title: Number-fact knowledge and mathematical problem-solving of five-to seven-year olds

authors: Young-Loveridge, Jennifer

abstract: This paper examines children's number fact knowledge in relation to mathematics problem solving. These findings are derived from a study that set out to explore the impact on mathematics learning of using multiplication and division contexts with 84 five- to seven-year-old children from diverse cultural and linguistic backgrounds. After a series of focused lessons, children's knowledge of number facts, including single-digit addition, subtraction, and doubles improved substantially. However, children did not always apply this knowledge to relevant problem-solving situations. The difficulty level for recalling number facts was not directly related to the magnitude of the numbers, with certain salient facts such as 5+5 and 10+10 learned earlier than facts with smaller sums such as 2+3 and 1+4.

text: Number-fact knowledge and mathematical problem-solving of five-to seven-year olds This paper examines children's number fact knowledge in relation to mathematics problem solving. These findings are derived from a study that set out to explore the impact on mathematics learning of using multiplication and division contexts with 84 five- to seven-year-old children from diverse cultural and linguistic backgrounds. After a series of focused lessons, children's knowledge of number facts, including single-digit addition, subtraction, and doubles improved substantially. However, children did not always apply this knowledge to relevant problem-solving situations. The difficulty level for recalling number facts was not directly related to the magnitude of the numbers, with certain salient facts such as 5+5 and 10+10 learned earlier than facts with smaller sums such as 2+3 and 1+4.

year: 2015

title: Future intentions, plans, and the problem of Buridan's Ass

authors: Ulatowski, Joseph W.

abstract: Suppose that:
1. an agent, S, is able to choose only one option, x or y;
2. S prefers neither x nor y in comparison to the other; and
3. S prefers having at least one of x or y to having none.1
Call this “the problem of Buridan’s Ass.” A theory of practical reasoning is supposed to tell us what to do. Which option, x or y, should S choose? Which theory of practical reasoning tells S to choose that option? While we are capable of overcoming the above situation, it seems that our choosing to act did not rely upon a theory of practical reasoning.
In response to the puzzle above, I show how Davidson’s theory faces a pair of difficulties, which are the result of his overly weak conception of the role of intentions and plans in practical reasoning. On one hand, Davidson’s theory seems unable to accommodate the possibility of a future intention in the face of equally desirable future options, and, on the other hand, his theory cannot ensure that rational intentions are agglomerative. Upon further inspection, however, it appears that Davidson’s theory is not an overly weak conception since he does seem to rule out the role of plans in practical reasoning. But even including plans in practical reasoning, as Bratman’s theory of intention does, fails to solve the seemingly insoluble problem of equipollent preference.

text: Future intentions, plans, and the problem of Buridan's Ass Suppose that:
1. an agent, S, is able to choose only one option, x or y;
2. S prefers neither x nor y in comparison to the other; and
3. S prefers having at least one of x or y to having none.1
Call this “the problem of Buridan’s Ass.” A theory of practical reasoning is supposed to tell us what to do. Which option, x or y, should S choose? Which theory of practical reasoning tells S to choose that option? While we are capable of overcoming the above situation, it seems that our choosing to act did not rely upon a theory of practical reasoning.
In response to the puzzle above, I show how Davidson’s theory faces a pair of difficulties, which are the result of his overly weak conception of the role of intentions and plans in practical reasoning. On one hand, Davidson’s theory seems unable to accommodate the possibility of a future intention in the face of equally desirable future options, and, on the other hand, his theory cannot ensure that rational intentions are agglomerative. Upon further inspection, however, it appears that Davidson’s theory is not an overly weak conception since he does seem to rule out the role of plans in practical reasoning. But even including plans in practical reasoning, as Bratman’s theory of intention does, fails to solve the seemingly insoluble problem of equipollent preference.

year: 2021

title: Life history of fluvial and lacustrine land-locked koaro (Galaxias brevipinnis) Günther (Pisces: galaxiidae) in the Tarawera lakes

authors: Young, Kim D.

abstract: Biological diversity in New Zealand has been seriously degraded as a result of human induced disturbances which include the introduction of many exotic species. Freshwater ecosystems have not escaped damage, with the introduction of primarily sports fish suspected to be a significant contributing factor in diminished native biological freshwater values. This is reflected by range and population reductions of several native fish species. 

One of these species is koaro (Galaxias brevipinnis), for which abundance in land-locked populations in the central North Island lakes has significantly declined. Koaro were once abundant in these lakes, and pre-European harvest in both its juvenile (whitebait) and adult (kokopu) form, comprised an important food resource for inland Maori. Since the introduction of recreational trout species to these lakes in the late 1880s, followed by the introduction of common smelt (Retropinna retropinna) in the early 1900s, the abundance of koaro has dramatically declined to the extent that, in these lakes, the species is now considered rare. 

To date, the interactions between recreational trout species, common smelt, and koaro populations have not been established, and the life-history of land-locked koaro is not fully understood. In particular, the extent of movement between lake and stream habitats remains unclear. However, a collaborative project between the indigenous people of the Rotorua Lakes (Te Arawa) and the Department of Conservation to restore a koaro population in one Rotorua lake, has driven a need to gain a better understanding of the biology and ecology of land-locked koaro. This includes identifying threats to important life-history stages and understanding the role of tributary streams.

During July 1999 to February 2001, lacustrine and fluvial koaro were studied in Lake Tarawera and Lake Okareka and their tributary streams. Both lakes are part of the Tarawera lakes group, a subgroup of the Rotorua lakes situated in the central North Island. Fyke netting was used to sample lacustrine koaro on a monthly basis from January 2000 to February 2001, and seasonal two-pass reduction electric fishing at five sites in the tributary streams took place in April, July and November 2000 and February 2001. All fish larger than 70 mm total length were tagged with a passive implant transponder. Spawning season and location, together with size and growth of lake and stream fish were determined. Movement of lake fish within the littoral zone was also investigated. 

The study found that lake and stream koaro may belong to two sub-populations indicated by differences in size, growth rate, spawning time and locality, and return of lake and stream koaro to natal habitats. The life-history of stream koaro has remained similar to that of its diadromous counterparts. Stream fish were found to spawn and hatch in stream environs, rear as larvae in the lake environs, and return to tributary streams as juvenile fish. Lake fish by contrast, most likely spawn in the lake itself, and results suggest that no juvenile migration of lake spawned fish to tributary streams occurs. Consequently, it was concluded that tributary streams may play little role in the life-history of lacustrine koaro.

Abundance of lacustrine koaro in both Lake Tarawera and Lake Okareka was low in comparison to lakes where trout species or common smelt are absent, and abundance of post-whitebait koaro (greater than 45 mm total length coloured and patterned) in both tributary streams studied was also low where rainbow trout (Oncorhynchus mykiss) were proportionally present in greater abundance. Important life-history stages were found to be subject to competition and predation by a combination of rainbow trout and common smelt in both lakes and streams.

Given the above, restoration programmes for land-locked koaro will need to be undertaken at the population level to enhance the survival of larval and juvenile life-history stages. This will need to occur at an ecosystem scale, and include the management of the combined effects of trout and common smelt in both lake and respective tributary stream environs.

text: Life history of fluvial and lacustrine land-locked koaro (Galaxias brevipinnis) Günther (Pisces: galaxiidae) in the Tarawera lakes Biological diversity in New Zealand has been seriously degraded as a result of human induced disturbances which include the introduction of many exotic species. Freshwater ecosystems have not escaped damage, with the introduction of primarily sports fish suspected to be a significant contributing factor in diminished native biological freshwater values. This is reflected by range and population reductions of several native fish species. 

One of these species is koaro (Galaxias brevipinnis), for which abundance in land-locked populations in the central North Island lakes has significantly declined. Koaro were once abundant in these lakes, and pre-European harvest in both its juvenile (whitebait) and adult (kokopu) form, comprised an important food resource for inland Maori. Since the introduction of recreational trout species to these lakes in the late 1880s, followed by the introduction of common smelt (Retropinna retropinna) in the early 1900s, the abundance of koaro has dramatically declined to the extent that, in these lakes, the species is now considered rare. 

To date, the interactions between recreational trout species, common smelt, and koaro populations have not been established, and the life-history of land-locked koaro is not fully understood. In particular, the extent of movement between lake and stream habitats remains unclear. However, a collaborative project between the indigenous people of the Rotorua Lakes (Te Arawa) and the Department of Conservation to restore a koaro population in one Rotorua lake, has driven a need to gain a better understanding of the biology and ecology of land-locked koaro. This includes identifying threats to important life-history stages and understanding the role of tributary streams.

During July 1999 to February 2001, lacustrine and fluvial koaro were studied in Lake Tarawera and Lake Okareka and their tributary streams. Both lakes are part of the Tarawera lakes group, a subgroup of the Rotorua lakes situated in the central North Island. Fyke netting was used to sample lacustrine koaro on a monthly basis from January 2000 to February 2001, and seasonal two-pass reduction electric fishing at five sites in the tributary streams took place in April, July and November 2000 and February 2001. All fish larger than 70 mm total length were tagged with a passive implant transponder. Spawning season and location, together with size and growth of lake and stream fish were determined. Movement of lake fish within the littoral zone was also investigated. 

The study found that lake and stream koaro may belong to two sub-populations indicated by differences in size, growth rate, spawning time and locality, and return of lake and stream koaro to natal habitats. The life-history of stream koaro has remained similar to that of its diadromous counterparts. Stream fish were found to spawn and hatch in stream environs, rear as larvae in the lake environs, and return to tributary streams as juvenile fish. Lake fish by contrast, most likely spawn in the lake itself, and results suggest that no juvenile migration of lake spawned fish to tributary streams occurs. Consequently, it was concluded that tributary streams may play little role in the life-history of lacustrine koaro.

Abundance of lacustrine koaro in both Lake Tarawera and Lake Okareka was low in comparison to lakes where trout species or common smelt are absent, and abundance of post-whitebait koaro (greater than 45 mm total length coloured and patterned) in both tributary streams studied was also low where rainbow trout (Oncorhynchus mykiss) were proportionally present in greater abundance. Important life-history stages were found to be subject to competition and predation by a combination of rainbow trout and common smelt in both lakes and streams.

Given the above, restoration programmes for land-locked koaro will need to be undertaken at the population level to enhance the survival of larval and juvenile life-history stages. This will need to occur at an ecosystem scale, and include the management of the combined effects of trout and common smelt in both lake and respective tributary stream environs.

year: 2002