Closing Time, Open All the...
Math Stuff Involving Timing
My last post was August 9, 2023, which was 283 days ago. For perspective, this is 77.5% of a year! I intend to be more regular with posting moving forward - I need to build a reinforcement system for doing so. But I have some good excuses: my two kids have been doing so many cool things, my wife and I had our wedding in October (Art was in the wedding), we are having a baby this summer, and work has been super busy. Okay - let’s get started!
Timing Math Stuff
I want to start by being transparent about my position on this topic. The conversation has become binary (yes/no) on timing math activities. This is not a space I feel comfortable working in.
Quick segway into the evidence-based practice conversation….If we look to a description of the evidence-based medicine model, we see three interlocking elements to consider: (1) scientific evidence, (2) clinician expertise, and (3) patient/client values. Thus, our question is rarely, should this be used yes/no but rather under what conditions and contexts should we make recommend a specific practice. Now clearly, certain practices might have “0” scientific evidence or results suggesting negative outcomes (see #1 above) and to act in good faith we will not recommend them. But in our conversations related to education, rarely are we discussing these types of activities but rather practices that have a time and place. Dr. Trina Spencer (and colleagues) has one of the most amazing articles I have read on thinking about reframing the “evidence-based practice” conversation in education to an active process versus a “noun” (i.e., what is it?). If you cannot access it just shoot me a message.
Back to our current conversation….“Good” systematic reviews and meta-analyses aim to identify how much effects vary across studies (this is called heterogeneity) and then to try and EXPLAIN (or hypothesize) which characteristics related to the studies may explain this variability.
Did effects vary based on specific student characteristics?
Pre-assessment scores
Other factors (e.g., working memory, phonemic awareness proficiency, age, gender-identity, ethnic-identity)
Did effects vary based on the interventionist's characteristics?
Years of experience
Qualifications/knowledge of the intervention
Teacher vs. researcher (Was the person’s only job to maintain fidelity or did they have lots of other job related tasks?)
Did studies have differences in intervention characteristics? Which characteristics may correlate more strongly with effects?
Did effects vary based on the “dosage” of the intervention? How often it occurred, the length of time of the intervention, the total duration?
Did studies use different types of measures to evaluate learning? Did effects vary based on the type of measure?
Did effects vary based on other contextual factors related to the setting?
Did effects vary based on the methodological quality of the study?
For something like timing math activities, many variables are present to influence both academic learning outcomes and child affect outcomes. I am exhausted by the conversation surrounding timing math activities and using timing as one way to assess a child’s math knowledge. I think I feel this way for many reasons.
In my opinion, other areas of disagreement deserve more energy.
Often, the conversation doesn’t address topics that should precede the discussion on timing.
I think (could be naive) there are ways to find a middle ground if point 2 (above) is discussed and a consensus can be reached.
A Critical Area of Disagreement
One issue that is not discussed enough is related to the actual content that our fields believe is worth teaching (i.e., what content in mathematics are we aiming to see mastery). For example, do we want to see fluency in the standard algorithms for addition, subtraction, multiplication, division? Do we see value in having students become fluent in solving word problems that represent situations involving the core operations? Do we see value in having students become fluent in using core properties of mathematics (e.g., associative, communicative, distributive)?
There are massive disagreements in what people deem important for students to know. These disagreements then influence the “value” individuals place on results from assessment data (e.g., PISA, NAEP, state assessments). These disagreements then influence what instructional approaches people claim are effective because to determine effectiveness we need an assessment which then ties back to what we are assessing which then ties back to what we deem as important.
I have no answers for this disagreement. We perhaps can look at correlational studies that suggest students who mastery “X” are more likely to master “Y” and see outcomes “Z” post school - this would be how you think about constructing standards for curriculum across grade spans. The “Z” dictate outcomes we hope students have the opportunity to experience post-school. The “X” and “Y” would be the skills that built across each other across grade spans - and might be identified as the most salient math content to focus instruction on.
Missing Topics of the Conversation
Is the automatic recall of math facts important?
This ties back to the point above but a central aspect missing from the conversation is whether individuals believe math facts are important. If someone does not believe the ability to provide a correct response to a math fact is important then they probably do not see the benefit of timing math activities. Thus, engaging in long winded conversations around timing math activities is useless because the disagreement between both sides is deeper than this issue.
How do we know if math facts are known?
This is a different conversation to be had. Now we are in a place where two groups of people perhaps agree the ability to provide a correct response to a math fact is important but the new conversation is around how to determine if it is “known.”
I am making an assumption here, but both groups likely are focused on “correct” responses. For example, if a student is present 8 + 7 both groups are focused on a student responding with 15. The difference becomes what is considered “known.”
In one approach, people might provide unlimited time for a student to provide the response of 15. The child can use counters (or their fingers) and work through a counting strategy to provide the response of 15. A student might use a different strategy, such as decomposition (7 can be decomposed into 2 + 5, and 8 + 2 is equivalent to 10 and the 5 can be added to yield 15) or use a related fact (doubles facts: 8 + 8 = 16 and I need to compensate for the extra 1, 16 - 1 = 15). Educators might attempt to identify the strategy used by the student to gauge their current approach to tackling this fact and the result is coded as correct.
In another approach, people might consider the latency (i.e., how long it takes a student to respond). For example, if 8 + 7 is presented to a student I can count how many seconds it takes a student to respond with 15. If a student responds within 1-2 seconds, I might assume this was pulled from memory because it is unlikely a strategy could have be identified as appropriate for this problem and then used within that time frame to provide the correct response. A correct response with a latency of 3+ seconds I might assume was derived through a strategy.1
Reaching a consensus on how we determine what is known can then allow for actual conversations on timing math activities. Disagreement however, will results in fruitless conversations in the “timing” math activities conversations.
It is possible for some students they may exhibit slower latency and yet are pulling from memory. However, this is something that will be known to teachers because you will have time-series data on that individual student. Thus, you will be able to see their latency decrease as you practice - the key to determine here is if they are pulling from memory or using a strategy (e.g., counting on) to provide the response.