When exploring the BC k-12 math curriculum number sense forms the backbone of the k-9 program with specific number sense outcomes listed for each grade as both big ideas and curricular competencies. Chapin and Johnson state, “Number sense is the primary focus of Elementary Mathematics, one of the goals of instruction in arithmetic is for students to become numerically powerful and proficient.” (Chapin & Johnson, 2006) Students who have strong number sense are better able to interact with the entire mathematics curriculum. Having number sense implies the ability to think flexibly about numbers and quantities and to interact with them in increasingly personal ways without relying on algorithms.
The purpose of my logic model is to examine one potential tool for creating a number sense assessment in my k-5 school. Our students are generally strong in literacy, but our district and provincial testing data shows an increasing number of students who are not proficient in numeracy. My goal is to zoom in on number sense as the backbone of numeracy instruction. The program that I have chosen has an assessment component as well as teaching strategies. The First Steps in Mathematics program includes a clear set of developmental phase as well as indicators of skill development for when learners enter each phase. Using the First Steps in Mathematics program we are able to select specific activities from the program to be used as assessments while others may be utilized in the classroom for learning and practice.
The outcomes use a mix of qualitative and quantitative data points to demonstrate success. Our initial focus is on building staff competency, first working with a small group of one teacher per grade then expanding after a pilot project with volunteer teachers. This allows for troubleshooting of the process along the way and accommodates the need for additional training and professional autonomy. By having a pilot group, problem areas can be adjusted before they can get out of hand and necessary changes made, the pilot group also allows for more productive conversations and planning around adapting and implementing First Steps in Mathematics as the group size is reduced to between ¼ and 1/3 of our total staff. This process and the implementation in the pilot group classrooms will need to undergo significant data analysis before moving to a full school implementation. This will include student work samples before and after as well as testing data and a variety of surveys and interviews. Throughout the process feedback will be gathered from staff, students and families as all are stakeholders in the educational process. Families need to have a voice in their child’s education and share their ideas and priorities for student learning to ensure that we fulfill the school mission of “Home and School Working Together”.
Logic Model
| How will a school wide number sense assessment enhance student learning and improve numeracy? | |
| Inputs | People School staff Classroom teachers Resource teachers Administration District staff District teachers for: Numeracy Primary grades Intermediate / middle grades Director of instruction School community Families / parents Students Materials Number sense resources First Steps in Mathematics – Number Sense https://www.arpdcresources.ca/resources/first_steps_in_mathematics/documents/number-sense.pdf Learning Trajectories https://www.learningtrajectories.org/ Curriculum documents District Essential Standards Funding for: Release time Printing Professional development Professional development Assessment usage Data analysis Number sense |
| Activities | Determining number sense goals by grade based on curriculum and research Gathering information about needs from staff, students and families. Adapting First Steps and Learning Trajectories Models to connect with BC Curriculum Determining which activities are to be used for assessment Piloting the assessment Gathering feedback from pilot teachers, students and families Analyze data from assessment and feedback Share findings with staff and school community Train other staff on implementing the assessment Implement assessment school wide Collect and analyze school wide data Determine areas of strength and weakness Share data at school and district level |
| Outputs | Assessment tools For each grade School wide Assessment components for progress monitoring Data Mix of qualitative and quantitative Individual student Class Grade group School wide By number sense strand / key understanding Professional development Number sense strands How to administer the assessment Plan for improving number sense Using the data as a school we can target specific areas of need Plan to work across classes / grades to share targeted activities |
| Outcomes | Short term Increased teacher understanding of number sense Accurate tool to assess number sense Common language to discuss number sense Targeted instruction to increase student skills |
| Medium term Increased student number sense Improved mathematical fluency Student progress can be tracked over several years Identify students requiring number sense intervention sooner Use of formative assessment to drive instruction | |
| Long term Increased math skills More students are meeting or exceeding expectations on District Numeracy Assessment and Foundation Skills Assessments Fewer intermediate students require numeracy support Development of an early math intervention programs in place similar to Reading Recovery or Leveled Literacy Intervention Strong foundations in numeracy Stronger number sense skills Targeted teaching for number sense Explicit number sense instruction | |
| Impacts | Increased use of data to inform numeracy instruction Common language and tools for assessing number sense Teachers are able to target specific skills More students receive support for number sense and numeracy related learning gaps Increased numeracy school wide Students are more prepared to apply numeracy skills to increasingly complex problems School wide collaboration on number sense |
| Constraints | Time Staff expertise Student attitudes towards assessments Funding for resources Inconsistent implementation of the assessment Availability of support staff to work with students with additional needs Staff reluctance to try new things Existing attitudes towards numeracy |
Staff Interview Questions
To be completed with staff including a mix of classroom teachers, non-enrolling teachers, support staff and school administrators. Where possible meeting with staff from more than one school site will give a better range of data for greater statistical significance.
Topic 1 – Number Sense
- What is your definition of number sense?
- What skills do you think some one needs to have to have number sense?
- What do you think the role of number sense is in math education? Life?
- What does strong number sense look like?
- How do you feel about your own number sense? General math skills?
- What resources do you have access to surrounding number sense?
- What professional development have you experienced related to number sense?
- How have professional development workshops, videos or courses influenced your view of number sense?
Topic 2 – Assessment Practices
- How do you know if a student has number sense?
- How do you assess number sense in your classroom?
- What does summative number sense assessment look like in your classroom? Formative?
- How often do you assess number sense?
- Do you feel a number sense specific assessment would be helpful? Why or why not?
- Do you feel like you have enough information about your student’s number sense? Why or why not?
- What do you know about your student’s number sense?
- What would you like to know about your student’s number sense?
Topic 3 – Future Assessment
- What could number sense assessment look like?
- What information do you want or need about students’ number sense?
- How would you like a number sense assessment structured? By grade? In groupings of 2-3 grades? Not linked to grade levels?
- How detailed would you like a number sense assessment to be?
- What are your priorities when assessing number sense?
- What would you need to implement a number sense assessment?
Closing
- What else would you like to share about number sense?
- Do you have any thoughts about creating a number sense assessment?
- What questions do you have about assessing number sense?
Staff Survey
To be completed by staff. Where possible having a mix of staff positions across multiple school sites and grade levels will give more rounded feedback and better statistical significance.
Student Interview questions
Topic 1 – Number Sense
- What do you think number sense is?
- What skills do you think some one needs to have to have number sense?
- What do you think the role of number sense is in math class? Life?
- What does strong number sense look like?
- How do you feel about your own number sense? General math skills?
Topic 2 – Current Practices
- How does your teacher have you practice your number sense skills?
- How does your teacher check on your number sense skills?
- Do you know what you’re good at with number sense?
- Do you know what you need to practice with number sense?
- How often do you practice numbers sense?
Topic 3 – Future Assessment
- How would you like your teacher to check on your number sense?
- What would you like your family to know about your number sense?
- Do you prefer paper check ins or conversations with your teacher to check in?
- What do you want to know about your number sense?
Closing
- What else would you like to share about number sense?
Student Survey
Family / Community Interview questions
Please note that the family and community survey uses the term student to refer to learners in the school rather than using child or children to be inclusive of all family types and structures.
Topic 1 – Number Sense
- What is your definition of number sense?
- What skills do you think some one needs to have to have number sense?
- What do you think the role of number sense is in math education? Life?
- What does strong number sense look like?
- How do you feel about your own number sense? General math skills?
- What resources do you have access to surrounding number sense?
- What could the school do to support your understanding of number sense?
Topic 2 – Current Practices
- How do you know if your student has number sense?
- What do you know about your student’s number sense?
- Do you feel like you have enough information about your student’s number sense? Why or why not?
- What would you like to know about your student’s number sense?
- How often is your student’s school / teacher communicating with you about their number sense?
- Has your student’s school / teacher ever shared concerns about your student’s number sense? If so what?
- Do you feel a number sense specific assessment would be helpful? Why or why not?
Topic 3 – Future Assessment
- What could number sense assessment look like?
- What information do you want or need about your student’s number sense?
- How would you like a number sense assessment structured? By grade? In groupings of 2-3 grades? Not linked to grade levels?
- How detailed would you like a number sense assessment to be?
- How would you like information about your student’s number sense to be shared with you?
- How often would you like information about your student’s number sense to be shared with you?
Closing
- What else would you like to share about number sense?
- Do you have any thoughts about creating a number sense assessment?
- What questions do you have about assessing number sense?
Family Survey
References
Centers for Disease Control and Prevention. (n.d.). Types of evaluation. National Center for HIV/AIDS, Viral Hepatitis, STD & TB Prevention.
Chapin, S. H., & Johnson, A. (2006). Number Sense. In M. M. K-8, Chapin, Suzzanne H.; Johnson, Art (Second ed., pp. 1-30). Sausalito, California, USA: Math Solutions.
Chen, H.-t. (2015). Practical program evaluation : theory-driven evaluation and the integrated evaluation perspective. Los Angeles: SAGE Publications.
Western Australian Minister for Education. (2013). First Steps in Mathematics: Number Sense. Don Mills: Pearson Canada.