‐day iterative Plan‐Do‐Study‐Act cycles
• Monthly co‐investigation meetings to share

experiences, observed outcomes, and plans

• Ongoing professional learning and visits from school‐

based co‐investigation team members

• Addition of a new cohort in summer 2015

Data Sources

• Teacher online logs
• Monthly PLC debriefing sessions
• Monthly reflection surveys
• Student artifacts: iPad recordings
• Classroom video
• Participant interviews

Emerging Findings:

Evidence from classroom video and student artifacts

Context

• January
• Strategy: student think about a problem on

their own, work with partners on EE, and share their work in groups & then as a whole class

• Always includes sentence starters (e.g. I know

my work is correct because…)

• Working on the MP3 critiquing by encouraging

questions, compliments, and “I noticed…”

Sharing Their Thinking in Groups

• Mrs. Hodgekin is

teaching a new game to 1st and 2nd

• graders. She needs

91 balls. How many could be small, how many could be medium, and how many could be large?

Context

• Cohort 2, Grade 2

– Tier 2 Intervention is push in/pull out

• First Explain Everything Video in December
• Make videos once every two weeks
• Purpose: to improve students’ mathematical

communication

– Intervention students have made additional videos

Teacher Strategy 1

• Co‐Constructed Anchor Chart:
• I know [what do you know about math in this

type of problem]. So [how did you solve this exact problem step by step]

– Example: I know that quarters = 25 cents, dimes = 10 cents, and nickels = 5 cents. So, I made 75 cents using the fewest coins by using 3 quarters.

Strategy 2: Checklist Indicators

• I can hear my explanation
• I can see a picture that helps to explain my

thinking

• My picture & writing is clear and easy to read
• I say what problem I am solving
• My explanation is easy to understand
• I explained the math words when needed
• My math is correct

Self Reflection / Revision

Demonstrating counting up strategy using a number line (1st attempt) Tier 2 Intervention Student Problem: You have $1.00 You spent 63¢ How much change will you have?

Self Reflection / Revision

Demonstrating counting up strategy using a number line (2nd attempt) Tier 2 Intervention Student Problem: You have $1.00 You spent 63¢ How much change will you have?

Creation of Dynamic Artifacts

• Evidence of what students know and understand

(or misunderstand)

• Context:
• These artifacts were generated using the Number

Pieces App & Explain Everything.

• The students used representations of base 10

blocks to create a house. Then they provided the house number based on how many blocks it took to create it.

Student 2

Snapshots of Practice

• Example

strategic use of tools (MP5)

Context: Lesson Part 1

• Provided students with a number story: Sam’s

family is at the library. Sam checks out 7 books. Her little sister checks out 3 books. How many books do they check out altogether?

• Students could choose the tool they wanted to

use to help solve the problem and represent their thinking (MP5)

• If they wanted to, they could bring into EE and

explain their thinking

Snapshots of practice (View Video)

Emerging Findings:

Evidence from logs, surveys, and interviews

Co‐investigation Research Questions

• How do teachers implement the recording strategy?
• What outcomes appear to emerge – for whom and

under what conditions?

• What are the critical components of the strategy that

may contribute to positive outcomes?

Strategy Implementation

‒ Subitizing ‒ Ordering numbers ‒ 10 as a friendly number ‒ Composing/decomposing numbers ‒ Fluency with:

• Counting on
• Skip counting
• Using doubles/near doubles

‒ Place value ‒ Equipartitioning ‒ Measurement ‒ Pattern recognition ‒ Problem solving ‒ Writing own problems

‐ Teacher strategy logs, Sep 2015 – Jan 2016

• Lesson goals focus on promoting student numeracy

Strategy Implementation

• Teachers use or create open math tasks

“_____ is going to make a game for the winter carnival, and it's a relay. She needs plastic cups, snowballs, and beanbags. She needs 96 items. How many could she have of each one of the beanbags, the plastic cups, and the snowballs?”

‐ Gr 2 teacher, Cohort 1 (#8500), interview

Strategy Implementation

• Multiple visual representation tools suggested

– iPad apps, pencil/paper, physical manipulatives, other – iPad apps suggested most often (40% of tools suggested) – Multiple tools suggested most often (82% of reported combinations)

• One tool: 18%
• Two tools (e.g., iPad app + pencil/paper): 58%
• Three tools: 22%
• Four tools : 2%

‐ Teacher strategy logs, Sep 2015 – Jan 2016

Strategy Implementation

• Students primarily do the strategy with others

– Teachers reported if strategy done individually, in pairs, in small groups, with whole group, with teacher, or other – Students rarely did the strategy only alone (4% of reported grouping combinations) – Students typically engaged in multiple groupings

• Two groupings (e.g., in small groups and with teacher; individually and

in pairs): 41%

• Three or four groupings (e.g., in pairs and with whole group and with

teacher): 35%

‐ Teacher strategy logs, Sep 2015 – Jan 2016

Student Benefits

• Stronger math communication

– Explaining one’s own thinking – Collaborating with peers, sharing solution strategies

• Stronger mathematical thinking and reasoning

– Generating multiple solutions to problems – Making connections among solutions – Understanding own and others’ thinking

• Positive socio‐emotional outcomes

– Engagement in math – Comfort with technology and sharing ideas – Perseverance in problem solving

‐ Teacher strategy logs, Sep 2015 – Jan 2016

Student Communication Benefits

• Strategy helps strengthen students’ mathematical

explanations

“In the past, my kids have said, ‘Well, this is how I did it.’ Or, ‘I just knew it,’ and they don’t discuss anymore. This year, they’re having discussions and talking about their thinking and responding to others.”

‐ Gr 2 teacher (#8405), Cohort 2, interview

Student Communication Benefits

• Strategy helps to promote mathematical

conversations

“I guess I didn’t realize how little I had students talking about math… And I’ll find now just sitting on the carpet students will… just be engaging in conversation while I’m writing something up on the board and it’s about a math problem. And they’re arguing with each other but being really reasonable and they’re doing those things that we’re practicing but without that scaffold of the video. Which I think is really the goal. I feel like the videos are a stepping stone towards just having math conversations with each other.”

‐ Gr 2 teacher (#8693), Cohort 1, interview

Student Thinking Benefits

• Strategy helps to promote flexible problem solving

“And the way my students look at numbers, and using ten frames, and the way they’re thinking about solving problems is a lot different than they have in years past… Since we’ve done a lot of work with breaking the numbers apart and using some of those ten frames apps and the number lines, they have multiple ways they’re solving these problems, multiple ways they’re answering these questions, and then they’re having discussions.”

‐ ‐ Gr 2 teacher (#8405), Cohort 2, interview

Student Thinking Benefits

• Strategy helps students make mathematical

connections

“They make the video together, and… they’re listening to somebody else’s video, so they’re thinking about what the other person is doing. So often they’ll jump in, ‘Oh, I can see you added the 9 and the 1 in the tenth column, and that’s how you got 100,’ and they start to make those connections.”

‐ Gr 2 teacher (#8500), Cohort 1, interview

Student Thinking Benefits

• Strategy helps to promote student self‐correcting

and metacognition

“I think a really big ‘aha’ is that kids will self‐correct. They self‐correct when they make a mistake.”

‐ Gr 2 teacher (#8500), Cohort 1, interview

“When they’re doing their work and recording, and then they go back and listen, they can either deepen their understanding, or be reflective in the sense of self‐correcting. Like, ‘Oh, wait a minute. I meant this.’ And within that piece, [they] may also clarify a misunderstanding they may have had.”

‐ Math coach (#8928), interview

Student Socio‐Emotional Benefits

• Strategy helps to promote student ownership over

their thinking

“They’re definitely constructing an argument about how they’re presenting what they’re doing. And that’s ownership of what they just

• explained. When kids own something, when they’re that invested, it’s
• theirs. They’re gonna keep it. They know it; they learned it; they can

explain it to someone else. That ownership is, I think, a really critical piece.”

‐ Gr 2 teacher (#8500), Cohort 1, interview

Student Socio‐Emotional Benefits

• Strategy helps students feel more comfortable

taking risks

“I feel students feel more comfortable taking risks when they have that app... When I think about a typical sharing and how it used to look… we would share with the whole class or with a teacher and it’s like the pressure is on. But when you’re recording if you mess up and you don’t want to share it right away… you can go ahead and go back and fix it.”

‐ Gr 2 teacher (#8693), Cohort 1, interview

Student Socio‐Emotional Benefits

• Strategy helps students feel their work has value

“It’s fantastic to be able to have a recap and to have the kids really feel like, ‘Oh, what I’m doing is worthwhile. I’m actually providing some teaching for my class,’ which they think is the coolest thing ever… They’ve started to do really well with their videos, because they’re thinking of themselves as teachers.”

‐ Gr K teacher (#8781), Cohort 2, interview

Student Socio‐Emotional Benefits

• Strategy helps students see and feel good about

their own growth

“I think it’s really important that kids are able to go back, and look at their videos, and see what they did in the past, and see how much they’ve grown… They love going back, and looking, and seeing what they did, and [thinking]: what can I do now?”

‐ Gr K teacher (#8300), Cohort 1, interview

Teacher Benefits

• Strategy helps teachers see importance of

mathematical explanations

“Honestly, in the past, I’d never really thought about how important it is to have [students] explain what they’re doing, what they’re thinking. So it has been huge for me, it’s really been an eye‐opener, and a changer, in how I teach my kids.”

‐ Gr K teacher (#8300), Cohort 1, interview

Teacher Benefits

• Strategy helps teachers become facilitators

“I’m trying harder to be less at the front of the classroom giving the instruction and trying to be more of a facilitator as students work through strategies. I’m finding myself trying to step away and talk less to allow the students to talk more. So that’s been big because I like to talk. But students can really learn a lot from each other and that’s valuable.”

‐ Gr 2 teacher (#8693), Cohort 1, interview

Teacher Benefits

• Strategy can help teachers see the value of

productive struggle

“That’s the piece we want to make sure, for some teachers, it’s not just regurgitating what you told them to do. It’s really letting children think and explore their own thinking and then being able to listen to what the children have said, and identify where they’re at, to find out where to move them next. This would be probably a challenge for some teachers, because, especially in the primary level, we’re still coddling and motherly

• types. We don’t like to teach in struggle. So needing to really have a

clear understanding that productive struggle is where kids learn might be new learning for some.”

‐ Math coach (#8928), interview

Teacher Benefits

• Strategy helps with formative assessment

“Whereas before it was one teacher and 20 students so I didn’t always get to listen to how every student was listening and sharing their

• thinking. [Now] I can look at those students who I know are struggling

and take time to review their recording later and then I can meet with them again. So it’s a nice snapshot of how students are doing with a particular problem at that moment.”

‐ Gr 2 teacher (#8693), Cohort 1, interview

Strategy Challenges

• File management

– Storage, access

• Classroom management

– Keeping students on‐task

• Time management

– Making time to learn the technology, to integrate strategy

• Supporting student explanations and critique
• Understanding development of numeracy
• Allowing time for productive struggle
• Overcoming teacher discomfort with technology

‐ Teacher and administrator interviews, monthly debriefing sessions

Strategy Critical Components

• Students should:

– Explore technology first, before using with more challenging math – Explain, record, review, and have opportunity to revise thinking – Listen to others’ recordings and discuss

• Teachers should:

– Explore technology first, before using with students – Provide open tasks, with multiple possible solutions – Provide choice of tools for problem solving – Use pairs or small groups for recording and sharing – Have classroom and technology routines in place – Receive PD in numeracy development, mathematical discourse – Collaborate on strategy implementation – Potentially provide younger students with more teacher support

‐ Strategy logs, interviews, monthly debriefing sessions

Discussant’s Reflections

Patricia Moyer‐Packenham Patricia.moyer‐packenham@usu.edu Utah State University

Strengths of the Research + Practice Collaboratory

• Relationship was built from the ground up
• Joint identification of problems and solutions
• Different levels of collaboration built into the model

(e.g., national network; focused short‐term convene researchers; ongoing local)

• Useful Guide Map of the elements for forming a

successful Research Practice Partnership

• Blurring the boundaries between professional

learning and research

Benefits of the Research + Practice Collaboratory for Children

• Screen casting strategy addresses a Mathematical Practice

Standard: “construct viable arguments and critique the reasoning of others”

• Screen casting strategy allows students to revise their work,

which means revisit their work. Promotes the idea that mathematics is a living thing that changes and evolves

• Results show increased communication, reasoning, and socio‐

emotional outcome

• ExplainEverything app uses multiple modalities for interaction

Sensory Modalities of the Screen Casting App: auditory, tactile, visual

Design Framework for Interactive Multimedia (Daghestani, 2013)

Things I am wondering about…

• Results show students increased their

communication, collaboration, and reasoning – I am wondering what mathematics the children are learning.

• The teachers are collaborating researchers – I am

wondering what type of analyses teachers are doing with their classroom level data to document student growth in mathematical reasoning and discourse.

Things I would like to know more about…

• One RQ was: What types of mathematical reasoning and discourse
• utcomes emerge from the use of this strategy? I would like to

know more about the results from students’ digital artifacts recorded with the iPad. What types of analyses are being conducted on the digital artifacts and are these methods of analysis sharable and transferrable to the research community?

• Teachers’ hypothesis was: When students record and review

explanations of their own mathematical thinking, engagement and learning improve. I would like to know more about how the teachers tested their hypothesis. What was their role in the analysis of their students’ data?

Areas for further development…

One area for further development is in the tools that are used for this type of

• research. An important contribution of this project could be the development of

research tools for use in dynamic classroom environments where children are engaged with a technology device. Tools for student outcomes:

• Tools to document change in reasoning, discourse and learning
• Tools to document improved use of mathematical language
• Tools to document improved use of mathematical justification

Tools for teacher outcomes:

• Tools to document changes in teacher learning
• Tools to document changes in teachers’ instructional practices

Areas for further investigation…

• One area for further investigation is in

understanding ways of connecting improvements in students’ mathematical learning with the ExplainEverything app, or other technology tools

• Another area for further investigation is the

potential of a multi‐tiered research design that engages teachers as researchers in the collection, analysis and interpretation of their own data that can then be combined with the data from classrooms of

• ther teachers

Q&A and Discussion

Interactive STEM Website

• interactivestem.org

Tools, Resources, Briefs

Project Website

• researchandpractice.org

Contact Us

• Pam Buffington, pbuffington@edc.org
• Jo Louie, jlouie@edc.org
• Kelly McCormick, kmccormick@maine.edu
• Patricia Moyer‐Packenham, patricia.moyer‐

packenham@usu.edu EDC Interactive STEM (RPC):

• Website: http://interactivestem.org/
• Twitter: @edcrpcollab

https://twitter.com/edcrpcollab