Question: David upheld his support for his niece, the former Empress-consort, who had how many children?

full_context: Document 1: Owain ap Dyfnwal (died 1015): Owain ap Dyfnwal (died 1015) may have been an eleventh-century ruler of the Kingdom of Strathclyde. He seems to have been a son of Dyfnwal ab Owain, King of Strathclyde, and may well have succeeded Dyfnwal's son, Máel Coluim, King of Strathclyde. During Owain's reign, he would have faced a massive invasion by Æthelræd II, King of the English. Owain's death is recorded in 1015, and seems to have been succeeded by Owain Foel, a man who may have been his nephew.
Document 2: Emma of Normandy: Emma of Normandy (c. 985 – 6 March 1052) was a queen consort of England, Denmark and Norway. She was the daughter of Richard I, Duke of Normandy, and his second wife, Gunnora. Through her marriages to Æthelred the Unready (1002-1016) and Cnut the Great (1017-1035), she became the Queen Consort of England, Denmark, and Norway. She was the mother of three sons, Edward the Confessor, Alfred, and Harthacnut, as well as two daughters, Goda of England, and Gunhilda of Denmark. Even after her husbands' deaths Emma remained in the public eye, and continued to participate actively in politics. She is the central figure within the "Encomium Emmae Reginae", a critical source for the history of early 11th-century English politics. As Catherine Karkov notes, Emma is one of the most visually represented early medieval queens.
Document 3: Isabella of England: Isabella of England (1214 – 1 December 1241), was Holy Roman Empress, Queen of the Germans, and Queen consort of Sicily.
Document 4: David de Bernham: David de Bernham (died 1253) was Chamberlain of King Alexander II of Scotland and subsequently, Bishop of St. Andrews. He was elected to the see in June 1239, and finally consecrated, after some difficulties, in January, 1240. He died in 1253, and was buried at Nenthorn, near Kelso.
Document 5: List of battles between Scotland and England: The Kingdom of England and the Kingdom of Scotland fought dozens of battles with each other. They fought typically over land, particularly Berwick-Upon-Tweed, and the Anglo-Scottish border frequently changed as a result. Prior to the establishment of the two kingdoms, in the 10th and 9th centuries, their predecessors, the Northumbrians and the Picts or Dal Riatans, also fought a number of battles. Major conflicts between the two parties include the Wars of Scottish Independence (1296–1357), and the Rough Wooing (1544–1551), as well as numerous smaller campaigns and individual confrontations. In 1603, England and Scotland were joined in a "personal union" when King James VI of Scotland succeeded to the throne of England as King James I. War between the two states largely ceased, although the Wars of the Three Kingdoms in the 17th century, and the Jacobite Risings of the 18th century, are sometimes characterised as Anglo-Scottish conflicts, despite really being British civil wars.
Document 6: List of Holy Roman Empresses: Holy Roman Empress or Empress of the Holy Roman Empire is the title given to the consort (wife) or regent of the Holy Roman Emperor. The elective dignity of Holy Roman Emperor was restricted to males only, therefore there was never a Holy Roman Empress regnant, though women such as Theophanu or Maria Theresa of Austria, who controlled the power of rule, served as de facto Empresses regnant.
Document 7: England in the High Middle Ages: England in the High Middle Ages includes the history of England between the Norman Conquest in 1066 and the death of King John, considered by some to be the last of the Angevin kings of England, in 1216. A disputed succession and victory at the Battle of Hastings led to the conquest of England by William of Normandy in 1066. This linked the crown of England with possessions in France and brought a new aristocracy to the country that dominated landholding, government and the church. They brought with them the French language and maintained their rule through a system of castles and the introduction of a feudal system of landholding. By the time of William's death in 1087, England formed the largest part of an Anglo-Norman empire, ruled by nobles with landholdings across England, Normandy and Wales. William's sons disputed succession to his lands, with William II emerging as ruler of England and much of Normandy. On his death in 1100 his younger brother claimed the throne as Henry I and defeated his brother Robert to reunite England and Normandy. Henry was a ruthless yet effective king, but after the death of his only male heir in the White Ship tragedy, he persuaded his barons to recognise his daughter Matilda as heir. When Henry died in 1135 her cousin Stephen of Blois had himself proclaimed king, leading to a civil war known as The Anarchy. Eventually Stephen recognised Matilda's son Henry as his heir and when Stephen died in 1154, he succeeded as Henry II.
Document 8: Battle of Clitheroe: The Battle of Clitheroe was a battle between a force of Scots and English knights and men at arms which took place on 10 June 1138 during the period of The Anarchy. The battle was fought on the southern edge of the Bowland Fells, at Clitheroe, Lancashire. It took place in the course of an invasion of England by King David I of Scotland. In the summer of 1138, King David split his army into two forces. One of them, commanded by William fitz Duncan, Mormaer of Moray, marched into Lancashire. There he harried Furness and Craven. On 10 June, William fitz Duncan was met by a force of knights and men-at-arms. A pitched battle took place and the result was that the English army was routed. The battle was a prelude to the Battle of the Standard later in the summer, where the result was reversed.
Document 9: Henry II of England: Henry II (5 March 1133 – 6 July 1189), also known as Henry Curtmantle (French: "Court-manteau" ), Henry FitzEmpress or Henry Plantagenet, ruled as Count of Anjou, Count of Maine, Duke of Normandy, Duke of Aquitaine, Count of Nantes, King of England and Lord of Ireland; at various times, he also controlled Wales, Scotland and Brittany. Henry was the son of Geoffrey of Anjou and Matilda, daughter of Henry I of England. He became actively involved by the age of 14 in his mother's efforts to claim the throne of England, then occupied by Stephen of Blois, and was made Duke of Normandy at 17. He inherited Anjou in 1151 and shortly afterwards married Eleanor of Aquitaine, whose marriage to Louis VII of France had recently been annulled. Stephen agreed to a peace treaty after Henry's military expedition to England in 1153, and Henry inherited the kingdom on Stephen's death a year later.
Document 10: Empress Matilda: Empress Matilda (c. 7 February 110210 September 1167), also known as the Empress Maude, was the claimant to the English throne during the civil war known as the Anarchy. The daughter of King Henry I of England, she moved to Germany as a child when she married the future Holy Roman Emperor Henry V. She travelled with her husband into Italy in 1116, was controversially crowned in St. Peter's Basilica, and acted as the imperial regent in Italy. Matilda and Henry had no children, and when Henry died in 1125, the crown was claimed by Lothair II, one of his political enemies.
Document 11: England and King David I: The relationship between the Kingdom of England and King David I, who was King of Scotland between 1124 and 1153, was partly shaped by David's relationship with the particular King of England, and partly by David's own ambition. David had a good relationship with and was an ally of Henry I of England, the King who was largely responsible for David's early career. After Henry's death, David upheld his support for his niece, the former Empress-consort, Matilda, and expanded his power in northern England in the process, despite his defeat at the Battle of the Standard in 1138.
Document 12: John Balliol: John Balliol (  1249 – late 1314), known derisively as "Toom Tabard" (meaning "empty coat") was King of Scots from 1292 to 1296. Little is known of his early life. After the death of Margaret, Maid of Norway, Scotland entered an interregnum during which several competitors for the Crown of Scotland put forward claims. Balliol was chosen from among them as the new King of Scotland by a group of selected noblemen headed by King Edward I of England. Edward used his influence over the process to subjugate Scotland and undermined Balliol's personal reign by treating Scotland as a vassal of England. Edward's influence in Scottish affairs tainted Balliol's reign and the Scottish nobility deposed him and appointed a council of twelve to rule instead. This council signed a treaty with France known as the Auld Alliance.
Document 13: Henry II, Holy Roman Emperor: Henry II (German: "Heinrich II" ; Italian: "Enrico II" ) (6 May 973 – 13 July 1024), also known as Saint Henry, Obl. S. B., was Holy Roman Emperor ("Romanorum Imperator") from 1014 until his death in 1024 and the last member of the Ottonian dynasty of Emperors as he had no children. The Duke of Bavaria from 995, Henry became King of Germany ("Rex Romanorum") following the sudden death of his second cousin, Emperor Otto III in 1002, was crowned King of Italy ("Rex Italiae") in 1004, and was crowned by the Pope as Emperor in 1014.
Document 14: Conrad IV of Germany: Conrad (25 April 1228 – 21 May 1254), a member of the Hohenstaufen dynasty, was the only son of Emperor Frederick II from his second marriage with Queen Isabella II of Jerusalem. He inherited the title of a King of Jerusalem (as Conrad II) upon the death of his mother in childbed. Appointed Duke of Swabia in 1235, his father had him elected King of Germany (King of the Romans) and crowned King of Italy (as Conrad IV) in 1237. After the emperor was deposed and died in 1250, he ruled as King of Sicily (Conrad I) until his death.
Document 15: Matilda of Brabant, Countess of Holland: Mathilde (c. 1200 – 22 December 1267) was the fourth child and daughter of Mathilde of Flanders and Henry I, Duke of Brabant. She married Henry II, Count Palatine of the Rhine (died 1214) in Aachen in 1212 and later married Floris IV, Count of Holland on 6 December 1224. Mathilde was a great-great-grandmother of Philippa of Hainault, wife of King Edward III of England and Queen consort, as well as being a great-granddaughter of King Stephen of England.
ground_truth: no children